Forecasting the Product of Two Time Series with a Linear Asymmetric Error Cost Function

Our objective is to present a methodology which minimizes the expected cost of predictive errors when: (a) predictions are obtained for the product of two separately attained but contemporaneous time series, and (b) a linear asymmetric error cost function reflects the costs associated with predictive errors. Integrated Autoregressive-Moving Average models characterize the two series. Each prediction is expressed as a quantile of the conditional distribution of the contemporaneous product of the two series (i.e., a quantile of the distribution of the product of two Gaussian random variables with nonzero means). An actually observed hospital food service demand problem exemplifies the procedure and utility of our methodology.