A Multi-Companion Method to Periodically Integrated Autoregressive Models

TL;DR

This paper introduces a multi-companion eigen-based method for estimating and forecasting periodically integrated autoregressive models with unit roots, improving robustness and efficiency in analyzing periodic time series.

Contribution

It presents a novel eigen-information approach for PIAR model estimation, enabling handling of multiple unit roots more effectively than traditional methods.

Findings

The method accurately estimates PIAR models with multiple unit roots.

It demonstrates robustness through Monte Carlo simulations.

Application results show improved forecasting performance.

Abstract

There has been an enormous interest in analysing and modelling periodic time series. The research on periodically integrated autoregressive (PIAR) models which capture the periodic structure and the presence of unit roots is widely applied in environmental, financial and energy areas. In this paper, we propose a multi-companion method which uses the eigen information of the multi-companion matrix in the multi-companion representation of PIAR models. The method enables the estimation and forecasting of PIAR models with a single, two and multiple unit roots. We show that the parameters of PIAR models can be represented in terms of the eigen information of the multi-companion matrix. Consequently, the estimation can be conducted using the eigen information, rather than directly estimating the parameters of PIAR models. A Monte Carlo experiment and an application are provided to illustrate the robustness and effectiveness of the multi-companion method.