Principles of Forecasting: Applications in Revenue and Expenditure Forecasting

1. Principles of Forecasting: Applications in Revenue and Expenditure Forecasting Michael L. Hand, Ph.D Professor of Applied Statistics and Information Systems Atkinson Graduate School of Management Willamette University, 900 State Street, Salem, OR 97301 mhand@willamette.edu, 503.370.6056

2. Presentation Overview • Philosophy/Perspective • Taxonomy of Methods • Forecasting Process (with Special Attention to Selected Dimensions of Knowledge Acquisition) • Data Understanding • Model Interpretation • Model Assessment Atkinson Graduate School of Management Willamette University

3. Example: Project Oregon Personal Income Tax Revenue Atkinson Graduate School of Management Willamette University

4. Challenges Prediction is very difficult, especially if it's about the future. Nils Bohr, Nobel laureate in physics (though this sounds a lot more like Yogi Berra) Atkinson Graduate School of Management Willamette University

5. Why Forecast? • The effectiveness of almost every human endeavor, every public initiative, depends in part upon unknown and uncertain future outcomes – the demand for services, the revenues to fund them. • The quality of decisions about whether or not to engage and at what level improves with the reliability of supporting forecasts. Atkinson Graduate School of Management Willamette University

6. Why Forecast? For every level of demand, there is a best level of service capacity. Atkinson Graduate School of Management Willamette University

7. Why Forecast? In short, we forecast because we have little choice. A forecast is implied by essentially every decision that we make, every action that we take. It is far better to foresee even without certainty than not to foresee at all. Henri Poincare in The Foundations of Science Atkinson Graduate School of Management Willamette University

8. Forecast Risks/Costs Prophesy is a good line of business, but it is full of risks. Mark Twain in Following the Equator • Forecast high • Cost of excess capacity, misallocations • Forecast low • Kicker Atkinson Graduate School of Management Willamette University

9. Forecast Objective Perfection? Forecasts that are without error? That’s a naïve and unproductive view in terms of the reasonable management of expectations for the forecasting process. Preoccupation with being “right” can be unhealthy and only serves to stifle the process. Objective: Minimize (the cost of) forecast errors It is sufficient to develop forecasts that systematically reduce uncertainty (and thereby reduce the risks and costs associated with forecast errors.) Atkinson Graduate School of Management Willamette University

10. Example: Project Oregon Personal Income Tax Revenue Atkinson Graduate School of Management Willamette University

11. Subjective Expert Opinion Survey Research Historical Analogy Objective/Data-Based Associative Multiple Regression Econometric Models Projective Decomposition Smoothing Time-Series Regr’n Box-Jenkins/ARIMA A Brief Taxonomy of Forecasting Methods Atkinson Graduate School of Management Willamette University

12. Subjective Methods • Judgment/expert opinion based methods with (little or) no direct data on the process to be forecast. • Generally no data/supporting forecast requirement May rely upon data from related process for historical analogy • Best for long-range forecasts More than two years out Atkinson Graduate School of Management Willamette University

13. Data-Based Forecasting In God we trust, all others bring data. W. Edwards Deming Atkinson Graduate School of Management Willamette University

14. Associative Methods • “Causal”, multiple regression models relating response to a general set of predictors • Data/supporting forecast requirement Increased model complexity and development effort • Assumes relationships among response and predictors are stable over time • Best for intermediate-term forecasts One- to two-year forecast time horizon Atkinson Graduate School of Management Willamette University

15. Associative Models Atkinson Graduate School of Management Willamette University

16. Econometric Models http://egov.oregon.gov/DAS/OEA/docs/revenue/pit_forecastmethod.pdf LOG(GIwages) = 20.7 + 0.93*LOG(PIwages + PIother_lab) + [AR(1)=0.85] LOG(GIdividends) = 16.7 + 0.49*LOG(PIdir) + 0.30*LOG(MKTw5000) LOG(GIinterest) = 19.6 + 0.34*LOG(PIwages) + 0.04* IR3mo_tbill + 0.039* IR3mo_tbill (-1) + [AR(1)=0.65] LOG(GIcapgains) = 11.5 + 1.14*LOG(MKTw5000) + [MA(4) = -0.86] LOG(GIretirement) = -0.12 + 1.24*LOG(POP_OR65+) + 0.97*LOG(PItotal – PIwages) + 0.32*LOG(MKTw5000) + [AR(1)=-0.50] LOG(GIproprietors) = -304.7 + 0.72*LOG(PIproprietors) + 2.10*LOG(EMPretail) + [AR(1)=1.0] LOG(GIschedule_e) = 14.4 + 1.1*LOG(CORP_PROFIT) + [AR(1)=0.78] LOG(GIother) = -2.1 + 4.14*LOG(EMPretail) Eff_tax_rate = 0.05 + 0.005* DMYtax_rate + 0.053* FDIST1mil + 0.04*(( GIschedule_e + GIproprietors)/ GIwages) + [AR(1)=0.58] GI - Gross Income from the source indicated PItotal – Total Oregon Personal Income PIwages – Wage and Salary Component of Personal Income PIother_lab – Other labor component of Personal Income PIdir – Dividends, Interest and Rent component of Personal Income PIproprietors – Proprietors’ Income component of Personal Income MKTw5000 – Wilshire 5000 stock index EMPretail – Oregon Retail Employment CORP_PROFIT – U.S. Corporate Profits POP_OR65+ – Oregon 65 and older population IR3mo_tbill – Discount rate of 3 month Treasury Bill FDIST1mil - Filer Distribution Model, Ratio of $1 million-plus filers to Total filers DMYtax_rate – Dummy variable for 1982 through 1984 tax rate increase Personal Income Tax Model Office of Economic Analysis DAS Atkinson Graduate School of Management Willamette University

17. Projection/Extrapolation I have seen the future and it is very much like the present, only longer. Dan Quisenberry Atkinson Graduate School of Management Willamette University

18. Projective Methods • Simple extrapolation in time • Predictors are time and functions of time Trend, seasonal, cyclical factors • Minimal data/supporting forecast requirement • Assumes current conditions will persist • Best for short-term forecasts One year out (two if we stretch) or less Atkinson Graduate School of Management Willamette University

19. Projective Models Winters’ Seasonal Exponential Smoothing Atkinson Graduate School of Management Willamette University

20. Forecasting Process • Enterprise Understanding • Data Understanding • Alternative Model Identification • Model Estimation • Model Assessment – Adequacy, Quality • Model Selection • Model Interpretation • Forecasting Important (oft overlooked) knowledge acquisition stages (see Class_Tools:Hand_Outs:Examples:0.Introduction:NNG_Paper.pdf) Atkinson Graduate School of Management Willamette University

21. Example: Oregon Personal Income Taxes, 1996 – 2005 Data Understanding Note dramatic shift in level and nature of seasonal variation (see Class Tools > Sitewide > Hand Outs > Public Finance > MultDecompPITFull.xls) Atkinson Graduate School of Management Willamette University

22. Example: Oregon Personal Income Taxes, 1996 – 2001 For simplicity, we restrict our initial view to the fairly stable period from 1996 – 2001 Data Understanding (see Class Tools > Sitewide > Hand Outs > Public Finance > MultDecompPIT.xls) Atkinson Graduate School of Management Willamette University

23. Example: Classical Multiplicative Decomposition Conceptual Decomposition: Trend: Long-term growth/decline Cycle: Long-term slow, irregular oscillation Seasonal: Regular, periodic variation w/in calendar year Irregular: Short-term, erratic variation Conceptual Forecast: Forecasting Model: Atkinson Graduate School of Management Willamette University

24. Example: Classical Multiplicative Decomposition Conceptual Decomposition: Atkinson Graduate School of Management Willamette University

25. Example: Classical Multiplicative Decomposition Visual Representation Atkinson Graduate School of Management Willamette University

26. Example: Classical Multiplicative Decomposition, Model Interpretation Model Interpretation Initial, time-zero (1995:Q4) level is $731.92 million Increasing at $18.5 million per quarter Seasonal pattern Peak in Q4 21% over trend Trough in Q3 11% below trend Atkinson Graduate School of Management Willamette University

27. Example: Classical Multiplicative Decomposition, Forecasts Forecasts Atkinson Graduate School of Management Willamette University

28. Forecast Model Assessment Residual analysis: A somewhat scatological endeavor, whereby we assess forecast quality through an analysis of residuals or what the forecast process leaves unexplained. Residual (Error) = Actual – Forecast Assessment possible for any type of forecasting process – statistical, organizational, ad hoc, arbitrary. Atkinson Graduate School of Management Willamette University

29. Example: Classical Multiplicative Decomposition, Residuals/Errors Atkinson Graduate School of Management Willamette University

30. Example: Classical Multiplicative Decomposition, Time Series Plot of Residuals Atkinson Graduate School of Management Willamette University

31. Desirable Properties of Residuals • Small aggregate error measure • Independent/random • No remaining pattern • Mean zero, Unbiased • Constant variance • Normality • Required for many statistical assessments These properties can be tested with a variety of charts and graphs too numerous to mention here. Atkinson Graduate School of Management Willamette University

32. Measures of Forecast Accuracy • Error Summary Measures • Mean Squared Error, MSE • Mean Absolute Deviation, MAD • Mean Absolute Percentage Error, MAPE • Mean Percentage Error, MPE (Bias) • R2 = (SSTO – SSE)/SSTO Percent of variation explained • Prediction Intervals Atkinson Graduate School of Management Willamette University

33. Example: Classical Multiplicative Decomposition, Measures of Forecast Accuracy • Error Summary Measures • Mean Squared Error, MSD • Std Deviation of Residuals, s ≈ √MSD • Mean Absolute Deviation, MAD • Mean Absolute Pct Error, MAPE • Mean Pct Error, MPE (Bias) • R2 = (SSTO – SSE)/SSTO Atkinson Graduate School of Management Willamette University

34. Conclusion • Forecasting process can be about far more than mere forecasts, it can also provide for essential Knowledge Acquisition/Key Insights • Data Understanding • Model Interpretation • Model Assessment Atkinson Graduate School of Management Willamette University

35. Basic Forecasting References Armstrong. Long-Range Forecasting: From Crystal Ball to Computer. Wiley-Interscience, 1985. (Also available in .pdf form at: http://www-marketing.wharton.upenn.edu/forecast/Long-Range%20Forecasting/contents.html Bowerman, O'Connell, Hand. Business Statistics in Practice, 2nd Edition. McGraw-Hill/Irwin, 2001. Bowerman, O'Connell, Koehler. Forecasting, Time Series and Regression, Fourth Edition. Duxbury Press, 2005. Hanke and Wichern. Business Forecasting, 8th Edition. Prentice-Hall, 2005. Makridakis, Wheelwright, Hyndman. Forecasting Methods and Applications, 3rd Edition. John Wiley and Sons, 1998 Atkinson Graduate School of Management Willamette University