On Locally Dyadic Stationary Processes

We introduce the concept of local dyadic stationarity, to account for nonstationary time series, within the framework of Walsh-Fourier analysis. We define and study time-varying, dyadic, autoregressive, moving average (tvDARMA) models. It is proven that the general tvDARMA process can be approximated locally by either a time-varying dyadic moving average and a time-varying dyadic autoregressive processes.