Estimation and Forecast Performance of a Multivariate Time Series Model of Sales

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Abstract
A unique form of a multivariate time series model—a “seemingly unrelated autoregressive moving average” model (SURARMA)—is developed in the context of forecasting unit sales of a product in four states. Data from an anonymous firm are used to test the appropriateness of the model and are found to conform to the model's constraints. The model provides substantial improvement in parameter estimation efficiency and forecast performance in comparison with individual state univariate models. SURARMA is potentially relevant to many market forecasting problems involving multiple constituent time series subunits such as states, regions, or products from a product line.