Non-Gaussian Autoregressive Processes with Tukey g-and-h Transformations

TL;DR

This paper introduces two non-Gaussian autoregressive models based on the Tukey g-and-h transformation, capable of modeling skewed and heavy-tailed time series data, with applications to wind speed data.

Contribution

The paper proposes novel non-Gaussian autoregressive models using Tukey g-and-h transformations, including estimation, order selection, and forecasting methods.

Findings

Models effectively fit skewed and heavy-tailed data.

Simulation studies demonstrate good performance.

Applied to wind speed data with successful results.

Abstract

When performing a time series analysis of continuous data, for example from climate or environmental problems, the assumption that the process is Gaussian is often violated. Therefore, we introduce two non-Gaussian autoregressive time series models that are able to fit skewed and heavy-tailed time series data. Our two models are based on the Tukey g-and-h transformation. We discuss parameter estimation, order selection, and forecasting procedures for our models and examine their performances in a simulation study. We demonstrate the usefulness of our models by applying them to two sets of wind speed data.