ADF-Tests
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This was the orignal question.
> Can someone briefly summarize the standard practice for lag
> length selection in ADF tests, along with some pointers on
> justification. My impression is that practice is to include
> enough lagged differences that the residuals look white
> according to, say, the Ljung-Box Q-statistic. Is this a good
> approach? Are the Poskitt and Tremayne (1981) concerns
> about use of such statistics in the presence of lagged
> dependent variables of any relevance here?
>
> *Any* suggestions here will be appreciated.
>
> --Alan G. Isaac
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I thank everyone who responded, and I am providing a summary of comments and
cites for general use. I am not noting the sources of the cites and
comments, which I hope slights no one. They are organized largely in order
received and lightly edited. --Alan G. Isaac
1. Given that the purpose of augmentation is to "whiten" the residuals of
the ADF regression, the use of a general autocorrelation test is intuitively
attractive - but there are plenty of other criteria one might wish to use as
well (information criteria for example). I generally only have 30-40
observations to deal with and typically set p=4 for the ADF lag length since
this was found to be best from the point of view of having a reliable true
significance level for the ADF test in: J.L. Dods & D.E.A. Giles,
"Alternative Strategies for 'Augmenting' the Dickey-Fuller Test: Size
Robustness in the Face of Pre-Testing", Journal of Statistical Computation &
Simulation, 1995, 53, 243-258.
2. The question of how to maximise the power of the ADF test, as distinct
from its size, has not been addressed as far as I know.
3. Don't use DF tests when your data has an MA representation. See JBES,
1994, 157 - 166.
4. Poskitt + Tremayne is relevent and what ever you do in the ADF the
residuals have to be noise for the size to be right.
5. The procedure recommended in Campbell and Perron ("Pitfalls and
Opportunities: what macroeconomists need to know about unit roots and
cointegration") is the standard lag length selection procedure. They
recommend starting at a maximum lag length, k*, and use a backward selection
procedure based on the significance of the last lag. There have been several
papers writtin on this subject, the most recent being Ng and Perron (1995)
"Unit Root tests in ARMA Models with data-dependent methods for selection of
the truncation lag" JASA, March 1995. They favor methods of choosing lags
based on sequential tests over those based on information criteria - like
AIC or BIC - because the sequential tests show less size distortion that the
information criteria. Another good reference is Hall (1994) "Testing for a
unit root in time series with pretest data based model selection" JBES.
6. Use of the information criteria (AIC, AICC, BIC etc.) to choose the
trunction lag parameter when performing ADF tests is incorrect since it
violates one of the basic assumptions in Said and Dickey's paper
(Biometrika, 1984). In short, the selected k grows too slowly with T, the
number of observations. This has been shown by Ng and Perron (JASA, 1995).
They suggest an approach based on sequential testing.
5. Perron has recent working papers on the subject with Serina Ng (U. de
Montreal working paper series.) (Does anyone know if these are in the WUStL
working papers archive?)
6. The GAUSS coint2.0 manual by Ouliaris and Phillips may also give some
guidance.
7. From a practical point of view, one may question any use of ADF tests if
"true" lag length is unknown. As simulation experiments of
Agiakloglou/Newboldwork(1992), Journal of Time Series Analysis, and
theoretical work of Blough(1992), Journal of Applied Econometrics show,
power of ADF tests cannot be higher than significance level if one tries to
estimate both (unit) root and lag length. So I can't recommend using model
selection criteria in connection with univariate ADF tests.
8. Reply (7) may give an overly pessimistic impression. Use of uninitialized value in concatenation (.) or string at E:\listplex\SYSTEM\SCRIPTS\filearea.cgi line 455, line 110.
Check out: Hall, A.
(1994), "Testing for a Unit Root in Time Series With Pretest Data-Based
Model Selection", Journal of Business and Economic Statistics, 12, 461-470.
Ng, S. and P. Perron, "Unit Root Tests in ARMA Models with Data- Dependent
Methods for the Selection of the Truncation Lag", Journal of the American
Statistical Association", 90, 268-281. The first deals with the case where
the "true" DGP is a finite-order autoregression, whereas the second paper
extends the analysis to ARMA processes. What I remember (but please check
for yourself) is that a general-to-specific lag selection method seems to do
quite well both asymptotically and in finite samples. Thus, one would start
with a maximum lag length p (depending on the sample size) and "test down"
using t- or F-tests for the signifance of the longest lag(s). In univariate
models, such tests can be reinterpreted as Lagrange- multiplier tests for
serial correlation in the smaller model. (E.g., testing for AR(1) errors in
an AR(1) model is equivalent to testing down from an AR(2) to an AR(1)).
This LM serial correlation test does not suffer from the drawbacks of the
Ljung-Box test in models with lagged dependent variables.
9. Harris (1992) Economic Letters shows the lag length should be set
according to the formula in Schwert (1989) lag length = 12*
int{(T/100)**(1/4)} where int means take value before decimal point and **
is raise to power of, and T is no. of observations (Example: 80
observations: use lage length of 11)
10. Cheung and Lai (J. Business and Economic Statistics, July 1995,
pp.277-80) discuss the effects of lag order on the critical values of the
ADF statistic.
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