美元对英镑均衡汇率分析

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
1.3
1.4
1.51.61.71.81.9
2.0
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 *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
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 *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
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 ln X2+β3ln X3+β4ln X4+β5ln X5+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
0.080042708 0.510825624 0 3.866062088 0.385262401 -2.02352685 0.080042708 0.481838087 0 3.870313881 0.400117502 -0.22702254
-0.13976194 0.581921545 0 3.876827308 0.354873322 -0.14523302
-0.33647224 0.390866309 -0.01371764 3.877118944 0.339325306 -0.51181927
-0.45953233 0.117783036 0 3.875994926 0.385262401 -0.56651443
-0.82667857 -0.15415068 0 3.877815905 0.371563556 -0.34328229
-0.82667857 -0.69314718 0 3.882228222 0.336472237 -0.18399772
-0.82667857 -0.37948962 0 3.882764299 0.405465108 -0.41313719
-0.82667857 0.064538521 0 3.883516933 0.470003629 -0.36026568
-1.16315081 -0.16705408 0 3.749296331 0.470003629
-1.09861229 0.322773392 0.916290732 3.736590589 0.457424847
-1.32175584 -0.12783337 0.944461609 3.745973015 0.500775288 -1.9578314
-1.25276297 0.146603474 0.95663378 3.758218069 0.506817602 -1.51762853
-1.32175584 -0.23361485 0.989246962 3.723442372 0.576613364
-1.38629436 0.057158414 1.006072129 3.730582195 0.609765572 -2.69430041
-1.28093385 0.241162057 1.019534962 3.739687523 0.593326845
-0.99852883 0.16034265 1.043002809 3.750215295 0.593326845 -2.25283201
-0.7472144 0.09237332 1.051329904 3.76016636 0.652325186 -1.9394351
-0.54654371 -0.06453852 1.07048039 3.775017803 0.636576829 -0.85197262
-0.37948962 -0.03390155 1.039215615 3.78421388 0.58221562 -1.35841033
再对该模型做图和单位根检验得知：
lyt,lx2,lx3,lx5都有带向下的趋势，；lx4也带有一定的趋势
lyt,lx2,lx3,lx4,lx5都是非平稳性的
检验协整性
le的ADF统计量小于5%，10%的临界值，平稳，有协整性
2、短期误差校正模型检验
建立短期动态关系，重新构造关系模型
ΔlnYt=
β1+β2∑ΔlnX2t-i-1+β3∑Δl nX3t-i-1+β4∑ΔlnX4t-i-1+β5∑ΔlnX5t-i-1+β6∑ΔlnY +λlnμt-1+νt
t-i-1
其中，∑表示L=0，1，2，3滞后期求和
检验L=0时为ΔlnYt=β1+λlnμt-1+νt，
Dependent Variable: YT
Method: Least Squares
Date: 12/13/05 Time: 22:36
Sample(adjusted): 2000:3 2005:1
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C -1.041532 0.164498 -6.331589 0.0001
R-squared 0.006272 Mean dependent var -1.025898 Adjusted R-squared -0.093101 S.D. dependent var 0.504523
S.E. of regression 0.527486 Akaike info criterion 1.709624
Sum squared resid 2.782418 Schwarz criterion 1.790442
Log likelihood -8.257745 F-statistic 0.063115 Durbin-Watson stat 0.185083 Prob(F-statistic) 0.806725
L=1时，t-i=t-1
ΔlnYt=β1+β2ΔlnX2+β3Δl nX3+β4ΔlnX4+β5ΔlnX5+β6ΔlnY+λlnμt-1+νt Yt=β1+β2X2+β3X3+β4X4+β5X5+β6lnY t-1+λlnμt-1+νt
Dependent Variable: YT
Method: Least Squares
Date: 12/13/05 Time: 23:02
Sample(adjusted): 2000:3 2005:1
Included observations: 12
Excluded observations: 7 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
X2 -0.375776 0.185982 -2.020498 0.0898
X3 -0.172344 0.181187 -0.951194 0.3782
X4 -0.548556 0.288195 -1.903423 0.1057
X5 -0.626108 0.351021 -1.783676 0.1247
UT 0.022285 0.080812 0.275761 0.7920
R-squared 0.941608 Mean dependent var -1.025898 Adjusted R-squared 0.892949 S.D. dependent var 0.504523
S.E. of regression 0.165073 Akaike info criterion -0.458001 Sum squared resid 0.163495 Schwarz criterion -0.215548 Log likelihood 8.748006 Durbin-Watson stat 1.214722
t检验值不显著，R2显著，dw显著
所以建模型为：Yt=β1+β2X2+β6lnY t-1+λlnμt-1+νt
Dependent Variable: YT
Method: Least Squares
Date: 12/14/05 Time: 10:13
Sample(adjusted): 2000:3 2005:1
Included observations: 12
C -0.067970 0.165905 -0.409693 0.6928
X2 -0.244434 0.187996 -1.300209 0.2297
YT(-1) 0.821237 0.096595 8.501871 0.0000
R-squared 0.903505 Mean dependent var -1.025898 Adjusted R-squared 0.867319 S.D. dependent var 0.504523
S.E. of regression 0.183775 Akaike info criterion -0.289012 Sum squared resid 0.270185 Schwarz criterion -0.127377 Log likelihood 5.734073 F-statistic 24.96854
建模型为：Yt=β1+β2X2+β3X3+β6lnY t-1+λlnμt-1+νt
Dependent Variable: YT
Method: Least Squares
Date: 12/14/05 Time: 10:15
Sample(adjusted): 2000:3 2005:1
Included observations: 12
C -0.080275 0.218813 -0.366868 0.7246
X2 -0.243988 0.200898 -1.214484 0.2639
X3 -0.018865 0.196719 -0.095900 0.9263
YT(-1) 0.803134 0.215141 3.733062 0.0073
UT 0.059435 0.093480 0.635804 0.5451 R-squared 0.903631 Mean dependent var -1.025898 Adjusted R-squared 0.848564 S.D. dependent var 0.504523 S.E. of regression 0.196334 Akaike info criterion -0.123658 Sum squared resid 0.269830 Schwarz criterion 0.078386 Log likelihood 5.741951 F-statistic 16.40943 Durbin-Watson stat 0.810011 Prob(F-statistic) 0.001157 建模型为：Yt=β1+β2X2+β3X3 +β4X4+β6lnY t-1+λlnμt-1+νt Dependent Variable: YT
Method: Least Squares
Date: 12/14/05 Time: 10:18
Sample(adjusted): 2000:3 2005:1
Included observations: 12
Excluded observations: 7 after adjusting endpoints
C 1.726462 0.699608 2.467755 0.0486
X2 -0.377232 0.155530 -2.425454 0.0515
X3 -0.187566 0.157539 -1.190603 0.2788
X4 -0.422382 0.159203 -2.653103 0.0379
YT(-1) 0.984601 0.171834 5.729963 0.0012
R-squared 0.955655 Mean dependent var -1.025898 Adjusted R-squared 0.918701 S.D. dependent var 0.504523 S.E. of regression 0.143855 Akaike info criterion -0.733174 Sum squared resid 0.124165 Schwarz criterion -0.490720 Log likelihood 10.39904 F-statistic 25.86057
T 检验值显著，R2显著，F 统计量显著，所以舍去X3，X5得到模型
Yt=1.726462-0.377232X2-0.422382 X4+0.984601lnY t-1+0.007675lnμt-1 T= 2.467755 -2.425454 -2.653103 5.729963 0.107765 R2=0.955655
上述模型即为所求
二、检验多重共线性，异方差性，自相关性
X2 X4 YT(-1) UT 1 -0.187132883642 -0.0173829893284 0.032625884
5095 -0.18713288
3642
1
0.825418362348 -0.110931081
665 -0.0173829893284 0.825418362348 1
0.007760570
31174 0.0326258845095
-0.110931081665
0.007760570
31174
1
解释变量之间不存在多重共线性
由上表知，DW 统计量为1.301532，Dl=0.697,Du=1.641,落在不可判断区
由残差序列的散点图，无明显的先行自回归，没有自相关性
-0.3-0.2-0.10.00.10.2-0.3
-0.2-0.1
0.00.10.2
E
E (-1)
用ARCH 检验法检验
Dependent Variable: E2 Method: Least Squares Date: 12/14/05 Time: 10:53 Sample(adjusted): 2000:4 2005:1 Included observations: 9
Excluded observations: 9 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob. C 0.006864 0.004455 1.540753 0.1673 E2(-1)
-0.144142
0.371462
-0.388040
0.7095 R-squared
0.021058 Mean dependent var 0.005737 Adjusted R-squared -0.118791 S.D. dependent var 0.009584 S.E. of regression 0.010137 Akaike info criterion -6.152137 Sum squared resid 0.000719 Schwarz criterion -6.108309 Log likelihood 29.68462 F-statistic 0.150575 Durbin-Watson stat
2.359829 Prob(F-statistic)
0.709517
R2=0.021058，（N-P ）R2=0.16864〈临界值。

无异方差性
所以模型
Yt=1.726462-0.377232X2-0.422382 X4+0.984601lnY t-1+0.007675lnμt-1即为所求。