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

• Published in: Management science Vol. 39; no. 3; pp. 275 - 293
• Main Authors: Duncan, George, Gorr, Wilpen, Szczypula, Janusz
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.03.1993; Institute of Management Sciences; Institute for Operations Research and the Management Sciences
• Series: Management Science
• Subjects: 1972-1986; Analytical forecasting; Applied sciences; Bayesian analysis; Bayesian forecasting; Data smoothing; Economic theory; Exact sciences and technology; Forecasting; Forecasting models; Forecasting techniques; Forecasts; Kalman filtering; Kalman filters; Kommunale Einnahmen; Local government; Multivariate analysis; multivariate time series methods; Operational research and scientific management; Operational research. Management science; Pennsylvania; Planning. Forecasting; Prognoseverfahren; School districts; seemingly unrelated time series; Statistical forecasts; Statistical variance; Studies; Theorie; Time series; Time series forecasting; Time series models; Zeitreihenanalyse; United States > US; Pennsylvania; Case study; Government; Time series; Bayes forecasting; Kalman filtering; Tax; Multivariate analysis; Algorithm
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.39.3.275

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.