A new approach is proposed for forecasting a time series with multiple seasonal patterns. A state space model is developed for the series using the innovations approach which enables us to develop explicit models for both additive and multiplicative seasonality. Parameter estimates may be...

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension has required the consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility...

Three general classes of state space models are presented, using the single source of error formulation. The first class is the standard linear model with homoscedastic errors, the second retains the linear structure but incorporates a dynamic form of heteroscedasticity, and the third allows for...

Outliers in time series have the potential to affect parameter estimates and forecasts when using exponential smoothing. The aim of this study is to show the way in which important types of outliers can be incorporated into linear innovations state space models for exponential smoothing methods....

A method is proposed for forecasting composite time series such as the market shares for multiple brands. Its novel feature is that it relies on multi-series adaptations of exponential smoothing combined with the log-ratio transformation for the conversion of proportions onto the real line. It...