時間序列分析——VAR模型實驗

1、基于VAR模型的我國房地產(chǎn)市場與匯率波動的因果關系VAR模型實驗第一部分 實驗分析目的及方法現(xiàn)選取人民幣對美元匯率以及商品房房價作為變量構建VAR模型。對于不滿足單位根檢驗的序列采取對數(shù)化或差分處理，使其成為平穩(wěn)序列再進行模型的擬合。對于商品房房價這一變量，由于全國各省市差異較大，故此處采用全國房地產(chǎn)開發(fā)業(yè)綜合景氣指數(shù)這一變量。此外，為了消除春節(jié)假期不固定因素帶來的影響，增強數(shù)據(jù)的可比性，按照國家統(tǒng)計制度，從2012年起，不單獨對1月份統(tǒng)計數(shù)據(jù)進行調(diào)查，1-2月份數(shù)據(jù)一起調(diào)查，一起發(fā)布。所以國房景氣指數(shù)p這一序列缺少每年一月份的相關數(shù)據(jù)，屬于非隨機、不可忽略缺失，在此采用平均值填充的方法，補足

2、數(shù)據(jù)。 第二部分 實驗樣本2.1數(shù)據(jù)來源數(shù)據(jù)來源于中經(jīng)網(wǎng)統(tǒng)計數(shù)據(jù)庫。具體數(shù)據(jù)見附錄表。2.2所選數(shù)據(jù)變量由于我國于2005年7月實行第二次匯改，此次匯改以市場供求為基礎、參考一籃子貨幣進行調(diào)節(jié)、有管理的浮動匯率制度取代了過去人民幣匯率長達10年的緊盯美元的固定匯率體制。故本實驗擬選取2005年07月到2014年10月我國以月為單位的數(shù)據(jù)。，用以上兩個變量來構建VAR模型，并利用該模型進行分析預測。第四部分 模型構建4.1判斷序列的平穩(wěn)性4.1.1匯率E序列首先繪制出E的折線圖，結果如下圖：圖4.1 匯率E的曲線圖從圖中可以看出，匯率E序列較強的趨勢性，由此可以初步判斷該序列是非平穩(wěn)的。為了減少

3、m的變動趨勢以及異方差性，先對m進行對數(shù)化處理，記為lm，其時序圖如下：圖4.2 lm的曲線圖 對數(shù)化后的趨勢性減弱，但仍存在一定的趨勢性，下面對lm進行一階差分處理，去除趨勢性，得到新變量dlm，觀察dlm的曲線圖。圖4.3 DLE的曲線圖從圖中可以看出，dle序列的趨勢性基本已經(jīng)消除，且新變量dle基本圍繞0上下波動，因此選擇形式為yt=yt-1+ut 進行單位根檢驗：表4.1 單位根輸出結果Null Hypothesis: DLE has a unit rootExogenous: ConstantLag Length: 2 (Automatic - based on SIC, maxl

4、ag=12)t-Statistic  Prob.*Augmented Dickey-Fuller test statistic-3.031673 0.0351Test critical values:1% level-3.4919285% level-2.88841110% level-2.581176*MacKinnon (1996) one-sided p-values.Augmented Dickey-Fuller Test EquationDependent Variable: D(DLE)Method: Least SquaresDate: 11/15/

5、14 Time: 20:20Sample (adjusted): 2005M11 2014M10Included observations: 108 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.  DLE(-1)-0.3530050.116439-3.0316730.0031D(DLE(-1)-0.5027300.115417-4.3557680.0000D(DLE(-2)-0.3115310.093265-3.3402580.0012C-0.0008880.000470-1.8875920.0

6、619R-squared0.450240    Mean dependent var1.15E-05Adjusted R-squared0.434382    S.D. dependent var0.005058S.E. of regression0.003804    Akaike info criterion-8.269046Sum squared resid0.001505    Schwarz criterion-8.16970

7、8Log likelihood450.5285    Hannan-Quinn criter.-8.228768F-statistic28.39119    Durbin-Watson stat2.061613Prob(F-statistic)0.000000單位根統(tǒng)計量ADF=-3.031673小于臨界值，且P為 0.0351，因此該序列不是單位根過程，即該序列是平穩(wěn)序列。4.1.2國房景氣指數(shù)P序列首先作出P序列的時序圖：圖4.4 P的曲線圖由于每年一月份的數(shù)據(jù)缺失，故取相鄰兩項進行平均補全數(shù)據(jù)，得到

8、新序列的時序圖如下：圖4.5 P的曲線圖(補全)由上圖可知，該序列P可能存在一定的趨勢性和季節(jié)性，先進行單位根檢驗，確定改序列是否平穩(wěn)。由于序列表4.2 單位根輸出結果Null Hypothesis: P has a unit rootExogenous: Constant, Linear TrendLag Length: 3 (Automatic - based on SIC, maxlag=12)t-Statistic  Prob.*Augmented Dickey-Fuller test statistic-3.972457 0.0124Test criti

9、cal values:1% level-4.0452365% level-3.45195910% level-3.151440*MacKinnon (1996) one-sided p-values.由單位根檢驗結果可知，T值小于臨界值，且P=0.0124，在5%的置信水平下，該序列不存在單位根過程。由于匯率E序列為一階單整序列，并進行了一階差分處理，因此樣本數(shù)量減少，在下面的操作中，所有的樣本序列調(diào)整為2005-08至2014-10。4.2模型參數(shù)識別先進行VAR模型的擬合，初步選定滯后階數(shù)為3：表4.3 擬合輸出結果 Vector Autoregression Estimates

10、 Date: 11/22/14 Time: 22:20 Sample (adjusted): 2005M11 2014M10 Included observations: 108 after adjustments Standard errors in ( ) & t-statistics in DLEPDLE(-1) 0.063183-19.12274 (0.09626) (14.1374) 0.65638-1.35263DLE(-2) 0.116798 15.42129 (0.096

11、04) (14.1052) 1.21615 1.09330DLE(-3) 0.245260 16.39171 (0.09617) (14.1243) 2.55030 1.16053P(-1)-9.04E-05 1.490708 (0.00066) (0.09765)-0.13593 15.2656P(-2)-0.000583-0.355442 (0.00118) (0.17380)-0.49226-2.04508P(-3) 0.000346-0.160740 (0.00067

12、) (0.09872) 0.51479-1.62821C 0.031328 2.571540 (0.01274) (1.87084) 2.45943 1.37454 R-squared 0.295033 0.979509 Adj. R-squared 0.253154 0.978292 Sum sq. resids 0.001390 29.99247 S.E. equation 0.003710 0.544936 F

13、-statistic 7.044848 804.6767 Log likelihood 454.8094-84.06138 Akaike AIC-8.292766 1.686322 Schwarz SC-8.118924 1.860164 Mean dependent-0.002527 100.2406 S.D. dependent 0.004293 3.698585 Determinant resid covariance (dof adj.) 

14、;4.08E-06 Determinant resid covariance 3.57E-06 Log likelihood 370.8871 Akaike information criterion-6.609021 Schwarz criterion-6.261337再進行滯后階數(shù)的確定：表4.4 最優(yōu)滯后階數(shù)的判斷VAR Lag Order Selection CriteriaEndogenous variables: DLE P Exogenous variables: C Date: 11/22/14 T

15、ime: 22:22Sample: 2005M07 2014M10Included observations: 99 LagLogLLRFPEAICSCHQ0 134.7784NA  0.000234-2.682392-2.629965-2.6611801 302.5627 325.3999 8.57e-06-5.991165-5.833886-5.9275302 329.0230 50.24783 5.45e-06-6.444909 -6.182775* -6.338849

16、*3 334.3733  9.943949*  5.30e-06* -6.472187*-6.105200-6.3237044 337.4531 5.599742 5.40e-06-6.453598-5.981758-6.2626915 339.7589 4.099176 5.60e-06-6.419372-5.842679-6.1860416 345.0498 9.192324 5.46e-06-6.445451-5.763905-6.1696

17、967 345.5484 0.846076 5.87e-06-6.374716-5.588316-6.0565378 346.7369 1.968760 6.23e-06-6.317917-5.426663-5.9573149 352.5801 9.443639 6.01e-06-6.355154-5.359047-5.95212810 353.7714 1.877082 6.39e-06-6.298411-5.197451-5.85296111 354.3649&

18、#160;0.911279 6.87e-06-6.229594-5.023780-5.74172012 356.4617 3.134644 7.18e-06-6.191146-4.880479-5.660848 * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike

19、information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion由上邊可知，根據(jù)信息準則，采取少數(shù)服從多數(shù)原則，取滯后階數(shù)為3，此外取滯后階數(shù)為2(SC為  -6.182775)或取滯后階數(shù)為3(SC為-6.105200)時，兩者SC值相差不是很大。3.3模型參數(shù)估計選取了最優(yōu)滯后階數(shù)3，進行模型的擬合。擬合結果如下：表4.5 VAR(3)模型估計結果 Vector Autoregression Estimates Dat

20、e: 11/22/14 Time: 22:23 Sample (adjusted): 2005M11 2014M10 Included observations: 108 after adjustments Standard errors in ( ) & t-statistics in DLEPDLE(-1) 0.063183-19.12274 (0.09626) (14.1374) 0.65638-1.35263DLE(-2) 0.116798 15.42129 (0.09604) 

21、(14.1052) 1.21615 1.09330DLE(-3) 0.245260 16.39171 (0.09617) (14.1243) 2.55030 1.16053P(-1)-9.04E-05 1.490708 (0.00066) (0.09765)-0.13593 15.2656P(-2)-0.000583-0.355442 (0.00118) (0.17380)-0.49226-2.04508P(-3) 0.000346-0.160740 (0.00067) (0

22、.09872) 0.51479-1.62821C 0.031328 2.571540 (0.01274) (1.87084) 2.45943 1.37454 R-squared 0.295033 0.979509 Adj. R-squared 0.253154 0.978292 Sum sq. resids 0.001390 29.99247 S.E. equation 0.003710 0.544936 F-statisti

23、c 7.044848 804.6767 Log likelihood 454.8094-84.06138 Akaike AIC-8.292766 1.686322 Schwarz SC-8.118924 1.860164 Mean dependent-0.002527 100.2406 S.D. dependent 0.004293 3.698585 Determinant resid covariance (dof adj.) 4.08E-06

24、 Determinant resid covariance 3.57E-06 Log likelihood 370.8871 Akaike information criterion-6.609021 Schwarz criterion-6.261337由回歸結果可知，VAR模型的參數(shù)估計一部分顯著。估計的方程為：4.4模型檢驗首先對模型進行平穩(wěn)性檢驗表4.6 VAR模型平穩(wěn)性檢驗的表格顯示Roots of Characteristic PolynomialEndogenous variables: DLE P Exogen

25、ous variables: C Lag specification: 1 3Date: 11/22/14 Time: 22:27     RootModulus 0.883466 - 0.097039i 0.888779 0.883466 + 0.097039i 0.888779 0.670300 0.670300-0.321875 - 0.501863i 0.596213-0.321875 + 0.501863i 0.596213-0.239592&#

26、160;0.239592 No root lies outside the unit circle. VAR satisfies the stability condition.圖4.6 VAR模型平穩(wěn)性檢驗的圖形顯示由上表和上圖可知，VAR模型的特征方程的根均在單位園內(nèi)，因此VAR模型是平穩(wěn)的。下面進行殘差的自相關性的檢驗，檢驗結果如下：圖4.7 VAR模型各方程殘差項的自相關圖由上圖可知，VAR模型允許不同方程的殘差之間存在交叉相關性，但是殘差自身不存在自相關性，因此，觀察殘差自身的自相關圖，可以看出自相關系數(shù)均位于置信區(qū)間內(nèi)，說明殘差不存在自相關性。第五部分 模型應用

27、5.1格蘭杰因果檢驗接下來做兩兩變量之間的格蘭杰因果檢驗。序列P與序列DLE:表5.1 序列P與序列DLE格蘭杰因果檢驗表Pairwise Granger Causality TestsDate: 11/21/14 Time: 23:32Sample: 2005M07 2014M10Lags: 3 Null Hypothesis:ObsF-StatisticProb.  P does not Granger Cause DLE 108 2.777600.0451 DLE does not Granger Cause P 1.

28、342860.2648由上述結果可知，在5%的置信水平下，P是dle的格蘭杰原因，即全國房地產(chǎn)開發(fā)業(yè)綜合景氣指數(shù)是人民幣對美元匯率變動幅度的格蘭杰原因。5.2脈沖響應由于脈沖響應函數(shù)收到變量順序的影響，因此其結果與分析的主觀因素有關，對于這三個變量：DLE、R、P,按照中國市場目前現(xiàn)狀，認為DLE外生性最強，p其次最后為r。故選取順序為DLE、P、R。圖5.1 脈沖響應圖5.3方差分解 表5.4 方差分解結果 Variance Decomposition of DLE: PeriodS.E.DLEP 1 0.003710 100.0000

29、60;0.000000 2 0.003718 99.98250 0.017500 3 0.003769 98.89311 1.106885 4 0.003929 97.90952 2.090481 5 0.003966 96.36508 3.634918 6 0.004019 94.21821 5.781793 7 0.004078 92.06035 7.9

30、39649 8 0.004129 89.81515 10.18485 9 0.004182 87.60545 12.39455 10 0.004231 85.59975 14.40025 11 0.004276 83.80638 16.19362 12 0.004316 82.24748 17.75252 13 0.004351 80.93658 19.06

31、342 14 0.004381 79.85384 20.14616 15 0.004406 78.97724 21.02276 16 0.004426 78.28318 21.71682 17 0.004442 77.74396 22.25604 18 0.004454 77.33345 22.66655 19 0.004464 77.02793 22.97

32、207 20 0.004471 76.80583 23.19417 21 0.004476 76.64855 23.35145 22 0.004479 76.54051 23.45949 23 0.004482 76.46887 23.53113 24 0.004483 76.42336 23.57664 25 0.004484 76.39600 23.60

33、400 26 0.004485 76.38071 23.61929 27 0.004485 76.37306 23.62694 28 0.004486 76.36989 23.63011 29 0.004486 76.36906 23.63094 30 0.004486 76.36919 23.63081 31 0.004486 76.36947 23.63

34、053 32 0.004486 76.36946 23.63054 33 0.004486 76.36900 23.63100 34 0.004486 76.36807 23.63193 35 0.004486 76.36675 23.63325 36 0.004486 76.36516 23.63484 Variance Decomposition of P: PeriodS

35、.E.DLEP 1 0.544936 0.257337 99.74266 2 0.983734 1.378912 98.62109 3 1.418724 1.207448 98.79255 4 1.825142 0.824892 99.17511 5 2.194895 0.599272 99.40073 6 2.522096 0.453882 99.5461

36、2 7 2.807026 0.385862 99.61414 8 3.050709 0.372890 99.62711 9 3.255840 0.405125 99.59488 10 3.425992 0.469786 99.53021 11 3.564913 0.553401 99.44660 12 3.676591 0.649292 99.35071&#

37、160;13 3.764936 0.750501 99.24950 14 3.833629 0.851271 99.14873 15 3.886088 0.948104 99.05190 16 3.925375 1.038145 98.96186 17 3.954180 1.119482 98.88052 18 3.974811 1.191169 98.80883&#

38、160;19 3.989207 1.252835 98.74717 20 3.998959 1.304640 98.69536 21 4.005342 1.347173 98.65283 22 4.009354 1.381278 98.61872 23 4.011756 1.407970 98.59203 24 4.013112 1.428338 98.57166&#

39、160;25 4.013827 1.443463 98.55654 26 4.014179 1.454362 98.54564 27 4.014351 1.461952 98.53805 28 4.014457 1.467028 98.53297 29 4.014560 1.470254 98.52975 30 4.014690 1.472167 98.52783&#

40、160;31 4.014856 1.473188 98.52681 32 4.015054 1.473635 98.52636 33 4.015274 1.473739 98.52626 34 4.015504 1.473662 98.52634 35 4.015734 1.473509 98.52649 36 4.015953 1.473349 98.52665附錄

41、具體數(shù)據(jù)指標國房景氣指數(shù)_當月人民幣對美元期末匯率地區(qū)全國全國頻度月月單位-人民幣/美元2005-07101.978.112005-08101.768.12005-09101.428.092005-10101.028.082005-11100.698.082005-12100.618.072006-01100.768.062006-02101.058.042006-03101.468.022006-04101.618.022006-05101.878.022006-06102.9382006-07103.517.972006-08103.317.962006-09103.147.912006-

42、10103.47.882006-11103.927.842006-12102.967.812007-01102.427.782007-02101.787.742007-03101.227.732007-04102.657.712007-05103.327.652007-06103.637.622007-071047.572007-08104.487.562007-09104.997.512007-10105.747.472007-11106.597.42007-12106.457.32008-01106.117.192008-02105.557.112008-03104.727.022008-04104.0772008-05103.346.942008-06103.086.862008-07102.366.8420