Fitting State-space Model for Long-term Prediction of the Log-likelihood of Nonstationary Time Series Models

TL;DR

This paper proposes a modified log-likelihood approach for fitting state-space models to improve long-term prediction accuracy of nonstationary time series, demonstrated on trend and seasonal models.

Contribution

It introduces a new method for parameter estimation tailored to long-term prediction in nonstationary time series models.

Findings

Modified log-likelihood improves long-term prediction accuracy

Effective for trend and seasonal models with or without AR components

Provides a new evaluation metric for long-term prediction in state-space models

Abstract

The goodness of the long-term prediction in the state-space model was evaluated using the squared long-term prediction error. In order to estimate the model parameters suitable for long-term prediction, we devised a modified log-likelihood corresponding to the long-term prediction error variance. Trend models and seasonally adjusted models with and without AR component are examined as examples.