Forecasting economic time series that require a power transformation: Case of state tax receipts

Abstract

In this study, time series analysis is applied to the problem of foreca\tin: state income tax receipts. The data series is of special interest since it exhibits a strong trend with a high multiplicative seasonal component. An appropriate model is identified by simultaneous estimation of the parameters of the power transformation and the ARMA model using the Schwarz (1978) Bayesian information criterion. The forecastins performance of the time series model obtained from this procedure i\ compared with alternative time series and regression models. The study illustrates how an information criterion can be employed for identifying time series models that require a power transformation, as exemplified by state tax receipts. It also establishes time series analysis as a viable technique for forecasting state tax receipts. KEY WORDS Seasonal models Power transformation Bayesian information criterionThe growing consequence of state income tax revenues makes their accurate forecasting important. The techniques currently used include both single equation econometric models such as those of Singer (1968), Barnard and Dent (1979), and Greytak and Thursby (1980), and simultaneous equation models such as the one developed by Auten and Robb (1976). The data may be either quarterly or annual a n d explanatory variables often include income, population, per capita income, and the tax rate. The purpose of this paper is t o demonstrate the application of another forecasting technique, time series analysis, t o the problem of forecasting state tax revenues.The data used in this study are for the state of Illinois but the techniques are readily applicable to those of other states. The data are quarterly Illinois income tax receipts for the period 1970 111 through 1982 IV measured in real dollars (see the Data Appendix). As seen in Exhibit 1, the data display a pattern very similar t o the 'Sales of Company X' investigated by Chatfield and Prothero (1973) in the sense that they show a high multiplicative seasonal component and a strong trend. The model constructed from the 1970 111 t o 1980 IV data is used

Fiscal Forecasting: Lessons from the Literature and Challenges*

“…In the same vein, Lawrence, Anandarajan and Kleinman (1998) back simple regression methods on the basis of transparency. Baguestani and McNown (1992) and Nazmi and Leuthold (1988) still ascertain time-series techniques as viable for tax receipts forecasting, while Fullerton (1989) and Litterman and Supel (1983) provide some evidence to support the combining of different forecasting techniques. Pike and Savage (1998), Sentance, Hall and O'Sullivan (1998), Cao and Robidoux (1998), Giles and Hall (1998) and Willman et al (2000) present the fiscal side of structural macroeconomic models.…”

Fiscal Forecasting: Lessons from the Literature and Challenges

“…In the same vein, Lawrence et al (1998) back simple regression methods on the basis of transparency. Baguestani and McNown (1992), and Nazmi and Leuthold (1988), still ascertain time series techniques as viable for tax receipts forecasting, while Fullerton (1989) and Litterman and Supel (1983) provide some evidence to support the combining of different forecasting techniques.…”

Bayesian Vector Auto-Regression Method as an Alternative Technique for Forecasting South African Tax Revenue

“…Various studies frequently use ARIMA models. The study conducted by Nazmi and Leuthold (1985) developed a time-series model for predicting state income tax receipts using the Hannan-Quinn criteria. The authors determined the linear and log-linear versions of the ARIMA (1,0,0) model and used a Box-Cox transformation to select a linear version of a time-series model.…”