A Time-varying Parameter Based Seasonally-adjusted Bayesian State-space Model for Forecasting

TL;DR

This paper introduces a Bayesian state-space model with time-varying parameters that effectively captures trend and seasonal components in non-stationary time series, enabling accurate forecasting without extensive data preprocessing.

Contribution

The model directly fits non-stationary data with seasonal adjustments, avoids matrix inversion, and simplifies computation using Gibbs sampling, handling missing data efficiently.

Findings

Accurately forecasts 25th-year temperature data across Indian meteorological stations.

Handles missing data effectively in long-term time series.

Reduces computational complexity with one-dimensional parameter updates.

Abstract

In this paper, we develop a time-varying parameter based seasonally-adjusted Bayesian state-space model for non-stationary time series datasets where both the trend and seasonal components are present and it is the general scenario for most of the real datasets in various scientific disciplines. In spite of removing such terms using some do-and-check procedure to make the data stationary, our model directly fits a dataset and forecasts a number of future observations. For a specific prior construction we have considered, every parameter update is one-dimensional so that we don't need to invert any matrix and also we overcome the difficulty of Metropolis-Hastings steps simply by Gibbs sampling which is another advantage of this model. It can handle missing data as well which occurs very often in time series contexts. We implement it on the sufficiently large (24 years of monthly average temperature series, i.e. the number of observations =288) for 57 meteorological stations across India and show that for most of the cases, our method forecasts quite accurately for the months of the 25-th year.