ASYMPTOTICS FOR COINTEGRATED PROCESSES WITH INFREQUENT STOCHASTIC LEVEL SHIFTS AND OUTLIERS

This is an analytical study of the effect of level-shift and temporary-change components, when present but neglected, on the trace test for cointegration+ The contribution is threefold+ First, we discuss in a multivariate framework, and jointly, effects that in the previous literature have been discussed in a univariate setting and in isolation+ Second, we consider a rather general specification of shifts and outliers with random size, number, and timing and with flexible dynamics+ It nests the classical cases of additive shifts, innovational outliers, and additive outliers+ Third, as an instrument for this analysis we develop an asymptotic theory for product moment matrices of linear processes with stochastic level-shift components, generalizing results of Leipus and Viano ~2003, Statistics and Probability Letters 61, 177–190!+