The paper suggests a~generalization of~widely used Holt--Winters smoothing and forecasting method for~seasonal time series. The~general concept of~seasonality modeling is introduced both for~the~additive and multiplicative case. Several special cases are discussed, including a~linear interpolation of~seasonal indices and a~usage of~trigonometric functions. Both methods are fully applicable for~time series with irregularly observed data (just the~special case of~missing observations was covered up to~now). Moreover, they sometimes outperform the~classical Holt--Winters method even for~regular time series. A~simulation study and real data examples compare the~suggested methods with the~classical one.
exponential smoothing, Holt-Winters method, irregular time series, seasonal indices, trigonometric functions
62M10, 62M20, 60G35, 65D10