Applications of quasi-periodic oscillation models to seasonal small count time series

Abstract

Quasi-periodic oscillation models for analysis of small count time series are considered within a framework of a generalized state space model (GSSM). In particular, we focus on the analysis of seasonal count data. The Monte Carlo filter (MCF) is fully employed in this study to handle a generalized state space model with higher state dimensions. To illustrate, we study three seasonal count data sets: polio incidence time series, the monthly number of drivers killed in road accidents, and the monthly number of the sun's spotless days. In addition, we demonstrate an application of the model proposed to the yearly occurrence of intense hurricanes with a quasi-periodic component associated with solar cycle activity.