Testing for a unit root in an AR(p) signal observed with MA(q) noise and model misspecification

Scope and method of study. Time series models with unit roots are known to provide good stochastic approximations for many nonstationary time series. Often the model parameters are restricted by a number of constraints. A simple and easy-to-compute Newton-Raphson estimator (Shin and Sarkar, 1995) approximates the restricted ML estimator and takes full advantage of the information contained in the restrictions. We study the problem of testing for a unit root in an AR(p) signal observed with MA(q) noise by using three different estimation methods (Hannan-Rissanen, Kohn and Shin-Sarkar). The objective is to check which of the three different unit root tests performs well with respect to both size and powers through a Monte Carlo study and thus apply these results to the practical fields such as the engineering science and economics. Model misspecification is a common problem in statistical data analysis. In the misspecified models, inference using the usual statistics such as t, DW and R{dollar}{bsol}sp2{dollar} can be very often misleading. A General regression model with integrated errors and one system of integrated regressors is introduced and the limiting distributions of the LS estimators and the usual LS statistics such as {dollar}{bsol}{bsol}sigma{bsol}sp2,{dollar} t, DW and R{dollar}{bsol}sp2{dollar} are discussed.; Findings and conclusions. In terms of normalized unit root test statistic, the Shin and Sarkar method can be a good alternative to the Kohn's method when we test for a unit root in an AR(1) signal observed with MA(1) noise. On the other hand, the Kohn's method is preferable while using the unit root t-test statistic. It is observed from the simulation results that DW and R{dollar}{bsol}sp2{dollar} can be in general used as diagnostic tools to detect spurious regression, misspecification of nonstationary AR and polynomial regression models. (Abstract shortened by UMI.)...