A new class of models for data showing trend and multiplicative seasonality is presented. The models allow the forecast error variance to depend on the trend and/ or the seasonality. It can be shown that each of these models has the same updating equations and forecast functions as the...

A new simple formula is found to correct the underestimation of the standard deviation for total lead time demand when using simple exponential smoothing. This new formula allows one to see readily the significant size of the underestimation of the traditional formula and can easily be...

The problem of constructing prediction intervals for linear time series (ARIMA) models is examined. The aim is to find prediction intervals which incorporate an allowance for sampling error associated with parameter estimates. The effect of constraints on parameters arising from stationary and...

The main objective of this paper is to provide analytical expression for forecast variances that can be used in prediction intervals for the exponential smoothing methods. These expressions are based on state space models with a single source of error that underlie the exponential smoothing...

We provide a new approach to automatic business forecasting based on an extended range of exponential smoothing methods. Each method in our taxonomy of exponential smoothing methods can be shown to be equivalent to the forecasts obtained from a state space model. This allows (1) the easy...