Dynamic linear regression models for forecasting time series with semi long memory errors

TL;DR

This paper introduces a new dynamic linear regression model that accounts for long-range dependence in errors, improving forecasting accuracy for time series with semi-long memory, and offers a fast Bayesian inference method.

Contribution

The paper proposes a novel error process for dynamic linear regression models that captures semi-long memory, enhancing parameter estimation and forecasting performance.

Findings

The new model outperforms traditional ARIMA-based models in forecasting accuracy.

The proposed Bayesian inference method is faster and nearly as accurate as traditional approaches.

Application to energy data demonstrates improved forecasts over existing methods.

Abstract

Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to follow a stationary autoregressive integrated moving average (ARIMA) model, or its seasonal variants, which are unable to capture a long-range dependence structure (long memory) of the error process. We propose a novel dynamic linear regression model that incorporates the long-range dependence feature of the errors and show that the proposed error process may: (i) have a significant impact on the posterior uncertainty of the estimated regression parameters and (ii) improve the model's forecasting ability. We develop a Markov chain Monte Carlo method to fit general dynamic linear regression models based on a frequency domain approach that enables fast, asymptotically exact Bayesian inference for large datasets. We demonstrate that our approximate algorithm is faster than the traditional time domain approaches, such as the Kalman filter and the multivariate Gaussian likelihood, while producing a highly accurate approximation to the posterior. The method is illustrated in simulated examples and two energy forecasting applications, showing that it outperforms approaches that do not account for semi-long memory, as well as a state-of-the-art neural-network-based forecasting procedure.