Nonparametric frequency domain analysis of nonstationary multivariate time series

Abstract

We analyse the properties of nonparametric spectral estimates when applied to long memory and trending nonstationary multiple time series. We show that they estimate consistently a generalized or pseudo-spectral density matrix at frequencies both close and away from the origin and we obtain the asymptotic distribution of the estimates. Using adequate data tapers this technique is consistent for observations with any degree of nonstationarity, including polynomial trends. We propose an estimate of the degree of fractional cointegration for possibly nonstationary series based on coherence estimates around zero frequency and analyse its finite sample properties in comparison with residual-based inference. We apply this new semiparametric estimate to an example vector time series.