A SIMPLE APPROACH TO THE STATISTICAL-INFERENCE IN LINEAR-TIME SERIES MODELS WHICH MAY HAVE SOME UNIT ROOTS

This paper proposes a simple method to circumvent the difficulties enc outered in the statistical inference for linear time series models whi ch may have some unit roots. Specifically, it proposes adding certain artificial regressors in the regression model in addition to the origi nal ones. The method can be applied without a priori knowledge of whet her the true process is stationary, integrated, or cointegrated. It is shown that the liner (or non-linear) restrictions of coefficient esti mates have an asymptotically chi-square distribution. Thus, by using t his method, the testing problem can be handled as a standard asymptoti c theory. The power of the test of the proposed method is rather low i n the small sample, but the simplicity of the method may be proved to be useful in situations where the conventional approach is difficult t o apply. Thus, it may be useful for analysis in financial market where a large body of data is available.