On Locally Dyadic Stationary Processes

TL;DR

This paper introduces local dyadic stationarity for non-stationary time series using Walsh-Fourier analysis, defining and analyzing time-varying dyadic ARMA models and their approximations.

Contribution

It presents the novel concept of local dyadic stationarity and develops the framework for time-varying dyadic ARMA models within Walsh-Fourier analysis.

Findings

tvDARMA processes can be locally approximated by tvDMA and tvDAR processes

The framework extends analysis of non-stationary time series using dyadic methods

Provides theoretical foundation for modeling non-stationary processes with Walsh-Fourier tools

Abstract

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