Positive Time Series Regression Models

TL;DR

This paper introduces a new class of dynamic ARMA-type regression models for positive-valued time series, including methods for estimation, hypothesis testing, diagnostics, and forecasting.

Contribution

It proposes a novel modeling framework for positive time series with dynamic mean structures, extending traditional ARMA models with link functions and time-varying regressors.

Findings

Developed partial maximum likelihood estimation methods.

Provided hypothesis testing and diagnostic tools.

Demonstrated forecasting capabilities for positive time series.

Abstract

In this paper we discuss dynamic ARMA-type regression models for time series taking values in $(0,\infty)$. In the proposed model, the conditional mean is modeled by a dynamic structure containing autoregressive and moving average terms, time-varying regressors, unknown parameters and link functions. We introduce the new class of models and discuss partial maximum likelihood estimation, hypothesis testing inference, diagnostic analysis and forecasting.