Abstract :
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!+
