Testing for Cointegration with Nonstationary Volatility

The paper generalises recent unit root tests for nonstationary volatility to a multivariate context. Persistent changes in the innovation variance matrix lead to size distortions in conventional cointegration tests, and possibilities of increased power by taking the time-varying volatilities and correlations into account. The testing procedures are based on a likelihood analysis of the vector autoregressive model with a conditional covariance matrix that may be estimated nonparametrically. We find that under suitable conditions, adaptation with respect to the volatility matrix process is possible, in the sense that nonparametric volatility estimation does not lead to a loss of asymptotic local power

Limiting distributions for explosive PAR(1) time series with strongly mixing innovation

This work deals with the limiting distribution of the least squares estimators of the coefficients a r of an explosive periodic autoregressive of order 1 (PAR(1)) time series X r = a r X r--1 +u r when the innovation {u k } is strongly mixing. More precisely {a r } is a periodic sequence of real numbers with period P \textgreater{} 0 and such that P r=1 |a r | \textgreater{} 1. The time series {u r } is periodically distributed with the same period P and satisfies the strong mixing property, so the random variables u r can be correlated