Decomposition of Multiple Seasonal Components in a Seasonal Adjustment Model

• Activity Number: 361 - Contributed Poster Presentations: Section on Nonparametric Statistics
• Type: Contributed
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Hiromichi Nagao* and Tomoya Haba and Shin-ichi Ito
• Companies: The University of Tokyo and The University of Tokyo and The University of Tokyo
• Keywords: seasonal adjustment; Kalman filter; time series; decomposition; state space model; data assimilation

Abstract

A conventional seasonal adjustment model (Kitagawa and Gersch, 1984) decomposes a given time series y_t into multiple components; y_t = u_t + s_t + w_t, where u_t is trend, s_t is seasonal, and w_t is observation noise components. The Kalman filter conducts such a decomposition based on an appropriate system model defined for each component. A unique decomposition is possible when the system model of s_t is given as (1 + B + ... + B^{p-1}) s_t = v_t, where B is a backward shift operator, p is the period of s_t, and v_t is a system noise that follows a normal distribution. However, when an observation model contains multiple seasonal components with different periods; y_t = u_t + s1_t + s2_t + w_t, the conventional method often fails to uniquely decompose, u_t, s1_t and s2_t. In this study, we propose a new method to extract such multiple seasonal components. In the case of two seasonal components, our method considers three cases in accordance with the relation between the periods of s1_t and s2_t, and gives a system model that achieves the unique decomposition for each of three cases. Numerical experiments and applications to real data show the validity of the proposed method.