Menzie Chinn, 9/11/2016 AGRIC09KS is March 2016 vintage AGR09KS1 is July 2016 vintage PDSI_KS_NEW is PDSI for Kansas Agriculture (March ’16 vintage)
ADF Fail to reject unit root null
Agriculture (July ’16 vintage)
Fail to reject unit root null (ERS rejects) Fail to reject unit root null
PDSI for Kansas
KPSS Fail to reject trend stationary null Reject trend stationary null Fail to reject trend stationary null
Using eviews defaults, 5% msl. 8,000 March 2016 vintage
7,000 6,000 5,000 4,000 July 2016 vintage
3,000 2,000 05
06
07
08
09
10
AGRIC09KS
11
12
13
14
15
16
AGR09KS1
PDSI_KS_NEW 6 4 2 0 -2 -4 -6 05
06
07
08
09
10
11
12
13
Null Hypothesis: AGRIC09KS has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic - based on AIC, maxlag=9)
Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level
t-Statistic
Prob.*
-2.306026 -4.192337 -3.520787 -3.191277
0.4216
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(AGRIC09KS) Method: Least Squares Date: 09/11/16 Time: 21:46 Sample (adjusted): 2005Q2 2015Q3 Included observations: 42 after adjustments Variable
Coefficient
Std. Error
t-Statistic
Prob.
AGRIC09KS(-1) C @TREND("2005Q1")
-0.327155 733.6700 32.00812
0.141870 401.1461 12.58008
-2.306026 1.828935 2.544349
0.0265 0.0751 0.0150
14
15
16
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
0.146656 0.102895 604.0869 14231918 -326.9953 3.351279 0.045386
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat
113.2857 637.7901 15.71406 15.83818 15.75956 1.807217
Null Hypothesis: AGRIC09KS has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic - based on AIC, maxlag=9) t-Statistic Elliott-Rothenberg-Stock DF-GLS test statistic Test critical values: 1% level 5% level 10% level
-2.522520 -3.770000 -3.190000 -2.890000
*Elliott-Rothenberg-Stock (1996, Table 1) Warning: Test critical values calculated for 50 observations and may not be accurate for a sample size of 42
DF-GLS Test Equation on GLS Detrended Residuals Dependent Variable: D(GLSRESID) Method: Least Squares Date: 09/11/16 Time: 21:46 Sample (adjusted): 2005Q2 2015Q3 Included observations: 42 after adjustments Variable
Coefficient
Std. Error
t-Statistic
Prob.
GLSRESID(-1)
-0.328790
0.130342
-2.522520
0.0156
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
0.132098 0.132098 594.1733 14474718 -327.3506 1.775173
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter.
32.12297 637.7901 15.63574 15.67711 15.65091
Null Hypothesis: AGRIC09KS is stationary Exogenous: Constant, Linear Trend Bandwidth: 4 (Newey-West automatic) using Bartlett kernel LM-Stat. Kwiatkowski-Phillips-Schmidt-Shin test statistic Asymptotic critical values*: 1% level 5% level 10% level *Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)
0.085017 0.216000 0.146000 0.119000
Residual variance (no correction) HAC corrected variance (Bartlett kernel)
529414.1 1234046.
KPSS Test Equation Dependent Variable: AGRIC09KS Method: Least Squares Date: 09/11/16 Time: 21:46 Sample (adjusted): 2005Q1 2015Q3 Included observations: 43 after adjustments Variable
Coefficient
Std. Error
t-Statistic
Prob.
C @TREND("2005Q1")
2463.408 77.33162
223.3592 9.156836
11.02891 8.445233
0.0000 0.0000
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
0.634978 0.626075 745.1437 22764806 -344.3742 71.32197 0.000000
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat
4087.372 1218.562 16.11043 16.19234 16.14063 0.734999
Null Hypothesis: AGR09KS1 has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic - based on AIC, maxlag=9)
Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level
t-Statistic
Prob.*
-3.231905 -4.180911 -3.515523 -3.188259
0.0916
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(AGR09KS1) Method: Least Squares Date: 09/11/16 Time: 21:46 Sample (adjusted): 2005Q2 2016Q1 Included observations: 44 after adjustments Variable
Coefficient
Std. Error
t-Statistic
Prob.
AGR09KS1(-1) C @TREND("2005Q1")
-0.413147 1303.912 11.62495
0.127834 423.3091 8.026685
-3.231905 3.080284 1.448287
0.0024 0.0037 0.1551
R-squared Adjusted R-squared
0.204140 0.165317
Mean dependent var S.D. dependent var
20.34091 632.6595
S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
578.0039 13697631 -340.7013 5.258283 0.009272
Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat
15.62278 15.74443 15.66790 1.919125
Null Hypothesis: AGR09KS1 has a unit root Exogenous: Constant, Linear Trend Lag Length: 0 (Automatic - based on AIC, maxlag=9) t-Statistic Elliott-Rothenberg-Stock DF-GLS test statistic Test critical values: 1% level 5% level 10% level
-3.319508 -3.770000 -3.190000 -2.890000
*Elliott-Rothenberg-Stock (1996, Table 1) Warning: Test critical values calculated for 50 observations and may not be accurate for a sample size of 44
DF-GLS Test Equation on GLS Detrended Residuals Dependent Variable: D(GLSRESID) Method: Least Squares Date: 09/11/16 Time: 21:47 Sample (adjusted): 2005Q2 2016Q1 Included observations: 44 after adjustments Variable
Coefficient
Std. Error
t-Statistic
Prob.
GLSRESID(-1)
-0.412614
0.124300
-3.319508
0.0018
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
0.203834 0.203834 564.5103 13702893 -340.7097 1.919389
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter.
-8.639367 632.6595 15.53226 15.57281 15.54730
Null Hypothesis: AGR09KS1 is stationary Exogenous: Constant, Linear Trend Bandwidth: 4 (Newey-West automatic) using Bartlett kernel LM-Stat. Kwiatkowski-Phillips-Schmidt-Shin test statistic Asymptotic critical values*: 1% level 5% level 10% level
0.159025 0.216000 0.146000 0.119000
*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)
Residual variance (no correction)
460933.1
HAC corrected variance (Bartlett kernel)
1132218.
KPSS Test Equation Dependent Variable: AGR09KS1 Method: Least Squares Date: 09/11/16 Time: 21:47 Sample: 2005Q1 2016Q1 Included observations: 45 Variable
Coefficient
Std. Error
t-Statistic
Prob.
C @TREND("2005Q1")
3063.276 30.91976
203.6647 7.972051
15.04078 3.878520
0.0000 0.0004
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
0.259169 0.241940 694.5299 20741988 -357.2749 15.04292 0.000355
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat
3743.511 797.6994 15.96777 16.04807 15.99771 0.830008
Null Hypothesis: PDSI_KS_NEW has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic - based on AIC, maxlag=9)
Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level
t-Statistic
Prob.*
-1.952605 -4.175640 -3.513075 -3.186854
0.6106
*MacKinnon (1996) one-sided p-values.
Augmented Dickey-Fuller Test Equation Dependent Variable: D(PDSI_KS_NEW) Method: Least Squares Date: 09/11/16 Time: 21:47 Sample: 2005Q1 2016Q1 Included observations: 45 Variable
Coefficient
Std. Error
t-Statistic
Prob.
PDSI_KS_NEW(-1) D(PDSI_KS_NEW(-1)) C @TREND("2005Q1")
-0.143852 0.292263 0.144761 -0.003347
0.073672 0.151703 0.353510 0.013615
-1.952605 1.926545 0.409497 -0.245829
0.0577 0.0610 0.6843 0.8070
R-squared Adjusted R-squared S.E. of regression Sum squared resid
0.131288 0.067723 1.118109 51.25688
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion
0.008148 1.158008 3.145842 3.306434
Log likelihood F-statistic Prob(F-statistic)
-66.78145 2.065430 0.119695
Hannan-Quinn criter. Durbin-Watson stat
3.205709 2.003607
Null Hypothesis: PDSI_KS_NEW has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic - based on AIC, maxlag=9) t-Statistic Elliott-Rothenberg-Stock DF-GLS test statistic Test critical values: 1% level 5% level 10% level
-2.049299 -3.770000 -3.190000 -2.890000
*Elliott-Rothenberg-Stock (1996, Table 1) Warning: Test critical values calculated for 50 observations and may not be accurate for a sample size of 45
DF-GLS Test Equation on GLS Detrended Residuals Dependent Variable: D(GLSRESID) Method: Least Squares Date: 09/11/16 Time: 21:48 Sample: 2005Q1 2016Q1 Included observations: 45 Variable
Coefficient
Std. Error
t-Statistic
Prob.
GLSRESID(-1) D(GLSRESID(-1))
-0.145463 0.294844
0.070982 0.146982
-2.049299 2.005990
0.0466 0.0512
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat
0.130896 0.110684 1.092043 51.28001 -66.79160 2.004759
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter.
0.043095 1.158008 3.057405 3.137701 3.087338
Null Hypothesis: PDSI_KS_NEW is stationary Exogenous: Constant, Linear Trend Bandwidth: 5 (Newey-West automatic) using Bartlett kernel LM-Stat. Kwiatkowski-Phillips-Schmidt-Shin test statistic Asymptotic critical values*: 1% level 5% level 10% level
0.095953 0.216000 0.146000 0.119000
*Kwiatkowski-Phillips-Schmidt-Shin (1992, Table 1)
Residual variance (no correction) HAC corrected variance (Bartlett kernel)
5.665377 23.84804
KPSS Test Equation Dependent Variable: PDSI_KS_NEW Method: Least Squares Date: 09/11/16 Time: 21:48 Sample: 2005Q1 2016Q1 Included observations: 45 Variable
Coefficient
Std. Error
t-Statistic
Prob.
C @TREND("2005Q1")
1.548119 -0.049524
0.714021 0.027949
2.168169 -1.771942
0.0357 0.0835
R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic)
0.068049 0.046376 2.434930 254.9420 -102.8756 3.139780 0.083490
Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Durbin-Watson stat
0.458593 2.493434 4.661139 4.741435 4.691073 0.230069