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LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power
Author(s) -
Ng Serena,
Perron Pierre
Publication year - 2001
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00256
Subject(s) - unit root , mathematics , autoregressive model , statistics , sample size determination , cube root , lag , unit root test , information criteria , monte carlo method , truncation (statistics) , econometrics , model selection , cointegration , computer science , computer network , geometry
It is widely known that when there are errors with a moving‐average root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag ( k ) that is very small. We consider a class of Modified Information Criteria ( MIC ) with a penalty factor that is sample dependent. It takes into account the fact that the bias in the sum of the autoregressive coefficients is highly dependent on k and adapts to the type of deterministic components present. We use a local asymptotic framework in which the moving‐average root is local to −1 to document how the MIC performs better in selecting appropriate values of k . In Monte‐Carlo experiments, the MIC is found to yield huge size improvements to the DF GLS and the feasible point optimal P T test developed in Elliott, Rothenberg, and Stock (1996). We also extend the M tests developed in Perron and Ng (1996) to allow for GLS detrending of the data. The MIC along with GLS detrended data yield a set of tests with desirable size and power properties.