ABSTRACT
We discuss the class of autoregressive models with time-varying parameters, or TVAR models. TVAR models are useful in describing nonstationary time series with quasiperiodic latent components. Such time series arise in several applications that involve, for example, biomedical and speech signal processing as well as financial time series. We summarize the results presented in West, Prado, and Krystal (1999) and Prado (1998) which extend the time series decompositions of West (1997c) to nonstationary cases. These decompositions allow us to partition a given time series into a collection of processes that are often scientifically meaningful in applied scenarios. We also show how the dynamic linear model (DLM) theory summarized in Chapter 4 can be used within this particular model class to achieve parameter estimation, forecasting, smoothing, and inference of latent structure in nonstationary time series.
