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Table 7 Unit root tests

From: How do supply or demand shocks affect the US oil market?

 

ADF

PP

KPSS

Ng-Perron

\({\overline{\text{M}}\text{Z}}_{\upalpha }^{{{\text{GLS}}}}\)

\({\overline{\text{M}}\text{Z}}_{{\text{t}}}^{{{\text{GLS}}}}\)

\({\overline{\text{M}}\text{SB}}^{{{\text{GLS}}}}\)

\({\overline{\text{M}}\text{PT}}^{{{\text{GLS}}}}\)

Level

WTI

 − 2.153

 − 2.166

0.243***

 − 9.509

 − 2.127

0.223

9.819

Conv. Gasoline

 − 2.260

 − 2.268

0.276***

 − 11.597

 − 2.319

0.200

8.334

RBOB

 − 3.529*

 − 3.559*

0.251***

 − 25.982***

 − 3.545***

0.136***

3.864***

Heating Oil

 − 3.352*

 − 3.521*

0.245***

 − 8.655

 − 2.009

0.232

10.795

Diesel NY

 − 2.009

 − 2.013

0.242***

 − 9.338

 − 2.072

0.222

10.137

Kerosene

 − 2.016

 − 2.011

0.236***

 − 9.199

 − 2.062

0.224

10.253

First differences

WTI

 − 24.849***

 − 24.874***

0.056

 − 409.220***

 − 14.304***

0.035***

0.059***

Conv. Gasoline

 − 22.862***

 − 22.916***

0.064

 − 393.127***

14.017***

0.036***

0.065***

RBOB

 − 23.159***

 − 23.303***

0.042

 − 386.337***

 − 13.896***

0.036***

0.066***

Heating Oil

 − 24.294***

 − 41.001***

0.082

 − 26.118***

 − 3.610***

0.138***

0.952***

Diesel NY

 − 24.361***

 − 33.136***

0.088

 − 49.624***

 − 4.980***

0.100***

0.496***

WTI

 − 24.326***

 − 43.328***

0.077

 − 16.821***

 − 2.875***

0.171***

1.552***

  1. ADF Augmented Dickey–Fuller, PP Philips–Perron, KPSS Kwiatkowski–Philips–Schmidt–Shin, SIC Schwartz information criterion, MSIC Modified Schwartz information criterion lag length used in ADF and PP based in SIC, MSIC in Ng-Perron, and Newey–West bandwidth used for KPSS
  2. ***, **, * indicate rejection of the null hypotheses (of unit root for ADF, PP, and NG-Perron, and of stationarity for KPSS) at 1%, 5%, and 10% levels