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# st: dfuller: Why is Stata using the t-distribution when I use "drift"

 From "Daniel Ilg" <[email protected]> To <[email protected]> Subject st: dfuller: Why is Stata using the t-distribution when I use "drift" Date Fri, 26 Aug 2011 01:44:40 +0200

```Hi!

I wonder why Stata is using the t-distribution for the critical values in
dfuller when I use a drift parameter. The normal dfuller uses the critical
values of "Interpolated Dickey-Fuller". For me it seems that both tests are
identical, except dfuller with the drift leads to a rejection of the
H0-Hypothesis.

. dfuller LPX_america, regress lags(10)

Augmented Dickey-Fuller test for unit root         Number of obs   =
122

---------- Interpolated Dickey-Fuller
---------
Test         1% Critical       5% Critical      10%
Critical
Statistic           Value             Value             Value
----------------------------------------------------------------------------
--
Z(t)             -2.571            -3.503            -2.889
-2.579
----------------------------------------------------------------------------
--
MacKinnon approximate p-value for Z(t) = 0.0991

----------------------------------------------------------------------------
--
D.           |
LPX_america |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
LPX_america |
L1. |  -.0617879   .0240325    -2.57   0.011    -.1094147
-.0141612
LD. |   .2827078   .0889924     3.18   0.002     .1063457
.45907
L2D. |  -.0179429   .0883804    -0.20   0.839    -.1930921
.1572064
L3D. |  -.0191534   .0883105    -0.22   0.829     -.194164
.1558573
L4D. |   .1765123   .0844759     2.09   0.039     .0091008
.3439238
L5D. |  -.0071433   .0853274    -0.08   0.933    -.1762422
.1619557
L6D. |  -.1130131   .0834153    -1.35   0.178    -.2783226
.0522964
L7D. |   .1712005   .0835844     2.05   0.043     .0055559
.3368451
L8D. |    .058436   .0842389     0.69   0.489    -.1085057
.2253777
L9D. |   .0355256   .0830961     0.43   0.670    -.1291514
.2002026
L10D. |   .1804269   .0798417     2.26   0.026     .0221994
.3386544
_cons |    10.3958   4.087999     2.54   0.012     2.294345
18.49725
----------------------------------------------------------------------------
--

. dfuller LPX_america, drift regress lags(10)

Augmented Dickey-Fuller test for unit root         Number of obs   =
122

----------- Z(t) has t-distribution
-----------
Test         1% Critical       5% Critical      10%
Critical
Statistic           Value             Value             Value
----------------------------------------------------------------------------
--
Z(t)             -2.571            -2.361            -1.659
-1.289
----------------------------------------------------------------------------
--
p-value for Z(t) = 0.0057

----------------------------------------------------------------------------
--
D.           |
LPX_america |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
LPX_america |
L1. |  -.0617879   .0240325    -2.57   0.011    -.1094147
-.0141612
LD. |   .2827078   .0889924     3.18   0.002     .1063457
.45907
L2D. |  -.0179429   .0883804    -0.20   0.839    -.1930921
.1572064
L3D. |  -.0191534   .0883105    -0.22   0.829     -.194164
.1558573
L4D. |   .1765123   .0844759     2.09   0.039     .0091008
.3439238
L5D. |  -.0071433   .0853274    -0.08   0.933    -.1762422
.1619557
L6D. |  -.1130131   .0834153    -1.35   0.178    -.2783226
.0522964
L7D. |   .1712005   .0835844     2.05   0.043     .0055559
.3368451
L8D. |    .058436   .0842389     0.69   0.489    -.1085057
.2253777
L9D. |   .0355256   .0830961     0.43   0.670    -.1291514
.2002026
L10D. |   .1804269   .0798417     2.26   0.026     .0221994
.3386544
_cons |    10.3958   4.087999     2.54   0.012     2.294345
18.49725
----------------------------------------------------------------------------
--

Can someone explain me the difference?

Best Regards,
Daniel

Mit freundlichen Grüßen/Best regards

Dipl.-Kfm. Daniel Ilg
wissenschaftlicher Mitarbeiter/Research Associate
Lehrstuhl für Wirtschaftstheorie/Chair of Economic Theory

Katholische Universität Eichstätt-Ingolstadt/Catholic University
Eichstaett-Ingolstadt
Auf der Schanz 49
85049 Ingolstadt
Tel.: +49 841 937 1857
Mobil: +49 171 653 113 1
E-Mail: [email protected]

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