The Information Criterion GIC of Trend and Seasonal Adjustment Models

TL;DR

This paper introduces an algorithm to compute the GIC and TIC for nonstationary state-space models, extending Kalman filtering techniques to improve model selection in trend and seasonal adjustment contexts.

Contribution

It develops a differential filter-based method to efficiently calculate GIC and TIC for complex nonstationary models, enhancing model evaluation tools.

Findings

Algorithm successfully computes GIC and TIC for various nonstationary models

Demonstrates application on trend and seasonal adjustment models

Provides structural matrix specifications for different time series models

Abstract

This paper presents an algorithm for computing the GIC and the TIC of the nonstationary state-space models. The gradient and Hessian of the log-likelihood neccesary in computing the GIC are obtained by the differential filter that is derived by extending the Kalman filter. Three examples of the nonstationary time series models, i.e., the trend model, statndard seasonal adjustment model and the seasonal adjustment model with stationary AR component are presented to exemplified the specification of structural matrices.