Table 7. ADF, ADF-GLS and KPSS Unit root...

Table 7.

ADF, ADF-GLS and KPSS Unit root tests for stationarity analysis of first differenced series (α = 0.05)

Series	Diff Log IBOVESPA_1	Diff Log CHISHA_1	Diff Log DAX 30_1	Diff Log IND_BOMB_1	DiffLog FTSE 100_1	DiffLog NYSE_1	DiffLog AL Index_1
ADF with const	−42.69	−43.58	−44.47	−40.85	−42.01	−43.82	−36.04
p-value	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*
ADF with const and trend	−43.23	−43.58	−44.49	−40.84	−42.01	−43.83	−36.04
p-value	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*
ADF_GLS τ	−2.12	−9.09^*	−3.85^*	−4.18^*	−42.00^*	−31.04^*	−28.23^*
Critical value	−2.89	−2.89	−2.89	−2.89	−2.89	−2.89	−2.89
KPSS	3.13	0.07^*	0.18^*	0.11^*	0.06^*	0.17^*	0.12^*
Critical value	0.462	0.462	0.462	0.462	0.462	0.462	0.462
Testing down from 25 lags and BIC criterion for ADF and ADF-GLS; Lag order 8 for KPSS
Series	DiffLog IBOVESPA_2	DiffLog CHISHA_2	DiffLog DAX 30_2	DiffLog IND_BOMB_2	DiffLog FTSE 100_2	DiffLog NYSE_2	DiffLog AL Index_2
ADF with const	−76.82	−73.07	−75.21	−69.61	−29.00	−80.77	−80.92
p-value	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*
ADF with const and trend	−76.82	−73.06	−75.21	−69.61	−29.00	−80.77	−80.93
p-value	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*
ADF_GLS τ	−2.36	−2.77	−17.39^*	−4.26^*	−29.63^*	−2.97^*	−10.73^*
Critical value	−2.89	−2.89	−2.89	−2.89	−2.89	−2.89	−2.89
KPSS	0.07^*	0.06^*	0.15^*	0.09^*	0.09^*	0.07^*	0.14^*
Critical value	0.462	0.462	0.462	0.462	0.462	0.462	0.462
Testing down from 32 lags and BIC criterion for ADF and ADF-GLS; Lag order 10 for KPSS

Series	Diff Log IBOVESPA_1	Diff Log CHISHA_1	Diff Log DAX 30_1	Diff Log IND_BOMB_1	DiffLog FTSE 100_1	DiffLog NYSE_1	DiffLog AL Index_1
ADF with const	−42.69	−43.58	−44.47	−40.85	−42.01	−43.82	−36.04
p-value	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*
ADF with const and trend	−43.23	−43.58	−44.49	−40.84	−42.01	−43.83	−36.04
p-value	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*
ADF_GLS τ	−2.12	−9.09^*	−3.85^*	−4.18^*	−42.00^*	−31.04^*	−28.23^*
Critical value	−2.89	−2.89	−2.89	−2.89	−2.89	−2.89	−2.89
KPSS	3.13	0.07^*	0.18^*	0.11^*	0.06^*	0.17^*	0.12^*
Critical value	0.462	0.462	0.462	0.462	0.462	0.462	0.462
Testing down from 25 lags and BIC criterion for ADF and ADF-GLS; Lag order 8 for KPSS
Series	DiffLog IBOVESPA_2	DiffLog CHISHA_2	DiffLog DAX 30_2	DiffLog IND_BOMB_2	DiffLog FTSE 100_2	DiffLog NYSE_2	DiffLog AL Index_2
ADF with const	−76.82	−73.07	−75.21	−69.61	−29.00	−80.77	−80.92
p-value	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*
ADF with const and trend	−76.82	−73.06	−75.21	−69.61	−29.00	−80.77	−80.93
p-value	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*	0.00^*
ADF_GLS τ	−2.36	−2.77	−17.39^*	−4.26^*	−29.63^*	−2.97^*	−10.73^*
Critical value	−2.89	−2.89	−2.89	−2.89	−2.89	−2.89	−2.89
KPSS	0.07^*	0.06^*	0.15^*	0.09^*	0.09^*	0.07^*	0.14^*
Critical value	0.462	0.462	0.462	0.462	0.462	0.462	0.462
Testing down from 32 lags and BIC criterion for ADF and ADF-GLS; Lag order 10 for KPSS

Notes:

Table resumes the formal unit-root tests for first differenced log-series. Augmented Dickey-Fuller (ADF), Augmented Dickey-Fuller Generalized Least Squares Regression (ADF-GLS) and Kwiatkowsky-Phillips-Schmidt-Shin (KPSS) test are calculated with the corresponding p-value. Lag adjustments are because of different sample sizes.

Indicates stationarity at 5% level (α = 0.05)

Source: Personal elaboration on Datastream (2021)

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