Bayesian Forecasting for Seemingly Unrelated Time Series: Application to Local Government Revenue Forecasting

Abstract

One important implementation of Bayesian forecasting is the Multi-State Kalman Filter (MSKF) method. It is particularly suited for short and irregular time series data. In certain applications, time series data are available on numerous parallel observational units which, while not having cause-and-effect relationships between them, are subject to the same external forces (e.g., business cycles). Treating them separately may lose useful information for forecasting. For such situations, involving seemingly unrelated time series, this article develops a Bayesian forecasting method called C-MSKF that combines the MSKF method with the Conditionally Independent Hierarchical method. A case study on forecasting income tax revenue for each of forty school districts in Allegheny County, Pennsylvania, based on fifteen years of data, is used to illustrate the application of C-MSKF in comparison with univariate MSKF. Results show that C-MSKF is more accurate than MSKF. The relative accuracy of C-MSKF increases with decreasing length of historical time series data, increasing forecasting horizon, and sensitivity of school districts to the economic cycle.