1 PUBLIC BUDGETING & FIN. MNGMT., 6(4), JUDGMENTAL VS. TIME SERIES VS. DETERMINISTIC MODELS IN LOCAL REVENUE FORECASTING: A FLORIDA CASE STUDY Howard A. Frank and XiaoHu Wang School of Public Policy and Management Florida International University North Miami Campus North Miami, Florida ABSTRACT This article presents a study of revenue forecasting in a Florida municipal government. Seven techniques, including the budget officers' judgmental approach, time series models, a deterministic model, and an optimized model, are employed with franchise and utility receipts in the Town of Davie. The authors found that simple time series models outperformed deterministic models and the judgmentally derived forecasts of local officials. Consistent with prior research, findings here suggest that the time series models are not only accurate, but also easy to implement and readily comprehensible by local officials. Copyright by PrAcademics Press
2 LOCAL REVENUE FORECASTING 495 INTRODUCTION After decades of inattention, recent years have seen a surge of academic interest in local government revenue forecasting. (1) Research efforts have been made on the selection of forecasting techniques, identification of forecasting difficulties, and the implementation of forecasting models in the municipal setting. (2) Ongoing fiscal stress, dwindling reserves, and burgeoning service demands have created a climate that requires enhanced forecasting capacity and accuracy. (3) Local governments' changing revenue portfolios have also served as an impetus to augmented forecast capacity. The politically unpopular property tax is being increasingly supplanted with sales and franchise taxes, user fees, and other charges for service. (4) These sources have far greater sensitivity to changes in the economy and season than the relatively stable ad valorem tax. Ad valorem revenues are often forecast as a simple accounting identity of taxable base times the millage rate minus a historically determined uncollectible component, (5) with a high degree of accuracy--plus or minus three percent in many jurisdictions. (6) The story is quite different for non ad valorem revenues, where economic and seasonal factors confound accounting or judgmental-based approaches. Forecast error for these sources is often at or near double-digits, (7) with serious consequences for establishing the annual budget constraint. This article explores how relatively simple time series models, used extensively in business and military planning for decades, (8) can be integrated into the annual local budgeting process. The authors' focus is on two sources--franchise fees and utility taxes--which are problematic for local forecasters. (9) The authors compare the performance of time series models against two benchmarks--a community's judgmental forecasting approach and a simple deterministic model. While these comparisons are frequently undertaken in the private sector and state and federal government, (10) they are rare in the local government sector. (11) Here the authors discuss the testing and implementation of these methods in Davie, Florida and assess their applicability in other settings.
3 496 FRANK & WANG THE FORECASTING SETTING The Town of Davie, Florida was incorporated in 1925, one of the first communities founded in Broward County (Greater Ft. Lauderdale). Davie has a current population of 50,259, and has experienced rapid albeit slowing growth over the past decade. General fund revenue growth has been significant: Fiscal Year 1983 revenues were $6.7 million, and have grown to $24.7 million in Revenue growth has slowed, however, in recent years--the 20 percent annual growth realized in the early 1980's has dwindled to average growth of under five percent annually. During this time, state revenue sharing and pass through funding from the fifth of the six cent state sales tax has grown but become increasingly unstable, reflecting recessions and the fact that Florida exempts food and other necessities from retail taxation. Moreover, the town's fiscally conservative leadership has been unwilling to raise ad valorem taxation significantly and has kept millage well below the Florida Constitution's 10 mill cap--unlike the Broward County Board of County Commissioners or the County School Board, which are rapidly approaching that limit. In essence, Davie's population growth and concomitant service demands are outstripping its general fund revenue growth. The town's leadership is learning--rather belatedly--that residential growth carries with it a steep incremental price tag. (12) This has resulted in 12 layoffs and 58 position eliminations in the past four years. The service demand increase and revenue growth decrease have given impetus to the need for enhanced forecast accuracy, particularly in the franchise and utility taxes which have ranged between 29.1 percent and 34.6 percent of general revenue over the past 10 years. The composition of these franchise and utility taxes is shown in Table 2. Consistent with the aforementioned national experience, (13) local officials have found these revenue components difficult to predict in absolute and relative terms, particularly when compared with local property taxation. It is this forecasting problem that the authors now address.
4 LOCAL REVENUE FORECASTING 497 TABLE 1 The Population and Revenue Growth in Davie (In Percentage) Year Population growth General revenue growth TABLE 2 Composition of Franchise and Utility Taxes in 1992 (In Percentage) Franchise Taxes Utility Taxes FPL 67 FPL 75 Southern sanitation 25 Telephone & Telegram 23 Southern bell 2 Gas 2 Cable 5 Towing 1 THE FORECASTING PROBLEM Table 3 shows budgeted versus actual receipts for Davie's franchise and utility taxes over the past ten fiscal years. Mean Absolute Percentage Error (MAPE) for the franchise taxes--the average of the forecast errors in absolute
5 498 FRANK & WANG terms--has been 13.2 from Fiscal Year 1982 to Fiscal Year 1992, and 7.6 percent over the last three fiscal years considered. MAPE for the utility taxes for the 10 year period was 9.1 and 5.2 for the FY period. By way of comparison, during the past decade ad valorem has experienced a MAPE of 5.1 and a FY MAPE of 1.2. From the Finance Director's vantage, plus or minus 5.0 percent is an acceptable forecast error. This makes the city's forecast performance in the franchise and utility taxation significantly below par by its own benchmark, and substantially above the 4.8 and 4.0 Mean Acceptable Errors for these respective sources as detailed in a recent nationwide survey of local forecast officials. (14) In theory, local officials forecast their annual franchise and utility taxes by regressing five years (60 months) of monthly data against time (described in detail below) to arrive at a one-month ahead forecast. This one month forecast was subsequently multiplied by 12 to arrive at a base annual forecast. Consistent with the usual bias towards underforecasting local revenue, (15) this base forecast is reduced by five percent to arrive at the final annual forecast. TABLE 3 The Percentage Error of Budgeted vs Actual Receipts for Franchise, Utility and Property Tax for the Past 10 Fiscal Years Year Franchise Utility Ad Valorem NA NA NA MAPE
6 LOCAL REVENUE FORECASTING 499 In practice, this algorithm is dispensed with. Generally, the Finance Director has relied on fewer than five years of data for his regression against time. His one-month ahead forecast is itself judgmental modified. This onemonth ahead forecast is then multiplied by 12 to arrive at a tentative franchise/utility forecast. This in turn is modified judgmentally, based on consultation with other finance officials. As such, the forecast is best described as a combination of judgmental and mathematical approaches, a widespread approach to many forecast problems. (16) FORECASTING METHODS AND PROCESS In this section, the authors detail the forecasting methods deployed in this research. The authors also establish the process by which these method were tested. Our methodological overview is brief--interested readers should consult Thomopoulous, Wheelright and Makridakis, or Frank (17) for detailed descriptions of the models discussed below. To amplify on these 'thumbnail sketches,' the authors have worked out example forecasts in Appendix A. The forecast methods tested include: regression against time, the firstorder transformation moving average, double exponential smoothing, a deterministic model, and an optimized model. In the regression model, the authors utilized Ordinary Least Squares (OLS) to fit a line with revenue data. In the first-order transformation, trend is taken into account by differencing successive terms in the series and adding an average of there differences to the prior year's receipts to arrive at the year-ahead forecast. In the double exponential model, trend and prior forecast errors are incorporated into the estimation of next year's forecast. In the deterministic model, franchise and utility receipts are estimated from the prior's year's receipts by utilizing changes in key socioeconomic variables. The optimized model's forecasts are obtained by aggregating forecasts of the individual franchise fees utilizing the most accurate technique for each. For estimation of the franchise tax receipts using regression, the moving average, and double exponential smoothing, the authors utilized annual data from Fiscal Year 1975 to Fiscal Year Data from 1975 to 1989 were used to forecast 1990 revenue. Actual receipts from FY 90 were then added to this series to derive FY 91's forecast. And lastly, FY 91's actual receipts
7 500 FRANK & WANG were added in the estimation of FY 92's receipts. This method of "holding out" of data with successive updating of actual receipts is thought to be the most robust approach for testing of forecast models (18) and allows us to see if forecasts for this study are consistent across fiscal years. For the deterministic model, detailed in Appendix A, a moving average of three fiscal years of prior actual receipts and key economic factors were used to arrive at one-year ahead forecasts. For the optimized model, the authors used monthly receipts from 1989 to 1992 in forecasting the receipts from the Florida Power and Light franchise tax, and annual data from the above-mentioned series (FY 75-FY 92) for other franchise sources. Utility taxes were estimated using annual data that were adjusted to account for several tax rate changes throughout the FY 79- FY 92 period. This adjustment process is detailed in Appendix B. Subsequent to adjustment, the same methods utilized for franchise estimation were redeployed for utilities with one exception: preliminary estimation with the optimized model was unsatisfactory, and hence dropped from further consideration. The time-series methods (time series regression, first-order transformation moving average, and double exponential smoothing) for this study were chosen because of the steep upward trend realized in the franchise and utility receipts. This a priori judgement regarding the efficacy of particular forecast models may not work in all communities. (19) But in this setting, the outstanding performance of the models tested suggested that simpler models without trend parameters (i.e., the simple moving average or single exponential smoothing) would have been deficient. FINDINGS AND DISCUSSION Findings from franchise and utility receipts are found in Table 4 and Table 5, respectively. The benchmark represents the city's forecast error in percent for the respective source and fiscal year. The percentage error represents the amount by which a given technique under- or overforecast actual receipts. So for example, in Table 4, in Fiscal Year 1990, regression underforecast actual receipts by 8.94 percent (-8.94). MAPE in this table represents the absolute percentage error averaged for the three fiscal years for which comparisons were undertaken. So for example, the MAPE for regression in Table 4 (6.19) is the average of the percentage errors from Fiscal Years 1990 through 1992, (-8.94, -5.29, -4.33). The authors chose MAPE to facilitate interperiod comparisons (i.e., a large over- or
8 LOCAL REVENUE FORECASTING 501 underforecast in one fiscal year cannot cancel out findings in two others) and it is the most frequently used and easily understood error function. Absolute percentage errors were averaged over three years to enhance the validity of the findings. Findings from Table 4 rank the double exponential model (a=0.3) first, and regression last. This suggests that while there was reasonably steep trend in this series, it could not be captured with a constant upward trend line, as modeled by regression against time. The first-order moving average also performed well. This is consistent with early comparative time series which suggests that a trend-adjusted moving average is an excellent "trial horse" for other time-series models. (20) The city's deterministic model was a mid-range performer which was more accurate than the optimized model but not as accurate as the "atheoretical" time series approaches. And lastly, all models tested delivered forecasts more accurate than those obtained by Davie officials. Results from utility receipts (Table 5) show both similarities and differences from those in franchises (Table 4). Once again, the double exponential model (a=0.3) is the "winner" in terms of accuracy. Similarly, the first-order transformation moving average is a close second. But here, regression against time outperforms both the double exponential (a=0.1) and deterministic models. These rankings suggest that the upward trend in this source was more consistent over time than that found in franchises. Overall, four of the five models tested outperformed the city's benchmark. There are some interesting commonalities to findings from both franchise and utility taxes. The first is that with the exception of the deterministic model forecast for utility taxes, the models tested in this study predict more accurately than the budgeted versus actuals realized in Davie. Finance staff in Davie felt this was largely attributable to the fact that they, like budget staff elsewhere, (21) intentionally underforecast revenue as a conservative buffer against economic downturns. It may also reflect the fact that the hybrid quantitative-qualitative method discussed earlier is becoming less accurate as Davie's socioeconomic base diversifies over time. And perhaps most
9 502 FRANK & WANG TABLE 4 The Percentage Errors and MAPE of the Franchise Receipts: Methodological Comparison Techniques MAPE Rank Regression The first-order transformation moving average Double exponential Smoothing (a=.1) Double exponential Smoothing (a=0.3) Deterministic model The optimized model N/A N/A City's bench mark importantly, the cornerstone of that hybrid approach, the regressing of receipts against time, performs quite poorly. This probably reflects a certain degree of "assumption drag" on the part of Davie budgeters, who may not care to acknowledge that revenue growth is slowing. The poor performance of time-series regression is noteworthy. Time series regression is the most commonly utilized quantitative forecasting technique in the state and local sector. (22) Yet empirical evidence from both the private and public sectors (23) indicates that it is one of the least accurate of
10 LOCAL REVENUE FORECASTING 503 TABLE 5 The Percentage Errors and MAPE of the Utility Receipts: Methodological Comparison Techniques MAPE Rank Regression The first-order transformation moving average Double exponential Smoothing (a=.1) Double exponential Smoothing (a=0.3) Deterministic model City's bench mark the time series methods. Regression results for the utility receipts may provide some insight as to why that is the case. In 1990, the percentage error was In 1992 the percentage error was This "hot" and "cold" performance is likely with a model that is fitting a line through all points being considered, with all observations receiving equal weight in the calculation. In contrast, the moving average and exponential smoothing techniques give more weight to the points closest to that being forecast and adjust to presence of non-linear trends. The time-series regression model will be accurate as long as the series being fit is linear: if it turns non-linear, serious forecast errors are inevitable. Time-series regression's performance in this study confirms earlier work, (24) which suggests that it performs less accurately than competing quantitative models. The results of the deterministic model were disappointing to the Finance Director, Mr. Chris Wallace. For franchise taxes, this model ranked third, for utility receipts, it ranked sixth--the worst performer. Mr. Wallace and city
11 504 FRANK & WANG officials believed that receipts for a coming fiscal year were largely determined by last year's receipts plus an increment affected by changes in the Consumer Price Index, growth in construction value, and population growth. The logic behind this model is that certain key socioeconomic variables are intertwined with city revenues. The fact that time series models which have no theory to drive them outperformed the deterministic model indicated that these variables may not have been as crucial as finance staff had anticipated. Conceivably, other causal variables implemented within the context of a multiple regression model may have captured key socioeconomic variables' relationship to franchise and utility receipts. However, it is unlikely that budget officials in Davie--and most other cities of under 100,000--would have the time, data, or inclination to invest in developing such models, even if they had the skill to do so in the first place. (25) Time-series models forecast by allowing the data "to speak for themselves" with no theoretical application and very straightforward implementation. Findings from Davie and elsewhere (26) suggest that for many time-pressed local officials, time series models (with the notable exception of regression against time) present a very cost-effective alternative to deterministic or causal approaches. Another key finding from the vantage of forecast implementation is the performance of the optimized forecast for franchise taxes. This "optimized" forecast was the result of the disaggregated forecasts of the component franchises, as discussed in Appendix A. The authors and Davie finance staff had hypothesized that disaggregation would enhance forecast accuracy. Consistent with earlier findings, (27) this was not the case. For franchise fees, the optimized model ranked fourth of seven. This is not a cost-effective performance given the time and labor required for its implementation. Experimentation with various revenue "bundles" may yield different results in a more representative sample of revenues and communities, but evidence in this study suggests that would-be implementers will not always benefit from disaggregation, as is often contended. (28) CONCLUSION The improvement in forecast accuracy derived from the models tested in this multi-year study suggests that time-series techniques may be of considerable utility in estimating economically and seasonally sensitive sources such as franchise and utility fees. Findings in this study are consistent with earlier work (29) which showed that time series models are more likely to
12 LOCAL REVENUE FORECASTING 505 outperform the hybrid, quantitative-qualitative approaches currently utilized by most local practitioners. Another key finding from this study is that these models are rather simple to implement. All forecasts were performed on a desktop personal computer with data that were readily available on spreadsheet. Forecast implementation was undertaken within one month of full-time work. Given the stability of time series models over time, (30) one could establish future forecasts within a few days time. This is in stark contrast to deterministic or causal approaches, which may take many months for implementation and updating. Concomitantly, officials in Davie found the models employed in this study to be both logical and comprehensible. Consideration of trend is relatively transparent to practitioners once they have seen how time series models deal with this critical component. Utilization of these models also facilitates understanding of how and why more recent data are more important to forecasts. While any introductory forecasting text will treat these points at length, local practitioners may be quite unaware of them, given their lack of forecasting training. (31) Viewed in this light, working with time series models not only enhances forecast accuracy--it also serves as a means by which local forecasters enhance their forecast repertoire, with possible applications outside of the budgetary realm. Lastly, this article provides some possible insight into an ongoing question within the emerging forecasting discipline--how does expert judgement "stack up" to quantitative approaches? (32) Findings from this study suggest that local budgeters may not have as firm a grasp on the determinants of change in their local environment as they imagine. The relatively poor showing of both the deterministic model and the hybrid approach used for current budgetary forecasts bears this out. Managers tend to grossly underestimate the complexity and fluidity of their operating environments. (33) As a class, local budgeters may be no different than their counterparts elsewhere in the public and private sectors. Further research such as that undertaken here may confirm this, and greatly benefit local forecasting practice and pedagogy. REFERENCES 1. Frank, Howard A. Budgetary Forecasting in Local Governments: New Tools and Techniques, Quorum, Westport, Connecticut, 1993.
13 506 FRANK & WANG 2. Frank, Howard A. "Municipal Revenue Forecasting with Time Series Models: A Florida Case Study." American Review of Public Administration 20 (Spring 1990): 45-59; Frank, Howard A., and Gianakis, Gerasimos A. "Raising the Bridge Using Time Series Models." Public Productivity and Management Review 14 (Winter 1990): ; Hall, Cindy. Revenue Forecasting Made Easy for Local Governments. Florida Innovation Group, Tampa, Florida, 1990; Agostini, Stephen J. "Searching for a Better Forecast: San Francisco's Revenue Forecast Model." Government Finance Review 7 (May 1992): 13-16; MacManus, Susan. "Forecasting Frustrations: Factors Limiting Accuracy." Government Finance Review 8 (June 1992): Gianakis, Gerasimos A., and Frank, Howard A. "Implementing Time Series Models: Some Considerations for Local Governments." State and Local Government Review 25 (Spring 1993): MacManus, Susan A., and Grothe, Barbara P. "Fiscal Stress as a Stimulant to Better Revenue Forecasting and Productivity." Public Productivity Review 12 (Summer 1989): Goldberg, Kalman and Scott, Robert C. "City Sales and Property Tax Restructuring: Household and Business Incidence Effects." Public Budgeting & Finance 5 (Autumn 1985): 76-88; Bahl, Roy, Sjoquist, David L., and Williams, Loren. "The Property Tax in the 1980's and Prospects for the 1990s." Public Budgeting and Financial Management 2 (1990): Lynch, Thomas D. Public Budgeting in America (3rd ed.), Prentice- Hall, Englewood Cliffs, New Jersey, McCollough, Jane and Frank, Howard A. "Incentives for Forecasting Reform Among Local Finance Officers." Public Budgeting and Financial Management 4 (1992): ; Bretschneider, Stuart, Bunch, Beverly, and Gorr, Wilpen. "Revenue Forecast Errors in Pennsylvania Local Government Budgeting: Sources and Remedies." Public Budgeting and Financial Management 4 (1992): See McCollough and Frank, note 6, supra. 8. See Frank, 1990, note 2, supra. 9. See McCollough and Frank, note 6, supra.
14 LOCAL REVENUE FORECASTING Armstrong, J. Scott. Long-Range Forecasting: From Crystal Ball to Computer (2nd ed.), Wiley, New York, New York, See Frank, note 1, supra. 12. Burchell, Robert W., and Listokin, David. "Fiscal Impact Analysis: A Practitioner's Guide," in John Matzer, (ed.). Practical Financial Management: New Techniques for Local Government. International City Management Association, Washington, pp See McCollough and Frank, note 6, supra. 14. McCollough and Frank, op cit. p See Frank,1990,note 2, supra. 16. See Armstrong, note 10, supra. 17. Thomopoulous, Nick. Applied Forecasting Methods, Prentice-Hall, Englewood Cliffs, New Jersey, 1980; Makridakis, Spyros and Wheelright, Steven. Forecasting Methods for Management (5th ed.), Wiley, 1987; See Frank, note 1, supra. 18. See Armstrong, note 10, supra. 19. See Gianakis and Frank, note 2, supra. 20. See Frank, note 1, supra. 21. See Frank, note 1, supra. 22. Bretschneider, Stuart and Gorr, Wilpen. "State and Local Government Revenue Forecasting," in Steven Wheelright and Spyros Makridakis (eds.), The Handbook of Forecasting: A Manager's Guide (2nd ed.), John Wiley, New York, New York, 1989: See Armstrong, note 10, supra; See Frank, note 1, supra. 24. See Frank, Frank and Gianakis, and Gianakis and Frank, note 2, supra. 25. See Frank, note 1, supra. 26. See Gianakis and Frank, note 2, supra. 27. Giankakis and Frank, op cit. 28. Armstrong, J. Scott. "Forecasting by Extrapolation: Conclusions from 25 Years of Research." Interfaces 14 (November-December 1984):52-66.
15 508 FRANK & WANG 29. Frank, Howard A. "Close Enough for Government Work: Thoughts on Local Government Revenue Forecasting in Florida." Paper presented at the Southeast Conference of Public Administration, Birmingham, 1988; Frank, note 1, supra. 30. See Giankakis and Frank, note 2, supra. 31. Frank, Howard A. and McCollough, Jane. "Municipal Forecasting Practice: 'Demand' and 'Supply' Side Perspectives." International Journal of Public Administration 15 (October 1992): Brown, Lawrence D. "Comparing Judgmental to Extrapolative Forecasts: It's Time to Ask Why and When." International Journal of Forecasting 4 (1988): ; Goodwin, Paul, and Wright, George. "Improving Judgmental Time Series Forecasting: A Review of the Guidance Provided by Research." International Journal of Forecasting 9 (1993): Ascher, William. Forecasting: An Appraisal for Policy-Makers and Planners, Johns Hopkins, Baltimore, Maryland, Regression Against Time APPENDIX A METHODOLOGICAL REVIEW In regression against time, the authors used Ordinary Least Squares (OLS) to fit a line which has the form: Revenue in Coming Fiscal Year = a + b(x), where a is the intercept, b is the slope and x is the year's receipts for which the authors are forecasting where a and b are chosen to minimize errors. Assume that the regression equation = $-252, ,525(x), a forecast for the 18th year in the series would be: $-252, ,525(18) = $3,015,393. First-Order Transformation Moving Average This model accounts for trend by differencing successive terms in the series. Forecast values are "smoothed" by averaging these differences. The revenue forecasted is a sum of this average smoothed value and the revenue in previous fiscal year. The process is "first order," since the values are smoothed only one time. An example of this forecasting process follows:
16 LOCAL REVENUE FORECASTING 509 Fiscal year Actual Franchise First-order differences MA (3) ($)1,933, ,020,830 ($) 86, ,372, , ,527, ,805 ($) 197, ,816, , , ,956, , ,793 The forecast for the franchise revenue in 1992 will be $3,151,238 ($2,956,445 + $194,793). Double Exponential Smoothing Model With the double exponential smoothing model, data are doublesmoothed to obtain forecast values using the following formula: Y t+1 = a t + b t T Where a t = 2 S t (1) - S t (2) b t = alpha /(1-alpha) [S t (1)-S t (2)] Y = revenue forecasted T = forecasting term S t (1) = smoothed value at time t. S t (2) = alpha S t (1) +(1-alpha) S t-1 (2) = Smoothing of the smoothed values (doublesmoothed statistics). The forecast for one year ahead is: Y t+1 = [2 + alpha/(1-alpha)] S t (1) - [1 + alpha/(1-alpha)]s t (2) As seen with these equations, mechanics of the double smoothing process are quite complex. But the mechanics of the single smoothing process are fairly straightforward. In essence, a forecast for one period ahead equals the forecast for the prior time period plus s (the smoothing coefficient) times the actual value of the prior period minus the forecast of the prior period: F t+1 = F t + s(a t - F t ). Consider the series 101, 103, and 102. Assuming a smoothing coefficient of 0.5, we could establish a forecast for the next period ahead as ( ) = = 104. If the actual receipts had been 106, we would forecast the next period as ( ) = = 104.
17 510 FRANK & WANG The double exponential smoothing model operates on the data that have been "smoothed" by this single process. The double application of the smoothing process is thought to enable this variant of the technique to better cope with trend than the single exponential model. Deterministic "Quasi-Causal" Model Forecasts with this model are based on the assumption that the next year's revenue is function of next year's consumption, with the latter being determined by last year's base and an increment estimated by changes in population and price. Davie's Finance Director suggested city financial director suggested that the authors use the Town's change in construction value as an estimate of consumption and CPI as the annual change in the price of the consumption. For example, the average change in the CPI for the "fuel and other utilities" for 1989, 1990 and 1991 was 3.37 percent and the average percentage gain of construction value in Davie for those years was 6.23 percent. Thus, the authors applied a growth factor of 9.81 percent ( * ) to 1991 actual receipts to arrive at Fiscal Year 1992's estimate of $3,246,472 (e.g., $2,956,446 x ). An Optimized Model The franchise and utility taxes are from various franchisees and vendors. In Davie, they are mainly from Florida Power and Light, Southern Bell, Southern Sanitation, and several cable and towing providers. In an optimized model, the authors forecast receipts from each franchisee/vendor and selected the most accurate model. These forecasts were then combined using the logic that over time, this "optimized model" should yield the most accurate forecasts for all franchise and utility taxes. The following process shows the forecast of the franchise taxes in 1992 by a combined model. Franchise Revenue from The Florida Power and Light (FPL) The FPL monthly receipts had an obvious seasonal component. Therefore, exponential smoothing with seasonal parameters was chosen for forecasting. Using a smoothing coefficient of a=0.3, the authors projected the