Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles

This paper introduces five new univariate exponentially weighted methods for forecasting intraday time series that contain both intraweek and intraday seasonal cycles. Applications of relevance include forecasting volumes of call centre arrivals, transportation, e-mail traffic and electricity loads. The first method that we develop extends an exponential smoothing formulation that has been used for daily sales data, and which involves smoothing the total weekly volume and its split across the periods of the week. Two new methods are proposed that use discount weighted regression (DWR). The first uses DWR to estimate the time-varying parameters of a model with trigonometric terms. The second introduces DWR splines. We also consider a time-varying spline that uses exponential smoothing. The final new method presented here involves the use of singular value decomposition followed by exponential smoothing. Empirical results are provided using a series of intraday call centre arrivals.