A univariate time varying analysis of periodic ARMA processes

TL;DR

This paper introduces a novel univariate approach to analyze periodic ARMA processes with time-varying coefficients, simplifying analysis and forecasting by avoiding vector formulations and enabling explicit predictor expressions.

Contribution

It presents an alternative to vector-based methods by treating periodic ARMA as a time-varying univariate process, facilitating easier analysis and forecasting.

Findings

Provides explicit formulas for optimal predictors.

Generalizes periodic models to match stationary case analysis.

Simplifies computational procedures for periodic ARMA.

Abstract

The standard approach for studying the periodic ARMA model with coefficients that vary over the seasons is to express it in a vector form. In this paper we introduce an alternative method which views the periodic formulation as a time varying univariate process and obviates the need for vector analysis. The specification, interpretation, and solution of a periodic ARMA process enable us to formulate a forecasting method which avoids recursion and allows us to obtain analytic expressions of the optimal predictors. Our results on periodic models are general, analogous to those for stationary specifications, and place the former on the same computational basis as the latter.