Comparing Time-Varying autoregressive Structures of Locally Stationary Processes

In this paper a novel statistical test is introduced to compare two locally stationary time series. The proposed approach is a Wald test considering time-varying autoregressive modelling and function projections in adequate spaces. The covariance structure of the innovations may be also time-varying. In order to obtain function estimators for the time-varying autoregressive parameters, we consider function expansions in splines and wavelet bases. Simulation studies provide evidence that the proposed test has a good performance. We also assess its usefullness when applied to a financial time series.