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Stationary Time Series

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2 ) = 1.25, and the autocoExample 1 (continued): In example 1, we see that E (Xt ) = 0, E (Xt variance functions does not depend on s or t. Actually we have γX (0) = 1.25, γX (1) = 0.5, and γx (h) = 0 for h > 1. Therefore, {Xt } is a stationary process. t Example 2 (Random walk) Let St be a random walk St = s=0 Xs with S0 = 0 and Xt is independent and identically distributed with mean zero and variance σ 2 . Then for h > 0,
2 γX (t, t) = E (Xt ) = 1.25,
when t = s + 1, γX (t, t + 1) = E [( t + 0.5 when t − s > 1, γX (s, t) = 0.
t−1 )( t+1
+ 0.5 t )] = 0.5,
3
Stationarity and Strict Stationarity
−0.2 1990 1992 1994 1996 1998 2000 2002 Time
Figure 1: Plots of some economic variables
2
then E (Xt ) = 0 and γX (s, t) = E (Xs Xt ). Let s ≤ t. When s = t,
2 ) < ∞ ∀ t ∈ Z. (I) E (Xt
(II) EXt = µ ∀ t ∈ Z. (III) γX (s, t) = γX (s + h, t + h) ∀ s, t, h ∈ Z. In other words, a stationary time series {Xt } must have three features: finite variation, constant first moment, and that the second moment γX (s, t) only depends on (t − s) and not depends on s or t. In light of the last point, we can rewrite the autocovariance function of a stationary process as γX (h) = Cov (Xt , Xt+h ) for t, h ∈ Z. Also, when Xt is stationary, we must have γX (h) = γX (−h). When h = 0, γX (0) = Cov (Xt , Xt ) is the variance of Xt , so the autocorrelation function for a stationary time series {Xt } is defined to be ρX (h) = γX () . γX (0)
0
−0.1
−0.2
1950 1960 1970 1980 1990 2000 Time
Monthly S&P 500 Index
1500
Monthly S&P 500 Index Returns
0.2
0.1
1000
0
500
−0.1
0 1990 1992 1994 1996 1998 2000 2002 Time
With autocovariance functions, we can define the covariance stationarity, or weak stationarity. In the literature, usually stationarity means weak stationarity, unless otherwise specified. Definition 2 (Stationarity or weak stationarity) The time series {Xt , t ∈ Z} (where Z is the integer set) is said to be stationary if
Lecture 1: Stationary Time Series∗
1
Introduction
If a random variable X is indexed to time, usually denoted by t, the observations {Xt , t ∈ T} is called a time series, where T is a time index set (for example, T = Z, the integer set). Time series data are very common in empirical economic studies. Figure 1 plots some frequently used variables. The upper left figure plots the quarterly GDP from 1947 to 2001; the upper right figure plots the the residuals after linear-detrending the logarithm of GDP; the lower left figure plots the monthly S&P 500 index data from 1990 to 2001; and the lower right figure plots the log difference of the monthly S&P. As you could see, these four series display quite different patterns over time. Investigating and modeling these different patterns is an important part of this course. In this course, you will find that many of the techniques (estimation methods, inference procedures, etc) you have learned in your general econometrics course are still applicable in time series analysis. However, there are something special of time series data compared to cross sectional data. For example, when working with cross-sectional data, it usually makes sense to assume that the observations are independent from each other, however, time series data are very likely to display some degree of dependence over time. More importantly, for time series data, we could observe only one history of the realizations of this variable. For example, suppose you obtain a series of US weekly stock index data for the last 50 years. This sample can be said to be large in terms of sample size, however, it is still one data point, as it is only one of the many possible realizations.
2
Autocovariance Functions
In modeling finite number of random variables, a covariance matrix is usually computed to summarize the dependence between these variables. For a time series {Xt }∞ t=−∞ , we need to model the dependence over infinite number of random variables. The autocovariance and autocorrelation functions provide us a tool for this purpose. Definition 1 (Autocovariance function). The autocovariance function of a time series {Xt } with V ar(Xt ) < ∞ is defined by γX (s, t) = Cov (Xs , Xt ) = E [(Xs − EXs )(Xt − EXt )]. Example 1 (Moving average process) Let
t
∼ i.i.d.(0, 1), and

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ARIMA模型在SPSS中的推算过程

ARIMA模型在SPSS中的推算过程

1 ARIMAThe ARIMA procedure computes the parameter estimates for a given seasonal or non-seasonal univariate ARIMA model. It also computes the fitted values, forecasting values, and other related variables for the model.NotationThe following notation is used throughout this chapter unless otherwise stated: y t (t =1, 2, ..., N ) Univariate time series under investigationN Total number of observationsa t (t = 1, 2, ... , N ) White noise series normally distributed with mean zero andvariance σa 2pOrder of the non-seasonal autoregressive part of the model qOrder of the non-seasonal moving average part of the model dOrder of the non-seasonal differencing POrder of the seasonal autoregressive part of the model QOrder of the seasonal moving-average part of the model DOrder of the seasonal differencing s Seasonality or period of the modelφp B ()AR polynomial of B of order p , φϕϕϕp p p B B B B ()...=−−−−1122 θq B ()MA polynomial of B of order q , θϑϑϑq q q B B B B ()...=−−−−1122 ΦP B () SAR polynomial of B of order P ,ΦΦΦΦP P P B B B B ()...=−−−−1122ΘQ B ()SMA polynomial of B of order Q , ΘΘΘΘQ Q Q B B B B ()...=−−−−1122 ∇ Non-seasonal differencing operator ∇=−1B∇s Seasonal differencing operator with seasonality s , ∇=−s s B 1BBackward shift operator with By y t t =−1and Ba a t t =−12 ARIMAModelsA seasonal univariate ARIMA(p ,d ,q )(P ,D ,Q )s model is given byφµθp P d s D t q Q t B B y B B a t N ()()[]()(),,ΦΘ∇∇−==1K (1)whereµ is an optional model constant. It is also called the stationary series mean, assuming that, after differencing, the series is stationary. When NOCONSTANT is specified, µ is assumed to be zero.When P Q D ===0, the model is reduced to a (non-seasonal) ARIMA(p ,d ,q ) model:φµθp d t q t B y B a t N ()[](),,∇−==1K (2) An optional log scale transformation can be applied to y t before the model is fitted. In this chapter, the same symbol, y t , is used to denote the series either before or after log scale transformation.Independent variables x 1, x 2, …, x m can also be included in the model. Themodel with independent variables is given byφµθp P d s D t i i m it q Q t B B y c xB B a ()()[()]()()ΦΘ∇∇−−==∑1or ΦΘ()[()()]()B B y c xB a t i i m it t ∇−−==∑1µ (3)whereΦΦ()()()B B B p P =φ∇=∇∇()B d s DΘΘ()()()B B B q Q =θand c i m i ,,,,=12K , are the regression coefficients for the independent variables.ARIMA 3EstimationBasically, two different estimation algorithms are used to compute maximum likelihood (ML) estimates for the parameters in an ARIMA model:• Melard’s algorithm is used for the estimation when there is no missing data inthe time series. The algorithm computes the maximum likelihood estimates of the model parameters. The details of the algorithm are described in Melard (1984), Pearlman (1980), and Morf, Sidhu, and Kailath (1974).•A Kalman filtering algorithm is used for the estimation when some observations in the time series are missing. The algorithm efficiently computes the marginal likelihood of an ARIMA model with missing observations. The details of the algorithm are described in the following literature: Kohn and Ansley (1986) and Kohn and Ansley (1985). Diagnostic StatisticsThe following definitions are used in the statistics below:N p Number of parametersN p q P Q m p q P Q m p =+++++++++%&'without model constant with model constant 1SSQ Residual sum of squaresSSQ =′e e , where e is the residual vector$σa 2 Estimated residual variance$σa SSQ df2=, where df N N p =−SSQ ’ Adjusted residual sum of squaresSSQ SSQ N ’=05Ω1/, where Ω is the theoretical covariancematrix of the observation vector computed at MLE4 ARIMA Log-LikelihoodL N SSQ N a a=−−−ln($)’$ln()σσπ2222 Akaike Information Criterion (AIC)AIC L N p =−+22Schwartz Bayesian Criterion (SBC)SBC L N N p =−+2ln 16Generated VariablesPredicted ValuesForecasting Method: Conditional Least Squares (CLS or AUTOINT)In general, the model used for fitting and forecasting (after estimation, if involved) can be described by Equation (3), which can be written asy D B y B B a c B B x t t t i i m it −=++∇=∑()()()()()ΦΘΦµ1 where D B B B 050505=∇−Φ1ΦΦB 0505µµ=1ARIMA 5Thus, the predicted values (FIT )t are computed as follows:FIT y D B y B B a c B B x t t t t ii m it 05==+++∇=∑$()$()()$()()ΦΘΦµ1 (4)where$$a y y t n t t t =−≤≤1 Starting Values for Computing Fitted Series . To start the computation for fitted values using Equation (4), all unavailable beginning residuals are set to zero and unavailable beginning values of the fitted series are set according to the selected method:• CLS. The computation starts at the (d +sD )-th period. After a specified log scaletransformation, if any, the original series is differenced and/or seasonally differenced according to the model specification. Fitted values for the differenced series are computed first. All unavailable beginning fitted values in the computation are replaced by the stationary series mean, which is equal to the model constant in the model specification. The fitted values are then aggregated to the original series and properly transformed back to the original scale. The first d +sD fitted values are set to missing (SYSMIS ).• AUTOINIT. The computation starts at the [d +p +s (D +P )]-th period. After anyspecified log scale transformation, the actual d +p +s (D +P ) beginning observations in the series are used as beginning fitted values in the computation. The first d +p +s (D +P ) fitted values are set to missing. The fitted values are then transformed back to the original scale, if a log transformation is specified.Forecasting Method: Unconditional Least Squares (EXACT)As with the CLS method, the computations start at the (d+sD)-th period. First, the original series (or the log-transformed series if a transformation is specified) is differenced and/or seasonally differenced according to the model specification. Then the fitted values for the differenced series are computed. The fitted values are one-step-ahead, least-squares predictors calculated using the theoretical autocorrelation function of the stationary autoregressive moving average (ARMA) process corresponding to the differenced series. The autocorrelation function is computed by treating the estimated parameters as the true parameters. The fitted values are then aggregated to the original series and properly transformed back to the original scale. The first d+sD fitted values are set to missing (SYSMIS ). The details of the least-squares prediction algorithm for the ARMA models can be found in Brockwell and Davis (1991).6 ARIMAResidualsResidual series are always computed in the transformed log scale, if a transformation is specified.()(),,,ERR y FIT t N t t t =−=12KStandard Errors of the Predicted ValuesStandard errors of the predicted values are first computed in the transformed log scale, if a transformation is specified.Forcasting Method: Conditional Least Squares (CLS or AUTOINIT)()$,,,SEP t N t a ==σ12KForecasting Method: Unconditional Least Squares (EXACT)In the EXACT method, unlike the CLS method, there is no simple expression for the standard errors of the predicted values. The standard errors of the predicted values will, however, be given by the least-squares prediction algorithm as a byproduct.Standard errors of the predicted values are then transformed back to the original scale for each predicted value, if a transformation is specified.Confidence Limits of the Predicted ValuesConfidence limits of the predicted values are first computed in the transformed log scale, if a transformation is specified:()()(),,,()()(),,,/,/,LCL FIT t SEP t N UCL FIT t SEP t N t t df tt t df t =−==+=−−12121212ααK Kwhere t df 12−α/, is the 12−α/16-th percentile of a t distribution with df degrees of freedom and α is the specified confidence level (by default α=005.).Confidence limits of the predicted values are then transformed back to the original scale for each predicted value, if a transformation is specified.ARIMA 7ForecastingForecasting ValuesForcasting Method: Conditional Least Squares (CLS or AUTOINIT)The following forecasting equation can be derived from Equation (3):$()()$()()$()(),y l D B y B B a c B B x t t l t l ii mi t l =+++∇++=+∑ΦΘΦµ1 (5)whereD B B B B 0505050505=∇−=ΦΦΦ11,µµ $()yl t denotes the l-step-ahead forecast of y t l + at the time t . $$()y y l iy l i l i t l i t l it +−+−=≤−>%&'if if$$()a y y l i l i t l j t l i t l i +−+−+−−=−≤>%&'110if ifNote that $()yt ′1 is the one-step-ahead forecast of y t ′+1 at time ′t , which is exactly the predicted value $yt ′+1as given in Equation (4). Forecasting Method: Unconditional Least Squares (EXACT)The forecasts with this option are finite memory, least-squares forecasts computed using the theoretical autocorrelation function of the series. The details of the least-squares forecasting algorithm for the ARIMA models can be found in Brockwell and Davis (1991).8 ARIMAStandard Errors of the Forecasting ValuesForcasting Method: Conditional Least Squares (CLS or AUTOINIT)For the purpose of computing standard errors of the forecasting values, Equation(1) can be written in the format of ψweights (ignoring the model constant):y a B a B a t t t i it i i q B Q B p B P B ===−=∞∑ϑφψψ()()()()()ΘΦ0, ψ01= (6)Let$()y l t denote the l -step-ahead forecast of y t l +at time t . Then se[$()]{...}$y l t l a =++++−112221212ψψψσ Note that, for the predicted value, l =1. Hence, ()$SEP t a =σat any time t . Computation of ψ Weights . ψ weights can be computed by expanding both sides of the following equation and solving the linear equation system established by equating the corresponding coefficients on both sides of the expansion:φψθp P d s D q Q B B B B B ()()()()()ΦΘ∇∇=An explicit expression of ψ weights can be found in Box and Jenkins (1976).Forecasting Method: Unconditional Least Squares (EXACT)As with the standard errors of the predicted values, the standard errors of the forecasting values are a byproduct during the least-squares forecasting computation. The details can be found in Brockwell and Davis (1991).ReferencesBox, G. E. P., and Jenkins, G. M. 1976. Time series analysis : Forecasting and control . San Francisco: Holden-Day.Brockwell, P. J., and Davis, R. A. 1991. Time series: Theory and methods , 2nd ed. New York: Springer-Verlag.。

matlab工具箱安装教程

matlab工具箱安装教程

1.1 如果是Matlab安装光盘上的工具箱，重新执行安装程序，选中即可；1.2 如果是单独下载的工具箱，一般情况下仅需要把新的工具箱解压到某个目录。

2 在matlab的file下面的set path把它加上。

3 把路径加进去后在file→Preferences→General的Toolbox Path Caching里点击update Toolbox Path Cache更新一下。

4 用which newtoolbox_command.m来检验是否可以访问。

如果能够显示新设置的路径，则表明该工具箱可以使用了。

把你的工具箱文件夹放到安装目录中“toolbox”文件夹中，然后单击“file”菜单中的“setpath”命令，打开“setpath”对话框，单击左边的“ADDFolder”命令，然后选择你的那个文件夹，最后单击“SAVE”命令就OK了。

MATLAB Toolboxes＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝/zsmcode.htmlBinaural-modeling software for MATLAB/Windows/home/Michael_Akeroyd/download2.htmlStatistical Parametric Mapping (SPM)/spm/ext/BOOTSTRAP MATLAB TOOLBOX.au/downloads/bootstrap_toolbox.htmlThe DSS package for MATLABDSS Matlab package contains algorithms for performing linear, deflation and symmetric DSS. http://www.cis.hut.fi/projects/dss/package/Psychtoolbox/download.htmlMultisurface Method Tree with MATLAB/~olvi/uwmp/msmt.htmlA Matlab Toolbox for every single topic !/~baum/toolboxes.htmleg. BrainStorm - MEG and EEG data visualization and processingCLAWPACK is a software package designed to compute numerical solutions to hyperbolic partial differential equations using a wave propagation approach/~claw/DIPimage - Image Processing ToolboxPRTools - Pattern Recognition Toolbox (+ Neural Networks)NetLab - Neural Network ToolboxFSTB - Fuzzy Systems ToolboxFusetool - Image Fusion Toolboxhttp://www.metapix.de/toolbox.htmWAVEKIT - Wavelet ToolboxGat - Genetic Algorithm ToolboxTSTOOL is a MATLAB software package for nonlinear time series analysis.TSTOOL can be used for computing: Time-delay reconstruction, Lyapunov exponents, Fractal dimensions, Mutual information, Surrogate data tests, Nearest neighbor statistics, Return times, Poincare sections, Nonlinear predictionhttp://www.physik3.gwdg.de/tstool/MATLAB / Data description toolboxA Matlab toolbox for data description, outlier and novelty detectionMarch 26, 2004 - D.M.J. Taxhttp://www-ict.ewi.tudelft.nl/~davidt/dd_tools/dd_manual.htmlMBEhttp://www.pmarneffei.hku.hk/mbetoolbox/Betabolic network toolbox for Matlabhttp://www.molgen.mpg.de/~lieberme/pages/network_matlab.htmlPharmacokinetics toolbox for Matlabhttp://page.inf.fu-berlin.de/~lieber/seiten/pbpk_toolbox.htmlThe SpiderThe spider is intended to be a complete object orientated environment for machine learning in Matlab. Aside from easy use of base learning algorithms, algorithms can be plugged together and can be compared with, e.g model selection, statistical tests and visual plots. 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That should help Video Quality project.Filter Design packagehttp://www.ee.ryerson.ca:8080/~mzeytin/dfp/index.htmlOctave by Christophe COUVREUR (Generates normalized A-weigthing, C-weighting, octave and one-third-octave digital filters)/matlabcentral/fileexchange/loadFile.do?objectType=file&object Id=69Source Coding MATLAB Toolbox/users/kieffer/programs.htmlBio Medical Informatics (Top)CGH-Plotter: MATLAB Toolbox for CGH-data AnalysisCode: http://sigwww.cs.tut.fi/TICSP/CGH-Plotter/Poster: http://sigwww.cs.tut.fi/TICSP/CSB2003/Posteri_CGH_Plotter.pdfThe Brain Imaging Software Toolboxhttp://www.bic.mni.mcgill.ca/software/MRI Brain Segmentation/matlabcentral/fileexchange/loadFile.do?objectId=4879Chemometrics (providing PCA) (Top)Matlab Molecular Biology & Evolution Toolbox(Toolbox Enables Evolutionary Biologists to Analyze and View DNA and Protein Sequences) James J. 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Chen/support/books/book5295.jsp?category=new&language=-1MATLAB M-files and Simulink models/matlabcentral/fileexchange/loadFile.do?objectId=3834&object Type=file•OPNML/MATLAB Facilities/OPNML_Matlab/Mesh Generation/home/vavasis/qmg-home.htmlOpenFEM : An Open-Source Finite Element Toolbox/CALFEM is an interactive computer program for teaching the finite element method (FEM)http://www.byggmek.lth.se/Calfem/frinfo.htmThe Engineering Vibration Toolbox/people/faculty/jslater/vtoolbox/vtoolbox.htmlSaGA - Spatial and Geometric Analysis Toolboxby Kirill K. Pankratov/~glenn/kirill/saga.htmlMexCDF and NetCDF Toolbox For Matlab-5&6/staffpages/cdenham/public_html/MexCDF/nc4ml5.htmlCUEDSID: Cambridge University System Identification Toolbox/jmm/cuedsid/Kriging Toolbox/software/Geostats_software/MATLAB_KRIGING_TOOLBOX.htmMonte Carlo (Dr Nando)http://www.cs.ubc.ca/~nando/software.htmlRIOTS - The Most Powerful Optimal Control Problem Solver/~adam/RIOTS/ExcelMATLAB xlsheets/matlabcentral/fileexchange/loadFile.do?objectId=4474&objectTy pe=filewrite2excel/matlabcentral/fileexchange/loadFile.do?objectId=4414&objectTy pe=fileFinite Element Modeling (FEM) (Top)OpenFEM - An Open-Source Finite Element Toolbox/NLFET - nonlinear finite element toolbox for MATLAB ( framework for setting up, solving, and interpreting results for nonlinear static and dynamic finite element analysis.)/GetFEM - C++ library for finite element methods elementary computations with a Matlabinterfacehttp://www.gmm.insa-tlse.fr/getfem/FELIPE - FEA package to view results ( contains neat interface to MATLA/~blstmbr/felipe/Finance (Top)A NEW MATLAB-BASED TOOLBOX FOR COMPUTER AIDED DYNAMIC TECHNICAL TRADINGStephanos Papadamou and George StephanidesDepartment of Applied Informatics, University Of Macedonia Economic & Social Sciences, Thessaloniki, Greece/fen31/one_time_articles/dynamic_tech_trade_matlab6.htm Paper: :8089/eps/prog/papers/0201/0201001.pdfCompEcon Toolbox for Matlab/~pfackler/compecon/toolbox.htmlGenetic Algorithms (Top)The Genetic Algorithm Optimization Toolbox (GAOT) for Matlab 5/mirage/GAToolBox/gaot/Genetic Algorithm ToolboxWritten & distributed by Andy Chipperfield (Sheffield University, UK)/uni/projects/gaipp/gatbx.htmlManual: /~gaipp/ga-toolbox/manual.pdfGenetic and Evolutionary Algorithm Toolbox (GEATbx)/Evolutionary Algorithms for MATLAB/links/ea_matlab.htmlGenetic/Evolutionary Algorithms for MATLABhttp://www.systemtechnik.tu-ilmenau.de/~pohlheim/EA_Matlab/ea_matlab.html GraphicsVideoToolbox (C routines for visual psychophysics on Macs by Denis Pelli)/VideoToolbox/Paper: /pelli/pubs/pelli1997videotoolbox.pdf4D toolbox/~daniel/links/matlab/4DToolbox.htmlImages (Top)Eyelink Toolbox/eyelinktoolbox/Paper: /eyelinktoolbox/EyelinkToolbox.pdfCellStats: Automated statistical analysis of color-stained cell images in Matlabhttp://sigwww.cs.tut.fi/TICSP/CellStats/SDC Morphology Toolbox for MATLAB (powerful collection of latest state-of-the-art gray-scale morphological tools that can be applied to image segmentation, non-linear filtering, pattern recognition and image analysis)/Image Acquisition Toolbox/products/imaq/Halftoning Toolbox for MATLAB/~bevans/projects/halftoning/toolbox/index.htmlDIPimage - A Scientific Image Processing Toolbox for MATLABhttp://www.ph.tn.tudelft.nl/DIPlib/dipimage_1.htmlPNM Toolboxhttp://home.online.no/~pjacklam/matlab/software/pnm/index.htmlAnotherICA / KICA and KPCA (Top)ICA TU Toolboxhttp://mole.imm.dtu.dk/toolbox/menu.htmlMISEP Linear and Nonlinear ICA Toolboxhttp://neural.inesc-id.pt/~lba/ica/mitoolbox.htmlKernel Independant Component Analysis/~fbach/kernel-ica/index.htmMatlab: kernel-ica version 1.2KPCA- Please check the software section of kernel machines.KernelStatistical Pattern Recognition Toolboxhttp://cmp.felk.cvut.cz/~xfrancv/stprtool/MATLABArsenal A MATLAB Wrapper for Classification/tmp/MATLABArsenal.htmMarkov (Top)MapHMMBOX 1.1 - Matlab toolbox for Hidden Markov Modelling using Max. Aposteriori EM Prerequisites: Matlab 5.0, Netlab. Last Updated: 18 March 2002./~parg/software/maphmmbox_1_1.tarHMMBOX 4.1 - Matlab toolbox for Hidden Markov Modelling using Variational Bayes Prerequisites: Matlab 5.0,Netlab. Last Updated: 15 February 2002../~parg/software/hmmbox_3_2.tar/~parg/software/hmmbox_4_1.tarMarkov Decision Process (MDP) Toolbox for MatlabKevin Murphy, 1999/~murphyk/Software/MDP/MDP.zipMarkov Decision Process (MDP) Toolbox v1.0 for MATLABhttp://www.inra.fr/bia/T/MDPtoolbox/Hidden Markov Model (HMM) Toolbox for Matlab/~murphyk/Software/HMM/hmm.htmlBayes Net Toolbox for Matlab/~murphyk/Software/BNT/bnt.htmlMedical (Top)EEGLAB Open Source Matlab Toolbox for Physiological Research (formerly ICA/EEG Matlabtoolbox)/~scott/ica.htmlMATLAB Biomedical Signal Processing Toolbox/Toolbox/Powerful package for neurophysiological data analysis ( Igor Kagan webpage)/Matlab/Unitret.htmlEEG / MRI Matlab Toolbox/Microarray data analysis toolbox (MDAT): for normalization, adjustment and analysis of gene expression_r data.Knowlton N, Dozmorov IM, Centola M. Department of Arthritis and Immunology, Oklahoma Medical Research Foundation, Oklahoma City, OK, USA 73104. We introduce a novel Matlab toolbox for microarray data analysis. This toolbox uses normalization based upon a normally distributed background and differential gene expression_r based on 5 statistical measures. The objects in this toolbox are open source and can be implemented to suit your application. AVAILABILITY: MDAT v1.0 is a Matlab toolbox and requires Matlab to run. MDAT is freely available at:/publications/2004/knowlton/MDAT.zipMIDI (Top)MIDI Toolbox version 1.0 (GNU General Public License)http://www.jyu.fi/musica/miditoolbox/Misc. (Top)MATLAB-The Graphing Tool/~abrecht/matlab.html3-D Circuits The Circuit Animation Toolbox for MATLAB/other/3Dcircuits/SendMailhttp://carol.wins.uva.nl/~portegie/matlab/sendmail/Coolplothttp://www.reimeika.ca/marco/matlab/coolplots.htmlMPI (Matlab Parallel Interface)Cornell Multitask Toolbox for MATLAB/Services/Software/CMTM/Beolab Toolbox for v6.5Thomas Abrahamsson (Professor, Chalmers University of Technology, Applied Mechanics,Göteborg, Sweden)http://www.mathworks.nl/matlabcentral/fileexchange/loadFile.do?objectId=1216&objectType =filePARMATLABNeural Networks (Top)SOM Toolboxhttp://www.cis.hut.fi/projects/somtoolbox/Bayes Net Toolbox for Matlab/~murphyk/Software/BNT/bnt.htmlNetLab/netlab/Random Neural Networks/~ahossam/rnnsimv2/ftp: ftp:///pub/contrib/v5/nnet/rnnsimv2/NNSYSID Toolbox (tools for neural network based identification of nonlinear dynamic systems) http://www.iau.dtu.dk/research/control/nnsysid.htmlOceanography (Top)WAFO. Wave Analysis for Fatigue and Oceanographyhttp://www.maths.lth.se/matstat/wafo/ADCP toolbox for MATLAB (USGS, USA)Presented at the Hydroacoustics Workshop in Tampa and at ADCP's in Action in San Diego /operations/stg/pubs/ADCPtoolsSEA-MAT - Matlab Tools for Oceanographic AnalysisA collaborative effort to organize and distribute Matlab tools for the Oceanographic Community /Ocean Toolboxhttp://www.mar.dfo-mpo.gc.ca/science/ocean/epsonde/programming.htmlEUGENE D. GALLAGHER(Associate Professor, Environmental, Coastal & Ocean Sciences)/edgwebp.htmOptimization (Top)MODCONS - a MATLAB Toolbox for Multi-Objective Control System Design/mecheng/jfw/modcons.htmlLazy Learning Packagehttp://iridia.ulb.ac.be/~lazy/SDPT3 version 3.02 -- a MATLAB software for semidefinite-quadratic-linear programming .sg/~mattohkc/sdpt3.htmlMinimum Enclosing Balls: Matlab Code/meb/SOSTOOLS Sum of Squares Optimi zation Toolbox for MATLAB User’s guide/sostools/sostools.pdfPSOt - a Particle Swarm Optimization Toolbox for use with MatlabBy Brian Birge ... A Particle Swarm Optimization Toolbox (PSOt) for use with the Matlab scientific programming environment has been developed. PSO isintroduced briefly and then the use of the toolbox is explained with some examples. A link to downloadable code is provided.Plot/software/plotting/gbplot/Signal Processing (Top)Filter Design with Motorola DSP56Khttp://www.ee.ryerson.ca:8080/~mzeytin/dfp/index.htmlChange Detection and Adaptive Filtering Toolboxhttp://www.sigmoid.se/Signal Processing Toolbox/products/signal/ICA TU Toolboxhttp://mole.imm.dtu.dk/toolbox/menu.htmlTime-Frequency Toolbox for Matlabhttp://crttsn.univ-nantes.fr/~auger/tftb.htmlVoiceBox - Speech Processing Toolbox/hp/staff/dmb/voicebox/voicebox.htmlLeast Squared - Support Vector Machines (LS-SVM)http://www.esat.kuleuven.ac.be/sista/lssvmlab/WaveLab802 : the Wavelet ToolboxBy David Donoho, Mark Reynold Duncan, Xiaoming Huo, Ofer Levi /~wavelab/Time-series Matlab scriptshttp://wise-obs.tau.ac.il/~eran/MATLAB/TimeseriesCon.htmlUvi_Wave Wavelet Toolbox Home Pagehttp://www.gts.tsc.uvigo.es/~wavelets/index.htmlAnotherSupport Vector Machine (Top)MATLAB Support Vector Machine ToolboxDr Gavin CawleySchool of Information Systems, University of East Anglia/~gcc/svm/toolbox/LS-SVM - SISTASVM toolboxes/dmi/svm/LSVM Lagrangian Support Vector Machine/dmi/lsvm/Statistics (Top)Logistic regression/SAGA/software/saga/Multi-Parametric Toolbox (MPT) A tool (not only) for multi-parametric optimization. http://control.ee.ethz.ch/~mpt/ARfit: A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive modelshttp://www.mat.univie.ac.at/~neum/software/arfit/The Dimensional Analysis Toolbox for MATLABHome: http://www.sbrs.de/Paper: http://www.isd.uni-stuttgart.de/~brueckner/Papers/similarity2002.pdfFATHOM for Matlab/personal/djones/PLS-toolbox/Multivariate analysis toolbox (N-way Toolbox - paper)http://www.models.kvl.dk/source/nwaytoolbox/index.aspClassification Toolbox for Matlabhttp://tiger.technion.ac.il/~eladyt/classification/index.htmMatlab toolbox for Robust Calibrationhttp://www.wis.kuleuven.ac.be/stat/robust/toolbox.htmlStatistical Parametric Mapping/spm/spm2.htmlEVIM: A Software Package for Extreme Value Analysis in Matlabby Ramazan Gençay, Faruk Selcuk and Abdurrahman Ulugulyagci, 2001.Manual (pdf file) evim.pdf - Software (zip file) evim.zipTime Series Analysishttp://www.dpmi.tu-graz.ac.at/~schloegl/matlab/tsa/Bayes Net Toolbox for MatlabWritten by Kevin Murphy/~murphyk/Software/BNT/bnt.htmlOther: /information/toolboxes.htmlARfit: A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models/~tapio/arfit/M-Fithttp://www.ill.fr/tas/matlab/doc/mfit4/mfit.htmlDimensional Analysis Toolbox for Matlab/The NaN-toolbox: A statistic-toolbox for Octave and Matlab®... handles data with and without MISSING VALUES.http://www-dpmi.tu-graz.ac.at/~schloegl/matlab/NaN/Iterative Methods for Optimization: Matlab Codes/~ctk/matlab_darts.htmlMultiscale Shape Analysis (MSA) Matlab Toolbox 2000p.br/~cesar/projects/multiscale/Multivariate Ecological & Oceanographic Data Analysis (FATHOM)From David Jones/personal/djones/glmlab (Generalized Linear Models in MATLA.au/staff/dunn/glmlab/glmlab.htmlSpacial and Geometric Analysis (SaGA) toolboxInteresting audio links with FAQ, VC++, on the topic机器学习网站北京大学视觉与听觉信息处理实验室北京邮电大学模式识别与智能系统学科复旦大学智能信息处理开放实验室IEEE Computer Society北京映象站点计算机科学论坛机器人足球赛模式识别国家重点实验室南京航空航天大学模式识别与神经计算实验室- PARNEC南京大学机器学习与数据挖掘研究所- LAMDA南京大学人工智能实验室南京大学软件新技术国家重点实验室人工生命之园数据挖掘研究院微软亚洲研究院中国科技大学人工智能中心中科院计算所中科院计算所生物信息学实验室中科院软件所中科院自动化所中科院自动化所人工智能实验室ACL Special Interest Group on Natural Language Learning (SIGNLL)ACMACM Digital LibraryACM SIGARTACM SIGIRACM SIGKDDACM SIGMODAdaptive Computation Group at University of New MexicoAI at Johns HopkinsAI BibliographiesAI Topics: A dynamic online library of introductory information about artificial intelligence Ant Colony OptimizationARIES Laboratory: Advanced Research in Intelligent Educational SystemsArtificial Intelligence Research in Environmental Sciences (AIRIES)Austrian Research Institute for AI (OFAI)Back Issues of Neuron DigestBibFinder: a computer science bibliography search engine 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T.W. ANDERSON (1971). The Statistical Analysis of Time Series. Series in Probability and Ma

T.W. ANDERSON (1971). The Statistical Analysis of Time Series. Series in Probability and Ma

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acf和adf代码

acf和adf代码

ACF and ADF CodesIntroductionIn time series analysis, two commonly used models for forecasting are the autoregressive conditional heteroskedasticity (ARCH) model and the autoregressive integrated moving average (ARIMA) model. These models are widely used in finance, economics, and other fields to predict future values of a time series based on its past behavior. In this article, we will explore the ACF (Autocorrelation Function) and ADF (Augmented Dickey-Fuller) codes, which are essential tools for analyzing and diagnosing time series data.Autocorrelation Function (ACF)The ACF measures the correlation between a time series and its lagged values. It helps us understand the relationship between the current value of a series and its past values at different lags. The ACF is a crucial tool for identifying patterns, seasonality, and dependencies in time series data.The ACF code calculates the correlation coefficient for each lag and plots it against the lag. The code snippet below demonstrates how to calculate and plot the ACF for a given time series using Python:import pandas as pdimport matplotlib.pyplot as pltfrom statsmodels.graphics.tsaplots import plot_acf# Load the time series datadata = pd.read_csv('time_series_data.csv')# Calculate and plot the ACFplot_acf(data, lags=20)plt.show()In the code above, we first load the time series data from a CSV file using the pandas library. Then, we use the plot_acf function from the statsmodels.graphics.tsaplots module to calculate and plot the ACF. The lags parameter specifies the number of lags to include in the plot. Finally, we use plt.show() to display the plot.The ACF plot helps us identify significant lags in the time series data. If a lag has a correlation coefficient close to 1 or -1, it indicates a strong positive or negative correlation, respectively. On the other hand, if the correlation coefficient is close to 0, it suggests no correlation.Augmented Dickey-Fuller (ADF) TestThe ADF test is a statistical test used to determine if a time series is stationary or not. Stationarity is a key assumption in many time series models, including ARIMA. A stationary time series has constant mean and variance over time, and its properties do not depend on the specifictime period.The ADF code allows us to perform the ADF test on a given time series to check for stationarity. The following code snippet demonstrates how to perform the ADF test using Python:import pandas as pdfrom statsmodels.tsa.stattools import adfuller# Load the time series datadata = pd.read_csv('time_series_data.csv')# Perform the ADF testresult = adfuller(data)# Extract and print the test statisticsprint('ADF Statistic:', result[0])print('p-value:', result[1])print('Critical Values:', result[4])In the code above, we first load the time series data from a CSV file using the pandas library. Then, we use the adfuller function from the statsmodels.tsa.stattools module to perform the ADF test. The function returns a tuple containing the test statistics, p-value, and critical values.The ADF Statistic is the test statistic of the ADF test. The p-value represents the probability that the null hypothesis of non-stationarity is true. If the p-value is less than a chosen significance level (e.g., 0.05), we can reject the null hypothesis and conclude that the time series is stationary. The Critical Values represent the threshold values for different significance levels.ConclusionThe ACF and ADF codes are essential tools for analyzing and diagnosing time series data. The ACF helps us understand the correlation between a time series and its lagged values, while the ADF test allows us to check for stationarity. By using these codes, we can gain insights into the patterns, dependencies, and stationarity of time series data, which are crucial for accurate forecasting and decision-making in various fields.。