ORDER DETERMINATION OF MULTIVARIATE AUTOREGRESSIVE TIME SERIES WITH UNIT ROOTS

Abstract. This paper deals with order determination of multivariate time series where roots of the characteristic equation are allowed to be equal to one. For estimation of parameters in such processes, least squares were used. For a familiar class of order determination criteria it is shown that results on weak consistency valid in the stationary case can be generalized to processes with unit roots in the characteristic equation. Then a discussion of the possibility of underestimating the order for finite samples is given for a particular model, and it is indicated that nonstationarity of this type decreases the probability of underestimating the order. Finally some Monte Carlo simulation results are given to supplement the theoretical results.