Constructing an Informative Prior Distribution of Noises in Seasonal Adjustment

Abstract

Time series data is very common in our daily life. Since they are related to time, most of them show a periodicity. The existence of this periodic in uence leads to our research problem, seasonal adjustment. Seasonal adjustment is generally applied around us, especially in areas of economy and nance. Over the last few decades, scholars around the world made a lot of contributions in this area, and one of the latest methods is X-13ARIMA-SEATS, which is built on ARIMA models and linear lters. On the other hand, state space modelling (abbreviated to SSM) is also a popular method to solve this problem and researchers including J. Durbin, S.J. Koopman and and A. Harvery have contributed a lot of work to it. Unlike linear lters and ARIMA models, the study on SSM starts relatively late, thus it has not been studied and developed widely for the seasonal adjustment problem. And SSMs have a lot advantages over those ARIMA-based and lter-based methods such as exibility, the understandable structure and the potential to do partial pooling, but in practice, its default decomposition result behaves bad in some cases, such as excessively spiky trend series; on the contrary, X-13ARIMA-SEATS could output good decomposition result for us to analyze, but it can't be tweaked or combined as easily as generative models and behaves like a black-box. In this paper, we shall use Bayesian inference to combine both methods' characteristics together. Simultaneously, to show the advantage of using SSMs concretely, we shall give a simple application in partial pooling and talk about how to apply the Bayesian analysis to partial pooling.