Nonparametric frequency domain analysis of nonstationary multivariate time series

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.Publicad

Gaussian semi-parametric estimation of fractional cointegration

We analyse consistent estimation of the memory parameters of a nonstationary fractionally cointegrated vector time series. Assuming that the cointegrating relationship has substantially less memory than the observed series, we show that a multi-variate Gaussian semi-parametric estimate, based on initial consistent estimates and possibly tapered observations, is asymptotically normal. The estimates of the memory parameters can rely either on original (for stationary errors) or on differenced residuals (for nonstationary errors) assuming only a convergence rate for a preliminary slope estimate. If this rate is fast enough, semi-parametric memory estimates are not affected by the use of residuals and retain the same asymptotic distribution as if the true cointegrating relationship were known. Only local conditions on the spectral densities around zero frequency for linear processes are assumed. We concentrate on a bivariate system but discuss multi-variate generalizations and show the performance of the estimates with simulated and real data.Publicad

A summary of methods for analyzing nonstation- ary data

Estimation of nonstationary mean values, spectral density, and correlation functions - summary of methods for analyzing nonstationary dat