Modeling time series with complex seasonal patterns using exponential smoothing

New innovations state space modeling tools, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, are introduced for modeling complex seasonal time series. Such complex seasonal time series include those with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. It is demonstrated that the new modeling practices provide alternatives to existing exponential smoothing approaches, but are shown to have several key advantages. The new approaches are complete with well-defined methods for initialization and estimation, including likelihood evaluation and the derivation of analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors, leading to simple, comprehensible approaches to modeling complex seasonal time series. The new approaches are capable of forecasting and decomposing non-seasonal, single seasonal and complex seasonal time series, and are useful in a broad range of applications. Their versatility is illustrated in various empirical studies, and it is also shown that the new approaches lead to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself. In addition, the new procedures are demonstrated as automated algorithms, and are shown to provide competitive forecast accuracy compared to the existing methods with several options. Relevant R software programs have been developed, and the implementation is presented using real life time series.