PDSI for Kansas Fail to reject unit root null Fail to reject trend stationary null Using eviews defaults, 5% msl

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)...
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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

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AGRIC09KS

 

11

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AGR09KS1

 

PDSI_KS_NEW 6 4 2 0 -2 -4 -6 05

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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