LAG LENGTH SELECTION AND THE CONSTRUCTION OF UNIT ROOT TESTS WITH GOOD SIZE AND POWER
Serena Ng  Pierre Perron y This Draft: February 1998

It is widely known that when there are negative moving average errors, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and BIC tend to select a truncation lag that is very small. Furthermore, size distortions increase with the number of deterministic terms in the regression. We trace these problems to the fact that information criteria omit important biases induced by a low order augmented autoregression. We consider a class of Modi ed Information Criteria MIC, de ned as mink ln^ 2 + CT  T k + k=T, where T k accounts for the fact that the bias in k the sum of the autoregressive coe cients is highly dependent on k. Using a local asymptotic framework in which the root of an MA1 process is local to -1, we show that the MIC allows for added dependence between k and the number of deterministic terms in the regression. Most importantly, the k selected by the recommended MAIC with CT = 2 is such that both its level and rate of increase with the sample size are desirable for unit root tests in the local asymptotic framework, whereas the AIC, MBIC and especially the BIC with CT = lnT are less attractive in at least one dimension. In monte-carlo experiments, the MAIC is found to yield huge size improvements to the DF GLS and the feasible point optimal PT 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 M GLS tests are shown to have power functions that lie very close to the power envelope. In addition, we recommend using GLS detrended data to estimate the required autoregressive spectral density at frequency zero. This