美元对英镑均衡汇率分析
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美元对英镑均衡汇率分析
建立模型:Yt=β1+β2 X2+β3X3+β4X4+β5X5+β6Yt-1+μt
其中,Yt----美元对英镑的汇率,Yt=exchange rate (us/uk)
X2---两国利率比率 x2=us rate/uk rate
X3---两国物价指数比率 x3=us cpi/uk cpi
X4---两国出口比率 x4=us export/uk export
X5---两国GDP比率 x5=us gdp/uk gdp
Yt-1--- 一阶滞后
相关数据
exchangerate(us/uk) UKEXPORT UKGDP UKCPI UKRATE USEXPORT USGDP USCPI USRATE
2000.01 1.595 65.9 202.5 2.3 6 65.9 9668.7 3.4 6
2000.02 1.512 67.5 204.6 3.1 6 67.5 9857.6 3.5 6.5
2000.03 1.47 72.2 208.1 2.1 6 72.2 9937.6 3.5 6.5
2000.04 1.492 73.4 209.1 2.1 6 73.4 10027.9 3.4 6.5
2001.01 1.426 74.7 210.1 1.9 5.75 74.7 10141.7 3.4 5
2001.02 1.404 73.4 211.3 2.3 5.25 72.4 10202.6 3.4 3.75
2001.03 1.47 71.2 212 2.4 4.75 71.2 10224.9 2.7 3
2001.04 1.45 70 212.2 2.1 4 70 10253.2 1.8 1.75
2002.01 1.4 69.3 212.5 2.4 4 69.3 10313.1 1.2 1.75
2002.02 1.5 71.4 213.7 1.9 4 71.4 10376.9 1.3 1.75
2002.03 1.6 71.6 216.2 1.5 4 71.6 10506.2 1.6 1.75
2002.04 1.6 65.8 249.2 2.6 4 65.8 10588.8 2.2 1.25
2003.01 1.58 69.4 256.1 2.1 3.75 173.5 10744.6 2.9 1.25
2003.02 1.65 67.9 257 2.5 3.75 174.6 10884 2.2 1
2003.03 1.66 68.5 259.3 1.9 3.5 178.3 11116.7 2.2 1
2003.04 1.78 69.5 272.2 2.4 3.75 186.9 11270.9 1.9 1
2004.01 1.84 70.9 275.1 1.7 4 193.9 11472.6 1.8 1
2004.02 1.81 71.9 277 2.2 4.5 199.3 11657.5 2.8 1.25
2004.03 1.81 72.1 277.8 2.3 4.75 204.6 11814.9 2.7 1.75
2004.04 1.92 72.9 279.1 3.1 4.75 208.6 11988.9 3.4 2.25
2005.01 1.89 73.3 279.8 3.2 4.75 213.8 12198.8 3 2.75
2005.02 1.79 76.3 281.2 3 4.75 215.7 12373.1 2.9 3.25
生成新序列:
x2 x3 x4 x5 Yt-1
1 1.4782609 1 47.746667
1.0833333 1.1290323 1 48.179863 1.512
1.0833333 1.6666667 1 47.753964 1.47
1.0833333 1.6190476 1 47.957437 1.492
0.8695652 1.7894737 1 48.270823 1.426
0.7142857 1.4782609 0.986376 48.284903 1.404
0.6315789 1.125 1 48.23066 1.47
0.4375 0.8571429 1 48.318567 1.45 0.4375 0.5 1 48.532235 1.4
0.4375 0.6842105 1 48.558259 1.5
0.4375 1.0666667 1 48.59482 1.6
0.3125 0.8461538 1 42.491172 1.6
0.3333333 1.3809524 2.5 41.954705 1.58
0.2666667 0.88 2.5714286 42.350195 1.65
0.2857143 1.1578947 2.6029197 42.871963 1.66
0.2666667 0.7916667 2.6892086 41.406686 1.78
0.25 1.0588235 2.7348378 41.703381 1.84
0.2777778 1.2727273 2.7719054 42.084838 1.81
0.3684211 1.173913 2.8377254 42.530238 1.81
0.4736842 1.0967742 2.861454 42.955571 1.92
0.5789474 0.9375 2.9167804 43.598284 1.89
0.6842105 0.9666667 2.8269987 44.001067 1.79
一、先检验时间序列的平稳性:
1、 长期协整性检验
(1)、作图:判断是什么性质的随机游走
1.31.41.51.61.71.81.92.000:100:301:101:302:102:303:103:304:104:305:1YT带一定趋势
同理可得,X2,X3,X4,X5也是带一定趋势的随机游走
(2)、做单位根检验
ADF Test Statistic -2.587484 1% Critical Value* -4.5000
5% Critical Value -3.6591
10% Critical Value -3.2677
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(YT)
Method: Least Squares
Date: 12/13/05 Time: 20:24
Sample(adjusted): 2000:3 2005:2
Included observations: 20 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
YT(-1) -0.482275 0.186388 -2.587484 0.0198 D(YT(-1)) 0.115264 0.232445 0.495878 0.6267
C 0.638449 0.246380 2.591317 0.0197
@TREND(2000:1) 0.013196 0.005444 2.424117 0.0276
R-squared 0.303443 Mean dependent var 0.013900
Adjusted R-squared 0.172839 S.D. dependent var 0.063982
S.E. of regression 0.058190 Akaike info criterion -2.673335
Sum squared resid 0.054178 Schwarz criterion -2.474189
Log likelihood 30.73335 F-statistic 2.323379
Durbin-Watson stat 1.713732 Prob(F-statistic)
0.113745
Yt序列是非平稳的
同理,x2,x3,x4,x5也是非平稳的
检查是否具有协整性
ADF Test Statistic -2.883999 1% Critical Value* -3.8572
5% Critical Value -3.0400
10% Critical Value -2.6608
*MacKinnon critical values for rejection of hypothesis of a unit root.
Augmented Dickey-Fuller Test Equation
Dependent Variable: D(E)
Method: Least Squares
Date: 12/13/05 Time: 20:28
Sample(adjusted): 2001:1 2005:2
Included observations: 18 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
E(-1) -1.046807 0.362971 -2.883999
0.0114
D(E(-1)) 0.042603 0.256461 0.166120 0.8703
C -0.053325 0.366713 -0.145414 0.8863
R-squared 0.507074 Mean dependent var
-0.029991
Adjusted R-squared 0.441351 S.D. dependent var 2.080603
S.E. of regression 1.555102 Akaike info criterion 3.871971
Sum squared resid 36.27512 Schwarz criterion 4.020366
Log likelihood -31.84774 F-statistic 7.715281
Durbin-Watson stat 2.024573 Prob(F-statistic) 0.004964
一般地,选择5%的临界值,所以没有协整性
采用对数建模:lnYt=β1+β2 lnX2+β3lnX3+β4lnX4+β5lnX5+β6lnYt-1+lnμt
产生新序列
lnx2 lnx3 lnx4 lnx5 lnYt-1 le
0 0.390866309 0 3.865909256
0.080042708 0.121360857 0 3.874941157 0.413433278