Dynamic seasonality in time series

This study introduces a new class of time series models capturing dynamic seasonality. Unlike traditional seasonal models that mainly focus on the mean process, our approach accommodates dynamic seasonality in the mean and variance processes. This feature allows us to statistically infer dynamic seasonality in heteroskedastic time series models. Quasi-maximum likelihood estimation and a model selection procedure are adopted. A simulation study is carried out to evaluate the efficiency of the estimation method. In the empirical examples, our model outperforms a deterministic seasonality model and Holt–Winters method in forecasting monthly Nino Region 3 Sea Surface Temperature Index and intraday stock return variations in an out-of-sample analysis.