An integrated approach for decomposing time series data into trend, cycle and seasonal components

This study presents a methodology for decomposing time series data into trend, seasonal, and cyclical components using the moving linear model approach by Kyo and Kitagawa (Journal of Business Cycle Research, 19(3): 373-397, 2023). Our approach integrates seasonal adjustment and decomposition into a single framework. We evaluated our approach with two case studies: examining daily COVID-19 case data and the Index of Industrial Production (IIP) in Japan, comparing the results to seasonally adjusted IIP data. Performance metrics included the discrimination power index and the variance of the adjusted cyclical component. Our findings show that our method effectively extracts business cycle information, achieving higher discrimination power and greater adjusted variance compared to seasonally adjusted IIP data, highlighting the superior performance of our integrated seasonal adjustment method. We compared the proposed approach with a state-space modelling method by introducing an overall stability as a new indicator. The results demonstrated the stability of the estimations obtained with our proposed method.