Solutions of midterm2010

Midterm Exam Solutions, Econ 6090-092, Summer 2012Directions: Answer all questions as completely as possible.1. (25 points) What follows are the supply and demand functions coconut oil:where is the price of coconut oil, is the price of peanut oil, and is income. Assume that the constant values for and are 0.75 and 15,000 respectively.a (10 points) Find the equilibrium price and quantity for coconut oil.ANSWER:Substitute in 0.75 for and 15,000 for to get:Set and solve for :Substitute into either the or equation to find . So the equilibrium price is 4 and the equilibrium quantity is 8348.b(5 points) Calculate the own-price elasticity of demand for coconut oil at the equilibrium price and quantity.Explain how you know whether demand for coconut oil is elastic or inelastic.ANSWER:The own-price elasticity of demand is given by:With this linear demand function,so that at the equilibrium price and quantity we have:Since the absolute value of the own-price elasticity of demand is less than 1, demand for this good is inelastic.c (5 points) Calculate the income elasticity for coconut oil at the equilibrium price and quantity. Is coconut oil anormal or inferior good, and if it is a normal good is it a luxury or necessity? Explain how you know.ANSWER:The income elasticity is given by:With this linear demand function,so that at the equilibrium price and quantity and the constant value of we have:Since the income elasticity is positive, coconut oil is a normal good. Since the income elasticity is positive and less than 1, it is classified as a necessity.d (5 points) Calculate the cross-price elasticity for coconut oil and peanut oil at the equilibrium price and quantity.Are coconut oil and peanut oil complements or substitutes? Explain how you know.ANSWER:The cross-price elasticity is given by:With this linear demand function,so that at the equilibrium price and quantity and the constant value of we have:Since the cross-price elasticity is positive, these good are substitutes.2. (40 points) Suppose the consumer has the following utility function:Let represent income, the price of good A, and the price of good B.a (5 points) Set up the consumer's optimization problem.ANSWER:The consumer's problem is:b (10 points) Find the consumer's utility at each of the two corners. Explain why you would or would not expect the interior solution to be optimal given this particular specification of the utility function.ANSWER:The consumer's utility at either corner solution is zero. Thus, we should expect there to be an interior solution, as consuming positive amounts of both goods leads to a higher utility than zero.c (10 points) Find the demand functions for goods A and B as a function of prices and income.ANSWER:Knowing that we have an interior solution (from part b) and that the budget constraint will be binding, we will have the following system of equations:Solving the first two equations for we get:so that:Substituting for in the budget constraint we have:Substituting into our equation for we have:So our demand functions for goods A and B are:d (10 points) Assume that , , and . Find the consumer's optimal bundle.ANSWER:Simply take the demand functions from part c and substitute in the numeric values to find:e (5 points) Show the marginal rate of substitution equals the marginal rate of transformation at the optimal bundle. ANSWER:The marginal rate of substitution is the ratio of marginal utilities. So we have:so that:The marginal rate of transformation is the ratio of the prices (be sure that they are in the proper order according to how you have set up your MRS):So at the optimal bundle we have MRS=MRT.3. (35 points) Short answer questionsa (5 points) Suppose an individual is given the choice to take $4 with certainty or to pick a number from 1-30 out of ahat. If the number drawn is from 1-10, the individual receives $3. If the number drawn is from 21-30, the individual receives $9. If the individual prefers the gamble to the $4 with certainty are they risk averse, risk neutral, or risk seeking? Explain.ANSWER:The individual is risk seeking. Both the $4 with certainty and the gamble have an expected value of $4. The expected value of the gamble is:Since the $4 with certainty has a lower variance (there is no variance) and the individual chooses the gamble, the individual is risk seeking.b (10 points) Assume for part a, problem 3 (directly above) that we can represent the individuals utility with thefunction , what is the certain amount of money that would make the individual indifferent between the gamble and accepting the certain amount of money?ANSWER:The expected utility of the game is the weighted average of the utilities, which is:Now, what amount of money gives the consumer an expected utility of 30? It is:c (10 points) Suppose the consumer in problem 2 has the utility function . Will theconsumer's optimal bundle change from the one you found in problem 2? Explain why or why not.ANSWER:No, the optimal bundle would not change. This utility function is just of the one in problem 2, so it is a positive monotonic transformation of that utility function. Thus, any consumer that has either utility function will have the same set of indifference curves and so the optimal bundle will be the same as that in problem 2.d (10 points) What does an Engel curve represent? Draw an Engel curve for a good that is both normal and inferior.Make sure to clearly label the axes and label both when the good is normal and when the good is inferior.ANSWER:The Engel curve is a graphical representation of the relationship between a consumer's income and his quantity demanded. An example (with proper labels) would be:。

Graduate School of Business,University of ChicagoBusiness41202,Spring Quarter2008,Mr.Ruey S.TsaySolutions to MidtermProblem A:(30pts)Answer briefly the following questions.Each question has two points.1.Describe two methods for choosing a time series model.Answer:Any two of(a)Information criteria such as AIC or BIC,(b)Out-of-sample forecasts,and(c)ACF and PACF of the series.2.Describe two applications of volatility infinance.Answer:Any two of(a)derivative(option)pricing,(b)risk management,(c)portfolio selection or asset allocation.3.Give two applications of seasonal time series models infinance.Answer:(a)Earnings forecasts and(b)weather-related derivative pricing or risk man-agement.4.Describe two weaknesses of the ARCH models in modelling stock volatility.Answer:Any two of(a)symmetric response to past positive and negative shocks,(b)restrictive,(c)Not adaptive,and(d)provides no explanation about the source ofvolatility clustering.5.Give two empirical characteristics of daily stock returns.Answer:any two of(a)heavy tails,(b)non-Gaussian distribution,(c)volatility clus-tering.6.The daily simple returns of Stock A for the last week were0.02,0.01,-0.005,-0.01,and0.025,respectively.What is the weekly log return of the stock last week?What is theweekly simple return of the stock last week?Answer:Weekly log return is0.03938;weekly simple return is0.04017.7.Suppose the closing price of Stock B for the past three trading days were$100,$120,and$100,respectively.What is the arithmetic mean of the simple return of the stock for the past three days?What is the geometric average of the simple return of the stockfor the past three days? Answer:Arithmetic mean=12120−100100+100−120120=0.017.and the geometric mean is120×100−1=0.8.Consider the AR(1)model r t=0.02+0.8r t−1+a t,where the shock a t is normally distrib-uted with mean zero and variance1.What are the variance and lag-1autocorrelation function of r t?Answer:Var(r t)=11−0.82=2.78and the lag-1ACF is0.8.19.For problems6and7,suppose the daily return r t,in percentages,of Stock A followsthe model r t=1.0+a t+0.3a t−1,where a t=σt t withσ2t =1.0+0.4a2t−1and t beingstandard normal.What is the unconditional variance of a t?What is the variance of r t?Answer:Var(a t)=11−0.4=1.67.Var(r t)=(1+0.32)σ2a=1.82.10.Suppose that a n=3.0,what is the1-step ahead forecast for r n+1at the forecast originn?What is the1-step ahead volatility forecast of r t at the forecast origin n?Answer:r n(1)=1+0.3a n=1.9,andσ2n (1)=1+0.4a2n=4.6.11.Consider the simple AR(1)model r t=100+0.8r t−1+a t,where a t is normally distributedwith mean zero and variance10.Is the r t series mean-reverting?If yes,what is the half-life of the series?Answer:Yes,r t series is mean-reverting.The half-life is ln(0.5)/ln(0.8)=3.11.12.Describe two test statistics for testing the ARCH effect of an asset return series.Writedown the associated null hypotheses.Answer:(a)The Ljung-Box statistic Q(m)of the squared shocks,i.e.a2t .The nullhypothesis is H o:ρ1=ρ2=···=ρm=0,whereρi is the lag-i ACF of a2t .(b)TheEngle F-test for the regression a2t =β0+β1a2t−1+···+βm a2t−m+e t.The null hypothesisis H o:β1=β2=···=βm=0.13.Consider the following two IGARCH(1,1)models for percentage log returns:Model A:σ2t =1.0+0.1a2t−1+0.9σ2t−1Model B:σ2t =0.1a2t−1+0.9σ2t−1.Suppose thatσ2100=20and a100=−2.0.What are the3-step ahead volatility forecastsfor Models A and B?Answer:For model A:3-step ahead volatility forecast isσ2100(3)=2+(1.0+0.1×(−2.0)2+0.9×20)=21.4.For model B,the3-step ahead volatility forecast isσ2100(3)=0.1(−2.0)2+0.9×20=18.4.14.Consider the following two models for the log price of an asset:Model A:p t=p t−1+a tModel B:p t=0.00001+p t−1+a twhere the shock a t is normally distributed with mean zero and varianceσ2>0.Suppose further that p100=5.Let p n( )be the -step ahead forecast at the forecast origin n.What are the point forecasts p100( )for both models as →∞?Answer:For model A,p100( )=5for all .For model B,p100( )converges to infinity as →∞.215.Suppose that we have T =1000daily log returns for the Decile 1portfolio.Supposefurther that the sample autocorrelation at lag-12is ˆρ12=0.15.Test the hypothesis H o :ρ12=0against the alternative hypothesis H a :ρ12=pute the test statistic and draw your conclusion.Answer :t =0.151/√1000=√1000×0.15=4.74,which is highly significant.Thus,the lag-12ACF is not zero.Problem B .(20pts)It is well-known in economics that growth rate of the domestic gross product (GDP)is negatively correlated with the change in unemployment rate.Consider the U.S.quarterly real GDP and unemployment rate from the first quarter of 1948to the first quarter of 2008.Let dgdp t be the growth rate of the GDP,i.e.dgdp t =ln(GDP t )−ln(GDP t −1),and dun t be the change in unempolyment rate,i.e.dun t =U t −U t −1with U t being the civilian unemployment rate.The data were seasonally adjusted and obtained from the Federal Reserve Bank at St.Louis.The sample size after the differencing is e the attached R output to answer the following questions.1.(5points)Write down the fitted linear regression model with dgdp t and dun t representing the dependent and independent variable,respectively,including residual standard error.What is the R 2of the linear regression?Is the fitted model adequate?Why?Answer :The fitted linear regression isdgdp t =0.017−0.017dun t +e t ,ˆσe =0.0088.The R 2is 0.37.The model is not adequate because the Q (m )statistics of the residuals show that the residuals have serial correlations,i.e.Q (12)=219.4with p-value close to zero.2.(5points)To take care of the serial correlations in the residuals,a linear regression model with time-series errors is built for the two variables.Write down the fitted model,including the residual variance.Answer :The fitted linear regression model with time-series errors is(1−0.21B −0.12B 2)(1−0.86B 4)(dgdp t −0.017+0.018dun t )=(1−0.72B 4)a t ,ˆσ2a =6.01×10−5.3.(2points)Is the model in Question 2adequate?Why?Answer :Yes,the model is adequate.The Q (m )statistics of the residuals fail to indicate the existence of any serial correlations.We have Q (12)=17.53with p-value 0.13.4.(4points)Based on the fitted model in Question 2,is the growth rate of GDP negatively correlated with the change in unempolyment rate?Why?Answer :Yes,the growth rate of GDP is negatively related to the change in unemploy-ment rate.The estimated coefficient is −0.018which is highly significant,because it standard error 0.0014is small,resulting in a large t -ratio.35.(4points)To check the predictive power of the model,it was re-estimated using thefirst236data points.This re-fitted model is used to produce1-step to4-step ahead forecasts at the forecast origin t=236.The actual value of the GDP growth rates are also given.Construct the1-step ahead95%interval forecast of the model.Is the actual growth rate in the forecasting interval?Answer:The95%interval forecast is0.012±1.96×0.0077,i.e.[−0.0031,0.027].The actual value is0.0159,which is in the interval.Problem C.(16pts)Consider the quarterly earnings per share of the Microsoft stock from thefirst quarter of1992to thefirst quarter of2008.The data were obtained from First Call. To take the log transformation,we add0.5to all data points.The R output is attached. Let x t=ln(y t+0.5)be the transformed earnings,where y t is the actual earnings per share.1.(5points)Write down thefitted model for x t,including the variance of the residuals.Answer:Thefitted model is(1−B)r t=(1−0.70B+0.39B2)(1+0.39B4)a t,ˆσ2a=0.0016, where r t=ln(x t+0.5)with x t being the earnings per share.2.(2points)Is there any significant serial correlation in the residuals of thefitted model?Why?Answer:No,the Q(m)statistics of the residuals give Q(12)=9.65with p-value0.65.3.(4points)Let T=65be the forecast origin,where T is the sample size.Based on thefitted model,and,for simplicity,use the relationship y t=exp(x t)−0.5,what are the 1-step and2-step ahead forecasts of earnings per share for the Microsoft stock?Answer:The1-step and2-step earnings forecasts are0.56and0.54,respectively.4.(2points)Test the null hypothesis H o:θ4=0vs H a:θ4=0.What is the test statistic?Draw your conclusion.Answer:The test statistic is t=0.39120.1442=2.71with two-sided p-value0.0067.Thus,the seasonal MA coefficientθ4is significantly different from zero.5.(3points)Consider the regular(i.e.,non-seasonal)part of the MA model.Is it invertible?Why?Answer:Yes,it is invertible,because the polynomial1−0.6953x+0.3889x2has roots0.89±1.33i so that the absolute value of the roots(Mod in R)is1.6,which is greaterthan1.[If you compute the roots of x2−0.6953x+0.3889,the the absolute value of the roots is less than1.]Problem D.(34pts)Consider the daily log returns of the Starbucks stock,in percentages, from January1993to December2007.The relevant R output is attached.Answer the following questions.41.(2points)Is the mean log return significant different from zero?Why?Answer:No,the basic statistics show the95%confidence interval of the mean is [−0.0103,0.1624],which contains zero.2.(2points)Is there any serial correlation in the log return series?Why?Answer:Yes,the Q(m)statistics show Q(15)=38.39with p-value0.0008.3.(2points)An MA model is used to handle the mean equation,which appears to beadequate.Is there any ARCH effect in the return series?Why?Answer:Yes,because the Q(m)statistics of the squared residuals show Q(15)=112.61 with p-value close to zero.4.(6points)A GARCH(1,1)model with Student-t distribution is used for the volatilityequation.Write down thefitted model,including the degrees of freedom of the Student-t innovations and mean equation.Answer:Thefitted model isr t=0.037+a t−0.043a t−1−0.048a t−2,a t=σt t, ∼t5.27.σ2 t =0.012+0.026a2t−1+0.973σ2t−1.5.(4points)Since the constant term of the GARCH(1,1)model is not significantly differentfrom zero at the1%level,an IGARCH(1,1)model is used.Write down thefitted IGARCH(1,1)model,including the mean equation.Answer:Thefitted IGARCH(1,1)model isr t=0.077+a t−0.029a t−1−0.044a t−2,a t=σt t, t∼N(0,1).σ2 t =0.022a2t−1+0.978σ2t−1.6.(3points)Is the IGARCH(1,1)model adequate?Why?What is the3-step aheadvolatility forecast with the last data point as the forecast origin?Answer:Yes,the Q(m)statistics for the standardized residuals give Q(10)=1.77, Q(15)=10.79,and Q(20)=18.66.The p-values of these statistics are all greater than0.05.In addition,the Q(m)statistics of the squared standardized residuals also havelarge p-values.The3-step ahead volatility forecast is √3.779=1.94.7.(5points)A GJR(or TGARCH)model with Student-t distribution is alsofitted to thelog return series.Write down thefitted model,including the mean equation and all parameters.Answer:Thwfitted GJR model isr t=0.032+a t−0.043a t−1−0.048a t−2,a t=σt t, t∼t5.31.σ2 t =0.015+(0.021+0.017N t−1)a2t−1+0.970σ2t−1,where N t−1=0if a t−1≥0and=1,otherwise.58.(2points)Is the fitted GJR (or TGARCH)model adequate?Why?Answer :Yes,the Q (m )statistics of the standardized residuals and those of the squred standardized residuals all have large p-values.9.(2points)Among the GARCH(1,1),IGARCH(1,1)and GJR(1,1)models,which one is preferred?Why?Answer :The GJR(1,1)model because it has the smallest AIC value.10.(2points)Is the leverage effect of the GJR model significant?Why?Answer :Yes,the t -ratio of the leverage parameter is 2.01,which is significant at the 5%level.11.(4points)To better understand the leverage effect,use the fitted GJR to calculate theratio σ2t (a t −1=−5.10)σ2t(a t −1=5.10),assuming σ2t −1=7.5.Answer :σ2t (a t −1=−5.10)σ2t (a t −1=5.10)=0.0154+0.0379×(−5.10)2+0.97×7.50.0154+0.0208×(5.10)2+0.97×7.5=1.057.6。

《系统分析和设计》教学大纲课程编号： MIS363课程类型：□通识教育必修课□通识教育选修课√专业必修课□专业选修课□□学科基础课总学时：54 学时讲课学时：36 实验（上机）学时：18学分：3适用对象：信管专业大三学生I.Course IntroductionManagement Information Systems (MIS) continues to be an eclectic mix of ideas, theories, and research methodologies. No other academic unit of the university studies the development of informationsystems, at least not from the particular perspective you find in MIS programs. While it is true that computer science departments are involved in building computer systems, computer sciencedevelopment is largely void of context. No one else in theuniversity, and for that matter in business organizations, has the combination of technical knowledge and organizational contextthat informs the systems development perspective of MIS.Accordingly, students will learn all about the particular MIS perspective on systems development in this course. Students will learn about the systems development life cycle and follow it from the birth of a new information system to the system's death and replacement. Along the way, students will learn about the tools, techniques, and methodologies used by systems analysts to develop information systems in organizations.II.Learning ObjectivesUpon completion of this course, students should be able to: •Demonstrate in-depth knowledge of the systems development lifecycleand the ability to explain the role of information systems within organizations•Demonstrate the ability to think critically and manage risk and reward when applying the systems development lifecycle •Demonstrate the ability to use analysis and design methods competently and effectively•Understand and articulate the roles of the system analyst in modern organizations and how the SA functions in each phase of the systems development life cycle. Competence is tested through written exams and by solving group cases.•Use Hypercase, a hypertext-based program to simulate organizational systems problems and develop solutions to them.•Demonstrate the ability to communicate effectively, orally and in writing, individually and in teamsIII.Connection between Teaching Content and Graduation Requirement MIS Undergraduate Program Learning Goals and Outcomes1. Knowledge: Our graduates will have in-depth disciplinary knowledge applicable in local and global contexts. You should be able to select and apply disciplinary knowledge to business situations in a local and global environment.2. Critical thinking and problem solving: Our graduates will be critical thinkers and effective problem solvers. You should be able to identify and research issues in business situations, analyze the issues, and propose appropriate and well-justified solutions.3. Communication: Our graduates will be effective professional communicators. You should be able to:a. Prepare written documents that are clear and concise, usingappropriate style and presentation for the intended audience,purpose and context.b. Prepare and deliver oral presentations that are clear,focused, well-structured, and delivered in a professional manner.4. Teamwork: Our graduates will be effective team participants. You should be able to participate collaboratively and responsibly in teams, and reflect on your own teamwork, and on the team’s processes an d ability to achieve outcomes.5. Ethical, social and environmental responsibility: Our graduates will have a sound awareness of the ethical, social, cultural and environmental implications of business practice. You should be able to:a. Identify and assess ethical, environmental and/orsustainability considerations in business decision-making andpractice.b. Identify social and cultural implications of businesssituations.The following table shows how the Course Learning Outcomes relate to the overall Program Learning Goals and Outcomes, and indicates where these are assessed:IV.Teaching methodsThis course consists of lectures, labs, discussions, research paper, group assignments and group presentations. Students must beprepared to discuss the assigned papers or cases before class. V.Topical Course OutlineVI.Course Content HighlightsThe course content is divided into five major parts: Systems AnalysisFundamentals (Part I), Information Requirements Analysis (Part II), The Analysis Process (Part III), The Essentials of Design (Part IV), and Quality Assurance and Implementation (Part V).错误!未找到引用源。

Solutions to Practice MidtermBy H˚akan NordgrenProblem1:Consider the systemx =x2+yy =x−y+a1.Explain how the nullclines change as a increases from0to positive values,and explainwhy a bifurcation is expected for some positive values of a.2.Sketch the phase-portrait of the system when a is greater than the bifurcation value.3.Determine the a for which there is bifurcation.Solution:Thefirst two questions are best answered using drawings so they are on the pdf with the sketches in it.Tofind the value of a for which there is bifurcation we need tofind the value of a for which the curve{(x,y)∈R2:y=−x2}and the curve{(x,y)∈R2:y=x+a}meet exactly once.This occurs at a point(x,y)where the line{(x,y)∈R2:y=x+a}has thesame gradient as{(x,y)∈R2:y=−x2}.That is,at(−12,−14).Now we need tofind the a forwhich the line{(x,y)∈R2:y=x+a}passes through(−12,−14).This happens when a=14.Problem2:Consider the systemx =−y−x(2−x2−y2)y =xe a Lyapunov function of the formL(x,y)=ax2+by2,where a,b>0to investigate the stability of the equilibrium point that the origin.If the origin is asymptotically stable,what can you say about the size of its basin of attraction?2.What happens to trajectories which do not go to the origin,as t→∞?Solution:1.To show that the origin is an asymptotically stable equilibrium point,we must show thatL,defined as above,is a strict Lyapunov function in some neighborhood of(0,0).It is clear that L(x,y)≥0for all(x,y)and also that L(x,y)=0if(x,y)=(0,0).It remains to check that˙L is strictly negative in a neighborhood containing the origin.We have˙L(x,y)=2ax2by·−y−x(2−x2−y2)x=2xy(b−a)−2ax2(2−x2−y2).We can see from this that if we pick a =b =1then L is a Lyapunov function in the ball of radius √2with center the origin,so the origin is stable.We can also see that ˙Lis strict on the set {(x,y )∈R 2:x 2+y 2<2and x =0}.At a point (x,y )with x =0and y =0,we see that x =−y and y =0,so the trajectory will go into the set {(x,y )∈R 2:x 2+y 2<2and x =0}again.Therefore,even though L is not a strict Lyapunov function on {(x,y )∈R 2:x 2+y 2<2and x =0},the origin is still asymptotically stable,and {(x,y )∈R 2:x 2+y 2<2}is contained in its basin of attraction.2.If we pick initial conditions (x 0,y 0)on the circle C ={(x,y )∈R 2:x 2+y 2=2}.Then the trajectory will be{(x,y )∈R 2:x 2+y 2=2}.Thus,a solution which starts on the circle C remains there.For solutions which start in the set {(x,y )∈R 2:x 2+y 2>2and x =0},we see that˙L=−2x 2(2−x 2−y 2)>0,so these solutions tend to infinity.If we have initial conditions with x 0=0then we know that the trajectory will end up in the region {(x,y )∈R 2:x 2+y 2>2and x =0}soon,so all solutions in {(x,y )∈R 2:x 2+y 2>2}tend to infinity.Problem 3:Now consider the system˙r =r (2−r )˙θ=r (1−sin(θ)).1.Show that there are exactly two equilibrium points,one of which is a source at the origin.2.Show that A ={(r,θ)∈[0,∞)×[0,2π):r =2}and B ={(r,θ)∈[0,∞)×[0,2π):θ=π2}are invariant sets.3.Explain why B is not periodic.4.Show that for p =(0,0)we have ω(p )={(r,π2)}5.Show that the equilibrium point at (r,π2)is nevertheless,not stable.Solution:1.For r =0we certainly have ˙r =0and ˙θ=0.Now suppose that we have r >0and ˙r =0and ˙θ=0.Then we have r =2,and sin(θ)=1,that is θ=π2.Thus there are two equilibrium points,one at the origin an one at (2,π2).Please note that these are thepolar coordinates of the points.We see that for r with 0<r <2,˙r >0so the origin is a source.2.For solutions starting on A we have˙r=0,so A is invariant.For solutions starting on Bwe haveθ=π,which means that˙θ=0,so B is invariant.3.The circle A is not a periodic solution because it contains an equilibrium point.4.This is best explained by a picture.5.For(2,π2)to be stable we require that for all neighborhoods U of(2,π2),there is a neigh-borhood V of(2,π2),such that if we start a solution inside V it remains inside U.This isnot the case,if we,for instance,start a solution at the right place on A,because it goes away from the equilibrium point for a while.。

《信息检索》模拟试题（一）一、填空1.小王在某个数据库中检索到了50篇文献，查准率和查全率分别为40％、80％，则全部相关文档有 25 篇。

2.INTERNET是基于 TCP/IP 协议的。

3.文件ABC.001.TXT的后缀名是 TXT 。

文件类型是文本文件。

4.多数网页采用HTML编写，这里的HTML指的是：超文本标识语言。

5.目录型搜索引擎主要提供族性检索模式，索引型搜索引擎主要提供特性检索模式。

6.在使用搜索引擎检索时，URL:ustc可以查到网址中带有ustc的网页。

7.根据索引编制方式的不同，可以将搜索引擎分为索引型搜索引擎和网络目录型搜索引擎。

8.按文献的相对利用率来划分，可以把文献分为核心文献、相关文献、边缘文献。

9.定期（多于一天）或不定期出版的有固定名称的连续出版物是期刊。

10.检索工具具有两个方面的职能：存储职能、检索职能。

11.以单位出版物为著录对象的检索工具为：目录。

12.将文献作者的姓名按字顺排列编制而成的索引称为：作者索引。

13.利用原始文献所附的参考文献，追踪查找参考文献的原文的检索方法称为追溯法，又称为引文法。

14.已知一篇参考文献的著录为：”Levitan, K. B. Information resource management. NewBrunswick: Rutgers UP,1986”，该作者的姓是： Levitan 。

15.检索语言可分为两大类：分类语言、主题词语言。

16.LCC指的是美国国会图书馆分类法。

17.当检索关键词具有多个同义词和近义词时，容易造成漏检，使得查全率较低。

18.主题词的规范化指的是词和概念一一对应，一个词表达一个概念。

19.国际上通常根据内容将数据库划分为：参考数据库、源数据库、混合数据库。

20.查询关键词为短语"DATA OUTPUT"，可以用位置算符(W)改写为： DATA (W) OUTPUT 。

21.著录参考文献时，对于三个以上的著者，可以在第一著者后面加上 et al. ，代表"等人"的意思。

WHO新冠疫苗技术线路(英文)A coordinatedGlobal ResearchRoadmapto respond to theD-19 epidemic and beyondThere is broad consensus on the need for research to focus on actions that can save lives now and to facilitate action so that those affected are promptly diagnosed and receive optimal care; while integrating innovation fully withineach research area.Moreover, there is an imperative to support research priorities in a way that leads to the development of sustainable global research platforms pre-prepared for the next disease Xepidemic; thus, allowing for accelerated research, innovative solutions and R&D of diagnostics, therapeutics and vaccines, as well as their timely and equitable access for thoseat highest risk.4 March 20212021 novel Coronavirus Global research and innovation forum: towards a research roadmapTable of contentsTable of contents _____________________________________________________________________ 2 ABOUT THIS DOCUMENT _______________________________________________________________ 7 GOALS OF THE GLOBAL RESEARCH ROADMAP __________________________________________ 9 PROPOSED STRATEGIC APPROACHES AND CRITICAL ACTIONS___________________________ 11 IMMEDIATE NEXT STEPS TO CONTRIBUTE TO CONTROL THE OUTBREAK_____________________ 13 SELECTED KNOWLEDGE GAPS _________________________________________________________ 14 CROSS-CUTTING RESEARCH PRIORITIES ________________________________________________ 15 SCALING UP RESEARCH AND INNOVATION ACTIONS ___________________________________ 16 TIMELINE FOR IMPLEMENTATION OF SELECTED RESEARCH ACTIONS ______________________ 17 MIDTERM AND LONGTERM PRIORITIES TO CONTRIBUTE TO CONTROL THE OUTBREAK _______ 231. Virus natural history, transmission and diagnostics ______________________________________ 232. Animal and environmental research on the virus origin, and management measures at the human-animal interface__________________________________________________________________ 23 3. Epidemiological studies _______________________________________________________________ 24 4. Clinical management _________________________________________________________________ 24 5. Infection prevention and control, including health care workers’protection ______________ 25 6. Candidate therapeutics R&D __________________________________________________________ 25 7. Candidate vaccines R&D______________________________________________________________ 25 8. Ethics Considerations for Research _____________________________________________________ 26 9. Social Sciences in the Outbreak Response _____________________________________________ 26 OPTIMIZNG FUNDING EFFORTS ________________________________________________________ 27 GOVERNANCE_____________________________________________________________________ _ 28 VIRUS NATURAL HISTORY, TRANSMISSION AND DIAGNOSTICS ___________________________ 31 State of the Art _____________________________________________________________________ _______ 31 Knowledge gaps _____________________________________________________________________ ____ 31Clinical virus detection _____________________________________________________________________ ______ 31 Immunity and immune diagnostics ________________________________________________________________ 32 Tools for infection control _____________________________________________________________________ ____ 32 Engineered solutions to clinical diagnostics ________________________________________________________ 32Ongoing research efforts __________________________________________________________________ 32 22021 novel Coronavirus Global research and innovation forum: towards a research roadmapResearch priorities _____________________________________________________________________ ___ 33Other research priorities _____________________________________________________________________ _____ 34What are the key milestones per research priority? _________________________________________ 34 ANIMAL AND ENVIRONMENTAL RESEARCH ON THE VIRUS ORIGIN, AND MANAGEMENT MEASURES AT THE HUMAN-ANIMAL INTERFACE _________________________________________ 36State of the art _____________________________________________________________________ _______ 36 Knowledge gaps _____________________________________________________________________ ____ 37 Ongoing research efforts __________________________________________________________________ 37 Research priorities _____________________________________________________________________ ___ 38 What are the key milestones per research priority___________________________________________ 40 Essential references_____________________________________________________________________ __ 41 EPIDEMIOLOGICAL STUDIES ___________________________________________________________ 42 State of the Art _____________________________________________________________________ _______ 42 Key epidemiological parameters__________________________________________________________ 42 Transmission dynamics ____________________________________________________________________ 42 Disease severity _____________________________________________________________________ _____ 43 Susceptibility _____________________________________________________________________ ________ 43 Control and mitigation measures __________________________________________________________ 44 Knowledge gaps _____________________________________________________________________ ____ 45Transmission dynamics _____________________________________________________________________ ______ 45 Severity _____________________________________________________________________ ____________________ 45 Susceptibility _____________________________________________________________________ _______________ 45 Control and mitigation measures _________________________________________________________________ 45 Ongoing research efforts __________________________________________________________________ 46 Research priorities _____________________________________________________________________ ___ 47 What are the key milestones per research priority___________________________________________ 49 Essential references_____________________________________________________________________ __ 50 CLINICAL CHARACTERIZATION AND MANAGEMENT____________________________________ 51 State of the art _____________________________________________________________________ _______ 51 Knowledge gaps _____________________________________________________________________ ____ 51Scientific gaps _____________________________________________________________________ ______________ 51 Operational gaps _____________________________________________________________________ ___________ 52Ongoing research efforts __________________________________________________________________ 52 32021 novel Coronavirus Global research and innovation forum: towards a research roadmapResearch priorities _____________________________________________________________________ ___ 53Objective 1: Define the natural history of COVID-19 infection _______________________________________ 53 Objective 2: Determine interventions that improve the clinical oute of COVID-19 infected patients53 Objective 3: Determine optimal clinical practice strategies to improve the processes of care_________ 53 Objective 4: Determine how best to link key research questions with researchers in affected regions who are able to recruit patients _____________________________________________________________________ __ 54 Objective 5: Develop platform(s) to of data collection across trials, and collaborations between trials _____________________________________________________________________ 54What are the research priorities for clinical research for this outbreak and beyond?___________ 55What are the key milestones per research priority___________________________________________ 57Essential references _____________________________________________________________________ __ 59INFECTION PREVENTION AND CONTROL, INCLUDING HEALTH CARE WORKERS’PROTECTION 60State of the art _____________________________________________________________________ _______ 60Knowledge gaps _____________________________________________________________________ ____ 61Modes and duration of transmission _______________________________________________________________ 61 Environmental stability of the virus and effective methods to minimize the role of the environment in transmission _____________________________________________________________________ ________________ 61 Personal protective equipment (PPE) and IPC measures____________________________________________ 61 Isolation, quarantine, and optimal health care pathways __________________________________________ 61 Understanding IPC pliance and perception using behavioural change and social science ______ 61 IPC in the munity setting _____________________________________________________________________ 62Ongoing research efforts __________________________________________________________________ 62 Research priorities _____________________________________________________________________ ___ 62Objective 1: Understand the effectiveness of movement control strategies to prevent secondary transmission in health care and munity settings ________________________________________________ 62 Objective 2: Optimize the effectiveness of PPE and its use in reducing the risk of transmission in health care and munity settings_____________________________________________________________ ________ 62 Objective 3: Minimize the role of the environment in transmission of the COVID-19 virus_______________ 62What are the research priorities for IPC for this outbreak and beyond? _______________________ 62What are the key milestones per research priority___________________________________________ 65Essential references _____________________________________________________________________ __ 66CANDIDATE THERAPEUTICS R&D _______________________________________________________ 67State of the art _____________________________________________________________________ _______ 67Knowledge gaps _____________________________________________________________________ ____ 68Ongoing research efforts __________________________________________________________________ 69 Research priorities _____________________________________________________________________ ___ 69Objective 1: Identification of candidates for clinical evaluation in addition to the ones already prioritised. _____________________________________________________________________ __________________ 6942021 novel Coronavirus Global research and innovation forum: towards a research roadmapObjective 2: Multicentre Master Protocol to evaluate efficacy and safety. ___________________________ 69 Objective 3: Coordinated collaboration to implement clinical trials, for evaluation of safety of therapeutics. _____________________________________________________________________ _______________ 69What are the research priorities for each individual thematic area -for this outbreak and beyond? _____________________________________________________________________ ____________ 70 What are the key milestones per research priority___________________________________________ 72 What are the most important actions to facilitate the successful evaluation and use of any of the investigational medical countermeasures? _________________________________________________ 73 Essential references_____________________________________________________________________ __ 74 CANDIDATE VACCINES R&D __________________________________________________________ 75 State of the art _____________________________________________________________________ _______ 75 Critical knowledge gaps __________________________________________________________________ 75 Key research priorities ____________________________________________________________________ 76 Independent Expert Groups _______________________________________________________________ 77 ETHICS CONSIDERATIONS FOR RESEARCH ______________________________________________ 78 State of the art_____________________________________________________________________ _______ 78 Knowledge gaps _____________________________________________________________________ ____ 79 Research priorities _____________________________________________________________________ ___ 80Objective 1: To enable the identification of key knowledge gaps and research priorities._____________ 80 Objective 2: To formulate a clearly defined research governance framework which enables effective and ethical collaboration between multiple stakeholders, including WHO, the global research munity, subject matter experts, public health officials, funders, and ethicists. ____________________ 80 Objective 3: To facilitate effective cross-working and collaboration across the research thematic areas._____________________________________________________________________ ________内容过长，仅展示部分文字预览，全文请查看图片预览。

Booth School of Business,University of ChicagoBusiness41202,Spring Quarter2012,Mr.Ruey S.TsaySolutions to MidtermProblem A:(34pts)Answer briefly the following questions.Each question has two points.1.Describe two improvements of the EGARCH model over the GARCHvolatility model.Answer:(1)allows for asymmetric response to past positive or negative returns,i.e.leverage effect,(2)uses log volatility to relax parameter constraint.2.Describe two methods that can be used to infer the existence of ARCHeffects in a return series,i.e.,volatility is not constant over time.Answer:(1)The sample ACF(or PACF)of the squared residuals of the mean equation,(2)use the Ljung-Box statistics on the squared residuals.3.Consider the IGARCH(1,1)volatility model:a t=σt t withσ2t =α0+β1σ2t−1+(1−β1)a2t−1.Often one pre-fixesα0=0.Why?Also,suppose thatα0=0and the1-step ahead volatility prediction at the forecast origin h is16.2%(annualized),i.e.,σh(1)=σh+1=16.2for the percentage log return.What is the10-step ahead volatility prediction?That is,what isσh(10)?Answer:(1)Fixingα0=0based on the prior knowledge that volatility is mean reverting.(2)σh(10)=16.2.4.(Questions4to8)Consider the daily log returns of Amazon stockfrom January3,2007to April27,2012.Some summary statistics of the returns are given in the attached R output.Is the expected(mean) return of the stock zero?Why?Answer:The data does not provide sufficient evidence to suggest that the mean return is not zero,because the95%confidence interval con-tains zero.5.Let k be the excess kurtosis.Test H0:k=0versus H a:k=0.Writedown the test statistic and draw the conclusion.1Answer:t-ratio =9.875√24/1340=73.79,which is highly significant com-pared with χ21distribution.6.Are there serial correlations in the log returns?Why?Answer:No,the Ljung-Box statistic Q (10)=10.69with p-value 0.38.7.Are there ARCH effects in the log return series?Why?Answer:Yes,the Ljung-Box statist of squared residuals gives Q (10)=39.24with p-value less than 0.05.8.Based on the summary statistics provided,what is the 22-step ahead point forecast of the log return at the forecast origin April 27,2012?Why?Answer:The point forecast r T (22)=0because the mean is not signif-icantly different from zero.[Give students 1point if they use sample mean.]9.Give two reasons that explain the existence of serial correlations in ob-served asset returns even if the true returns are not serially correlated.Answer:Any two of (1)bid-ask bounce,(2)nonsynchronous trading,(3)dynamic dependence of volaitlity via risk premuim.10.Give two reasons that may lead to using moving-average models inanalyzing asset returns.Answer:(1)Smoothing (or manipulation),(2)bid-ask bounce in high frequency returns.11.Describe two methods that can be used to compare different modelsfor a given time series.Answer:(1)Information criteria such as AIC or BIC,(2)backtesting or out-of-sample forecasting.12.(Questions 12to 14)Let r t be the daily log returns of Stock A.Assume that r t =0.004+a t ,where a t =σt t with t being iid N(0,1)random variates and σ2t =0.017+0.15a 2t −1.What is the unconditionalvariance of a t ?Answer:Var(a t )=0.0171−0.15=0.02.13.Suppose that the log price at t =100is 3.912.Also,at the forecastorigin t =100,we have a 100=−0.03and σ100=pute the21-step ahead forecast of the log price (not log return)and its volatility for Stock A at the forecast origin t =100.Answer:r 100(1)=0.004so that p 100(1)=3.912+0.004=3.916.Thevolatility forecast is σ2100(1)= 0.017+0.15(−0.03)2=pute the 30-step ahead forecast of the log price and its volatilityof Stock A at the forecast origin t =100.Answer:p 100(30)=3.912+0.004×30=4.032and the voaltility is the unconditional stantard error √0.02=0.141.15.Asset volatility has many applications in finance.Describe two suchapplications.Answer:Any two of (1)pricing derivative,(2)risk management,(3)asset allocation.16.Suppose the log return r t of Stock A follows the model r t =a t ,a t =σt t ,and σ2t =α0+α1a 2t −1+β1σ2t −1,where t are iid N(0,1).Under whatcondition that the kurtosis of r t is 3?That is,state the condition under which the GARCH dynamics fail to generate any additional kurtosis over that of t .Answer:α1=0.17.What is the main consequence in using a linear regression analysis whenthe serial correlations of the residuals are overlooked?Answer:The t -ratios of coefficient estimates are not reliable.Problem B .(30pts)Consider the daily log returns of Amazon stock from January 3,2007to April 27,2012.Several volatility models are fitted to the data and the relevant R output is attached.Answer the following questions.1.(2points)A volatility model,called m1in R,is entertained.Write down the fitted model,including the mean equation.Is the model adequate?Why?Answer:ARCH(1)model.r t =0.0018+a t ,a t =σt t with t being iidN(0,1)and σ2t =7.577×10−4+0.188a 2t −1.The model is inadequatebecause the normality assumption is clearly rejected.2.(3points)Another volatility model,called m2in R,is fitted to the returns.Write down the model,including all estimated parameters.3Answer:ARCH(1)model.r t=4.907×10−4+a t,a t=σt t,where t∼t∗3.56with t∗vdenoting standardized Student-t distribution with v degreesof freedom.The volatility equation isσ2t =7.463×10−4+0.203a2t−1.3.(2points)Based on thefitted model m2,test H0:ν=5versus H a:ν=5,whereνdenotes the degrees of freedom of Student-t distribution.Perform the test and draw a conclusion.Answer:t-ratio=3.562−50.366=−3.93,which compared with1.96is highlysignificant.If you compute the p-value,it is8.53×10−5.Therefore, v=5is rejected.4.(3points)A third model,called m3in R,is also entertained.Writedown the model,including the distributional parameters.Is the model adequate?Why?Answer:Another ARCH(1)model.r t=0.0012+a t,a t=σt t,where t are iid and follow a skew standardized Student-t distribution with skew parameter1.065and degrees of freedom3.591.The volatility equationisσ2t =7.418×10−4+0.208a2t−1.Ecept for the insigicant mean value,thefitted ARCH(1)model appears to be adequate based on the model checking statistics shown.5.(2points)Letξbe the skew parameter in model m3.Does the estimateofξconfirm that the distribution of the log returns is skewed?Why?Perform the test to support your answer.Answer:The t-ratio is1.065−10.039=1.67,which is smaller than1.96.Thus,the null hypothesis of symmetric innovations cannot be rejected at the 5%level.6.(3points)A fourth model,called m4in R,is alsofitted.Write downthefitted model,including the distribution of the innovations.Answer:a GARCH(1,1)model.r t=0.0017+a t,a t=σt t,where t are iid and follow a skew standardized Student-t distribution with skew parameter1.101and degrees of freedom3.71.The volatility equationisσ2t =1.066×10−5+0.0414a2t−1+0.950σ2t−1.7.(2points)Based on model m4,is the distribution of the log returnsskewed?Why?Perform a test to support your answer.Answer:The t-ratio is1.101−10.043=2.349,which is greater than1.96.Thus,the distribution is skew at the5%level.48.(2points)Among models m1,m2,m3,m4,which model is preferred?State the criterion used in your choice.Answer:Model4is preferred as it has a smaller AIC value.9.(2points)Since the estimatesˆα1+ˆβ1is very close to1,we consideran IGARCH(1,1)model.Write down thefitted IGARCH(1,1)model, called m5.Answer:r t=a t,a t=σt t,whereσ2t =3.859×10−5+0.85σ2t−1+0.15a2t−1.10.(2points)Use the IGARCH(1,1)model and the information providedto obtain1-step and2-step ahead predictions for the volatility of the log returns at the forecast origin t=1340.Answer:From the outputσ21340(1)=σ21341=3.859×10−5+0.85×(0.02108)2+0.15(.146)2=0.00361.Therefore,σ21340(2)=3.859×10−5+σ2 1340(1)=0.00365.The volatility forecasts are then0.0601and0.0604,respectively.11.(2points)A GARCH-M model is entertained for the percentage logreturns,called m6in the R output.Based on thefitted model,is the risk premium statistical significant?Why?Answer:The risk premium parameter is−0.112with t-ratio−0.560, which is less than1.96in modulus.Thus,the risk premium is not statistical significant at the5%level.12.(3points)Finally,a GJR-type model is entertained,called m7.Writedown thefitted model,including all parameters.Answer:This is an APARCH model.The model is r t=0.0014+a t,a t=σt t,where t are iid and follow a skew standardized Student-tdistribution with skew parameter1.098and degrees of freedom3.846.The volatility equation isσ2 t =7.583×10−6+0.0362(|a t−1|−0.478a t−1)2+0.953σ2t−1.13.(2points)Based on thefitted GJR-type of model,is the leverage effectsignificant?Why?Answer:Yes,the leverage parameterγ1is signfiicantly different from zero so that there is leverage effect in the log returns.5Problem C.(14pts)Consider the quarterly earnings per share of Abbott Laboratories(ABT)stock from1984.III to2011.III for110observations.We analyzed the logarithms of the earnings.That is,x t=ln(y t),where y t is the quarterly earnings per share.Two models are entertained.1.(3points)Write down the model m1in R,including residual variance.Answer:Let r t be the log earnings per share.Thefitted model is=0.00161.(1−B)(1−B4)r t=(1−0.565B)(1−0.183B4)a t,σ2a2.(2points)Is the model adequate?Why?Answer:No,the Ljung-Box statistics of the residuals give Q(12)=25.76with p-value0.012.3.(3points)Write down thefitted model m2in R,including residualvariance.Answer:Thefitted model is=0.00144.(1−B)(1−B4)r t=(1−0.470B−0.312B3)a t,σ2a4.(2points)Model checking of thefitted model m2is given in Figure1.Is the model adequate?Why?Answer:Yes,the model checking statistics look reasonable.5.(2points)Compare the twofitted model models.Which model ispreferred?Why?Answer:Model2is preferred.It passes model checking and has a smaller AIC value.6.(2points)Compute95%interval forecasts of1-step and2-step aheadlog-earnings at the forecast origin t=110.Answer:1-step ahead prediction:0.375±1.96×0.038,and2-step ahead prediction:0.0188±1.96×0.043.(Some students may use2-step ahead prediction due to the forecast origin confusion.)Problem D.(22pts)Consider the growth rate of the U.S.weekly regular gasoline price from January06,1997to September27,2010.Here growth rate is obtained by differencing the log gasoline price and denoted by gt in R output.The growth rate of weekly crude oil from January03,1997to September24,2010is also obtained and is denoted by pt in R output.Note that the crude oil price was known3days prior to the gasoline price.61.(2points)First,a pure time series model is entertained for the gasolineseries.An AR(5)model is selected.Why?Also,is the mean of the gtseries significantly different from zero?Why?Answer:An AR(5)is selected via the AIC criterion.The mean of g tis not significantly different from zero based on the one-sample t-test.The p-value is0.19.2.(2points)Write down thefitted AR(5)model,called m2,includingresidual variance.Answer:Thefitted model is=0.000326.(1−0.507B−0.079B2−0.136B3+0.036B4+0.086B5)g t=a t,σ2a3.(2points)Since not all estimates of model m2are statistically signifi-cant,we refine the model.Write down the refined model,called m3.Answer:Thefitted model is=0.000327.(1−0.504B−0.074B2−0.122B3+0.101B5)g t=a t,σ2a4.(2points)Is the refined AR(5)model adequate?Why?Answer:Yes,the Ljung-Box statistics of the residuals give Q(14)=10.27with p-value0.74,indicating that there are no serial correlationsin the residuals.5.(2points)Does the gasoline price show certain business-cycle behavior?Why?Answer:Yes,thefitted AR(5)polynomial contains compplex solutions.6.(3points)Next,consider using the information of crude oil price.Writedown the linear regression model,called m4,including R2and residualstandard error.Answer:Thefitted linear regression model isg t=0.287p t+ t,σ =0.0184,and the R2of the regression is33.66%.7.(2points)Is thefitted linear regression model adequate?Why?Answer:No,because the residuals t are serially correlated based onthe Ljung-Box test.78.(3points)A linear regression model with time series errors is enter-tained and insignificant parameters removed.Write down thefinalmodel,including allfitted parameters.Answer:The model is(1−0.404B−0.164B2−0.096B3+0.101B5)(g t−0.191p t)=a t,σ2=0.000253.a9.(2points)Model checking shows that thefittedfinal model has noresidual serial correlations.Based on the model,is crude oil pricehelpful in predicting the gasoline price?Why?Answer:Yes,because thefitted coefficient of p t is signficantly differentfrom zero.10.(2points)Compare the pure time series model and the regression modelwith time-series errors.Which model is preferred?Why?Answer:The regression model with time series error is preferred as ithas a smaller AIC criterion.8。

Graduate School of Business,University of ChicagoBusiness41202,Spring Quarter2005,Mr.Ruey S.TsaySolutions to MidtermAll tests are based on the5%significance level.Problem A:(30pts)Answer briefly the following questions.1.For problems1to6,consider the daily log return,in percentages,of the S&P500composite index from January1996to December31,2004for2267data points.Sum-mary statistics of the percentage log returns from SCA and Splus are attached.See Page 1of the attached output.Is the mean of percentage log returns significantly different from zero?Why?A:t-ratio=1.187<1.96.Thus,the mean return is not significantly different from zero.2.Suppose one invested$1dollar on the S&P500index at the very beginning of1996andheld the investment until the end of2004.What was the value of the investment at the market closing on December31,2004?A:total log return=0.0299*2267/100=0.67783so that the value=exp(0.67783)≈1.97.3.Test the null hypothesis that the skewness of the log returns is zero.Draw your conclu-sion.A:t-ratio=−0.0939/0.0514=−1.83<1.96so that the skewness is no signifiacnt different from zero.4.Given that the last percentage log return was−0.134(i.e.T=December31,2004),which is the corresponding simple return?A:R t=exp(−0.134/100)−1=−0.001339=.1339%.5.Are the log return serially correlated?You may use Q(10)of the series to answer thequestion.A:Q(10)=13.9with p-value0.178so that there is no serial correlation.6.Is there any ARCH effect in the log return series?You may use Q(12)of the squaredseries to answer the question.A:Yes,Q(12)of squared return is large at490(in SCA)and has a p-value of0.0from Splus.7.Give two empirical features of daily log returns of afinancial asset.A:Any two of(a)high kurtosis,(b)volatility clustering,(3)skew to left.18.What is the purpose of studying kurtosis of an asset return series?A:Understanding the tail behavior(or risk)of the return.9.Describe two applications of studying sample autocorrelation function(ACF)of an assetreturn series.A:(a)To test serial correlations in the return series,(b)to identify MA order.10.Describe two methods that can be used to identify the order of an AR model.A:(a)PACF,(b)Criterion functions such as AIC or BIC.11.Consider the AR(1)model(1−0.9B)r t=0.2+a t,where{a t}is an independent andidentically distributed random variables with mean zero and variance1.0.What is the half-life of the series?A:Half-life=ln(0.5)/ln(0.9)=6.58time units.12.Suppose that the log return r t of an asset follows the model below:r t=0.02+a t,a t=σt t,σ2t=0.116+0.42a2t−1.Let p t be the log price of the asset at time t and p T( )be the -step ahead forecast of the log price at the forecast origin T.Then,what is the value of p T( )as increases?A:0.02is the slope of time trend so that p T( )→∞as increases.13.For problems13-14,consider quarterly series of U.S.unit labor cost from1947to2004.The data were seasonally adjusted and obtained from the Federal Reserve Bank of St Louis.Let x t=(1−B)ULC t be thefirst-differenced series of the data at time t.The model(1−0.371B2)x t=0.265+(1+0.171B4)a t,σa=0.5998,fits the data reasonably well.Under thefitted model,what is the mean of x t,i.e.E(x t) =?A:E(x t)=0.265/(1−0.371)=0.421.14.Does the model imply that there exist business cycles in the unit labor cost?Why? A:No,because the two roots are real.From1−0.371x2,we have x=±1/ (0.371).15.Give two weaknesses of the GARCH-type of models for modeling asset volatility.A:Any two of(a)symmetric response to past positive and negative returns,(b)restric-tive,(c)providing no explanation of volatility clustering,(d)no adaptive in forecasting.2Problem B.(20pts)This problem is concerned with the analysis of quarterly earnings per share of the Procter&Gamble(PG)Company from1992to thefirst quarter of2003 for45data points.The data were obtained from First Call.Log transformation was taken to stabilize the variability of the puter output is attached;p.2-6of output. Due to strong seasonal pattern,which results in models that are close to being non-invertible, we analyze the seasonally differenced series in Splus.Let x t be the logarithm of quarterly earnings per share and w t=(1−B4)x t.Thus,SCA uses x t and Splus uses w t.1.(5points)Because ACF of the log earnings shows strong seasonal pattern,the seasonaldifference(1−B4)is taken.The ACF of the seasonally differenced data indicates no further differencing is necessary.Write down thefitted model for the x t series(not the differenced w t).A:(1−0.47B)(1−B4)x t=0.0508+(1−0.307B4)a t,σa=0.0502.2.(4points)Is the AR coefficient of thefitted model statistically significant?Why?A:Yes,the t-ratio is3.26,which is greater than the critical value1.96.3.(4points)Is there any serial correlation in the residuals of thefitted model?Use Q(12)of the ACF of residuals to answer the question.[Hint:for a chi-square distribution with m degrees of freedom,the expected value is m.]A:Q(12)=8.8which is less than E(χ210)=10so that p-value>0.05.4.(4points)Let T=45be the forecast origin.What are the1-step and2-step aheadforecasts of thefitted model(after taking anti-log transformation)?A:x45(1)=0.912and x45(2)=3.95(from SCA).For Splus,x45(1)=exp(0.0087−.1743)=0.847,x45(2)=exp(−.012479+1.278152)=3.55.5.(3points)Give an interpretation of the estimated constant0.0508of thefitted modelfor x t.A;Slope of time trend.3and the S&P500index from January1999to December2004with sample size T=1508.We employ the market model:r t=α+βr m,t+e t,where r t and r m,t are Wal-Mart stock return and S&P500index return,respectively.Splus output is attached;page6of output.Answer the following questions.1.(4points)Write down thefitted market model.A:r t=0.0205+0.9606r m,t+e t.2.(4points)The Ljung-Box statistics of the ACF of residuals show some minor serialcorrelations,but the ACFs are relatively small so we ignore the serial correlations and perform the ARCH effect test.Is there an ARCH effect in the residuals of thefitted market model?A:Yes,archTest gives a p-value about0.0.3.(4points)We employ a GARCH(1,1)model(called“m2”in the output).Write downthefitted ment on thefitted model.A:Let r t and r m,t be the Wal-Mart stock return and S&P500index return,respectively.The model isr t=0.9386r m,t+a t=0.9386+σt t, t∼t6.41σ2t=−4.29×10−5+0.0377a2t−1+0.963σ2t−1.The negative estimate ofα0does not make sense,but it is statistically not different from0.Also,theˆα1+ˆβ1≈1so that thefitted model indicates an IGARCH(1,1)model without the constant.4.(6points)Further analysis indicates that an EGARCH(2,1)modelfits the data better.There are two leverage effect parameters.Are these two effects statistically significant?Why?You may test the effect individually.A:Examine the t-ratio of the two leverage parameter estimates.For Lev(1),the t-atio is−2.129.For Lev(2),the t-ratio is−1.847.In both cases,the p-values are less tha0.05so that they are both significant.[It you use two-sided tests,then Lev(2)is notsignificant.]5.(2points)What are the1-step ahead forecasts for the return and its volatility of Wal-Mart stock at the forecast origin T=1508using the EGARCH model.A:zero for return and0.7082for volatility.4from January1995to December2004with2519observations.Splus output is attached;page 8of output.Answer the following questions.The ACFs of the returns are small so that the mean equation consists of a constant term only.1.(5points)Consider thefitted GARCH(1,1)model.The volatility equation isσ2t=0.042+0.049a2t−1+0.944σ2t−1.Letηt=a2t−σ2t.Rewrite the prior volatility equation in an ARMA form for the{a2t} series.A:a2t=0.042+0.993a2t−1+ηt−0.944ηt−1.2.(5points)Write down thefitted EGARCH(1,1)model with leverage effect(both meanand volatility equations and the parameter of the conditional distribution used).A:The model isr t=0.04918+a t=0.04918+σt t, t∼t6.68ln(σ2t)=−0.06316+0.1033(|a t−1|−0.5464a t−1σt−1)+0.989ln(σ2t−1).3.(4points)Test the hypotheses H o:v=5vs H a:v=5,where v is the degrees offreedom of the conditional Student t distribution.Draw your conclusion.[Hint:you may use the usual t-ratio test.]A;t-ratio=6.684−5=2.62>1.96.Thus,reject H o:v=5.4.(5points)To better understand the leverage effect,use thefitted EGARCH(1,1)modelto calculate the ratioσ2t( =−3)2t ,where t denotes the iid sequence of the innovationsdefined in class.A:From thefitetd volatility equation,we haveσ2t=exp(−0.06316)(σ2t−1).989exp(0.1033| t−1|−0.0564 t−1). Therefore,σ2t( =−3)σ2t( =3)=exp(−0.0564(−3))exp(−0.0564(3))=exp(0.0564×6)=1.403.5.(4points)Used thefitted EGARCH model and T=2519as the forecast origin.Whatare the1-step ahead forecasts of log return and volatility?A:Forecast of log return is0.0492and forecast of volatility is1.184.6.(4points)Write down the mean equation of thefitted GARCH-M model for the data.A:r t=0.058+0.00629σ2t+a t.7.(3points)Based on the GARCH-M model,is the risk premium statistically significant?Why?A:No,the t-ratio is0.453with p-value=0.65(two-sided).5。

山东省潍坊市大联考2024-2025学年高三上学期10月月考英语试题一、阅读理解Mathematics for Computer ScienceThis subject offers an introduction to discrete mathematics(离散数学)oriented toward computer science and engineering.Course Meeting TimesLectures:3 sessions/week, 1. 5 hour/session Problem Sets (psets)Problem sets account for 20% of the final grade. Making a reasonable effort on the problem sets is, for most students, crucial for mastering the course material. Problem sets are designed to be completed in at most 3 hours; the time is monitored through student reports. Online Feedback ProblemsOnline problems to be completed before most class meetings are posted on the class website. These consist of straightforward questions that provide useful feedback about the assigned material. Some students prefer to try the online problems before reading the text or watching videos as an advance guide to going over the material; that’s fine. Watching designated videos, or at least looking at the lecture-slide handouts, is generally helpful but optional.Like team problem-solving in class, online problems are graded only on participation: Students receive full credit as long as they try the problem, even if their answer is wrong. Online feedback problems account for 10% of the final grade. Midterm ExamsThree 80-minute midterm exams will be given. The midterm exams each account for 15%of the final grade.Midterm questions will typically be variations of prior problems from class and psets, and the best way to prepare is to review on the published solutions to these problems. The first exam covers all previous weeks’ material;subsequent exams focus on the material after the previous exam. Final ExamThere will be a three-hour final exam. This exam is worth 25% of the final class grade. The final exam will cover the entire subject with somewhat greater emphasis on material from after Midterm 3. Most exam questions will be variants of problems assigned during the term(psets,class, midterm, and online). It may include a few questions which combine topics that were originally covered separately.1．What determines students’ grade in Online Feedback Problems?A．Active involvement.B．Submission time.C．Accuracy of answers.D．Completion of assignments2．What is the main focus of the final exam?A．Variants of problem sets.B．Combined topics in class.C．The content after midterm exams.D．The whole-term course materials. 3．Which of the following weighs the most in the final grade?A．Final Exam.B．Midterm Exams.C．Problem Sets.D．Online Feedback ProblemsIt all started with a simple question;“Can I paint your portrait (肖像)?”In the summer of 2015, Brian Peterson was reading the book Love Does, about the power of love in action, when his quiet was disturbed by a homeless man. Inspired by the book, Peterson made an unexpected decision: He was going to introduce himself. In that first conversation, Peterson learned that the man’s name was Matt Faris who failed to pursue a career in music and ended up being homeless.“I saw beauty on the face of a man who hadn’t shaved in probably a year, had overgrown fingernails, and probably hadn’t had a shower in close to a year. ”Even though Peterson hadn’t pioked up a paintbrush in about eight years, he asked if he could paint Faris’s portrait. Faris said yes.Peterson’s connection with Faris led him to form Faces of Santa Ana, a nonprofit organization focused on befriending and painting portraits of members of the community who are unhoused. Working from a black-and-white photo of the subject, Peterson chooses colors inspired by the subject’s personality and life story, creating an impressive portrait.Peterson sells the striking artwork, signed by both subject and artist, dividing the proceeds and putting half into what he calls a“love account”for his model. He then helps people use the money to get back on their feet. Many of Peterson’s new friends use the donations to secure immediate necessities. But Peterson has learned not to make assumptions about what a personneeds most. “I’ve made a mistake thinking I knew what people wanted, ” he says, “but why don’t we just ask them?”Peterson has discovered that there’s more to the finished products than the money they bring to someone who’s down and out. The buyers tend to connect to the story of the person in the painting, finding similarities and often friendship with someone they might have otherwise overlooked. “People often tell me, ‘I was the one that would cross the street. But I see homeless people differently now, ’ ”Peterson says.4．What brought Peterson and Faris together?A．Beauty on Faris’ face.B．Inspiration from a book.C．Peterson’s passion for art.D．Faris’ suffering in his life.5．What does the underlined word “mistake” in paragraph 5 refer to?A．Selling the homeless’ portraits for profits.B．Giving instant necessities to the homeless.C．Asking the homeless for their needs directly.D．Taking what the homeless want for granted.6．What does Peterson imply in the last paragraph?A．The homeless are gaining more concern.B．The life of the homeless is different now.C．Buyers value friendship with the homeless.D．Figures in Peterson’s paintings are popular.7．What can we learn from this text?A．A good model is key to a fine artwork.B．An expected decision makes a great artist.C．A picture really is worth a thousand words.D．Each unfortunate person has his own misfortune.The Malagasy baobab tree, whose thick trunks and tiny branches dot Madagascar’s landscape, should not, by rights, have survived to the present day. Scientists believe that its large seeds were once spread by the giant tortoises and lemur monkeys that wandered the island. When these species went extinct over one thousand years ago owing to human activity, the baobab treeshould have disappeared too. It did not. Seheno Andriantsaralaza at the University of Antananarivo and Onja Razafindratsima at the University of California, now think they may know the reason why.Together with their colleagues, the scientists monitored 15 tree canopies (树冠) in a western region of Madagascar, to identify any animals that might have claimed the role of baobab-seed spread. The researchers also set up camera traps around seed-containing fruits lying on the ground, and searched any faeces (粪便) that they encountered along the way for the presence of seeds.They report in the journal Biotropica that a native rodent (啮齿动物) known as the western bunch-tailed rat was caught on camera handling whole fruits on four occasions. Although there was no footage of the rat breaking the fruits open, the team did chance upon 13 fruits that had been chewed into and had their seeds removed. Though the bite marks were not clear enough to identify an initiator, this was clear evidence that a seed- distributing animal was out there. They then found the ecological equivalent of a smoking gun:baobab seeds in seven different piles of bush-pig faces.While the finding is important in its own right, it also provides valuable evidence that introduced species may not be entirely harmful. Madagascar’s pigs, for example, though not native, have made themselves essential to the survival of truly native species. Similar relationships are suspected to hold in South America between rabbits native to Europe and plants with no seed distributors. For Dr Andriantsaralaza, that suggests the full ecological role of introduced species should be considered before talk of extinction begins.8．What made scientists think the baobab tree should have disappeared?A．The extinction of its seed spreader.B．The destruction of human activitiesC．The inadaptation of the baobab tree.D．The increase of its natural enemies. 9．What are camera traps used for?A．Seeking seed-containing fruits.B．Tracking the footprints of seeds.C．Recording the animals’ activities.D．Monitoring the baobab tree canopies. 10．Which is most probably the seed-eater according to the report?A．The giant tortoise B．The bunch-tailed rat.C．The European rabbit.D．The bush-pig.11．What is the author’s purpose in writing the text?A．To introduce a new way to protect the baobab tree.B．To show non-native species are not always harmful.C．To compare different kinds of seed-distributing methods.D．To explain the importance of protecting endangered species.The concepts of delayed satisfaction, self-control, and self-regulation are often used interchangeably and inconsistently. The ability to delay an impulse (冲动) for an immediate reward to receive a more favorable reward at a later time is the standard definition of delayed satisfaction.Studies show that delayed satisfaction is one of the most effective personal characteristics of successful people. People who learn how to manage their need to be satisfied in the moment develop more in their careers, relationships, health, and finances than people who give in to it.Being able to delay satisfaction isn’t the easiest skill to acquire. It involves feeling dissatisfied, which is why it seems impossible for people who haven’t learned to control their impulses. Choosing to have something now might feel good, but making the effort to have discipline and manage your impulses can result in bigger or better rewards in the future. Over time, delayed satisfaction will improve your self-control and ultimately help you achieve your long-term goals faster.The Seinfeld Strategy is one of several helpful self-satisfaction techniques you can use to put off satisfaction for longer periods of time. Every day that you delay satisfaction and avoid temptation (诱惑) , you cross it off your calendar. After a few days, this creates a chain. This strategy works well for people who enjoy gamification (游戏化). If you find it satisfying to keep the chain going, you’re less likely to give in to temptation.Do you find yourself going back to your temptations without thinking about it?If this is the case, you can practice mindfulness to become more aware of what you do. When you notice yourself doing something out of habit, stop for a moment. Ask yourself why you’re doing what you’re doing. Take some time to analyze how you’re feeling. Pay attention to the details. Take a moment of mindulness to interrupt your autopilot every time this happens. The more you practice this, the more you’ll break the habit of going for instant satisfaction.12．What is delayed satisfaction?A．Making quick decisions.B．Giving in to desires instantly.C．Immediate rewards for impulses.D．Postponing rewards for better outcomes. 13．Why is delayed satisfaction hard to attain?A．It can lead to missed opportunities B．It’s bad for achieving long-term goals.C．It’s impossible to resist the inner needs D．It’s a comfort to possess something at once. 14．What does paragraph 4 mainly talk about?A．The complexity of the Seinfeld Strategy B．An example of self-discipline techniques.C．A method of practicing delayed satisfaction.D．The effectiveness of keeping the chain going.15．What does the author suggest people do for returning temptations?A．Ignore useless details.B．Get rid of old bad habits.C．Concentrate on true inner wants.D．Cancel temptations from the calendar.Facing hard things is, well, hard. Sometimes we are forced to simply shift, such as with a loss or failure; however, much of the time, we may recognize the difficulties underneath that need attention but feel too overwhelmed to address them. 16 The difficulties might be an outdated habit, a troubling memory or a long- ignored conflict.Some individuals fool themselves into thinking there really is not a problem. It’s like someone trying to hold active mice under a blanket by holding down the edges of the moving blanket. Pulling back the blanket to let the mice out is needed, despite being terrifying. Once the mice are released, there may be further challenges to get them out of the house. 17 People often encounter similar problems. Avoiding or leaving the situation appears to fix the problem but fails to tackle the underlying cause. Rather than repeatedly cutting weeds, getting down on the ground and pulling the roots is more effective. Facing issues is like uncovering roots for new beginnings to blossom. 1819 It feels like a balled-up mess of wires. Pulling hard at only one wire actually tightens the knot. We have to take a calmer look and pull apart each wire one at a time. We can’t expect the wires to loosen or unwind themselves. 20 Nevertheless, once they have been freed, they can sometimes be separated, put aside, and used as needed. A．They are just there and part of the chaos.B．And humans are masters of avoidance and denial.C．The overall benefits from tough work enable growthD．Making changes in one’s life is hard and complicated.E．Sadly, it often worsens when we approach it with anger.F．However, problems cannot be faced if they are not first recognized.G．Quick fixes might provide relief in the short term but often not in the long term.二、完形填空Madeline sat on her bed and tried to write. Tears dropped onto the page, making the ink 21 . Her best friend was moving, and her heart 22 as she penned how much she would miss him.She heard her mother speaking downstairs, but the words were 23 . This was a 24 , as her mother said, “Kids her age don’t know what love is!”Uncle Joe responded in a low tone. 25 , Madeline couldn’t catch what was said. She continued to write until she reached the end and 26 , she laid her head on the pillow and sobbed. Then, she felt a 27 hand on her shoulder. “It’s going to be okay. You can 28 each other, right?” Madeline 29 her head. “Mom says I’m not old enough for a phone.”Uncle Joe answered 30 , “But I’m friends with Leo’s dad. Your mom said you can talk to Leo on my phone. Plus, I gave her his number.” He didn’t tell her that her mom had thought it all silly and unnecessary.Madeline 31 , throwing her arms around Uncle Joe’s neck. “Thank you!”“No problem.” His eyes fell on the 32 . “Want me to ensure this gets to Leo?” Madeline nodded “Feel like playing a game? I promise I won’t mess around.”Madeline smiled — small but 33 .Uncle Joe wouldn’t read the letter; she 34 him. A sure thing was that his sister was mistaken. Though only eight, Madeline and Leo shared a pure, innocent bond — untouched by 35 .21．A．emerge B．bleed C．leak D．escape 22．A．raced B．hesitated C．ached D．melted23．A．indistinct B．sharp C．pale D．impolite 24．A．burden B．warning C．bonus D．blessing 25．A．Instead B．Anyway C．Again D．Moreover 26．A．worried B．confused C．bored D．exhausted 27．A．comforting B．firm C．smooth D．trembling 28．A．greet B．call C．miss D．visit 29．A．dropped B．shook C．covered D．touched 30．A．proudly B．slowly C．quietly D．casually 31．A．sat up B．turned over C．looked up D．bent down 32．A．toy B．phone C．note D．pen 33．A．friendly B．genuine C．unique D．tight 34．A．refused B．begged C．respected D．trusted 35．A．romance B．doubt C．mood D．status三、语法填空阅读下面短文，在空白处填入1个适当的单词或括号内单词的正确形式。