Principles of Forecasting: Applications in Revenue and Expenditure Forecasting

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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_at_willamette.edu, 503.370.6056

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Presentation Overview

• Philosophy/Perspective
• Taxonomy of Methods
• Forecasting Process with Special Attention to
  Knowledge Acquisition
• Data Understanding
• Model Interpretation
• Model Assessment

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What is (a/to) Forecast?

• A Forecast (noun) a prophecy, estimate, or
  prediction of a future happening or condition
• To Forecast (verb) to calculate or predict some
  future event or condition, usually as a result of
  study and analysis of available pertinent data
• The forecast process offers far greater potential
  return than merely the forecast that is, the
  journey is more important than the destination.

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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)
  

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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.

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Why Forecast?
For every level of demand, there is a best level
of service capacity.
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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

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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

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Forecast Objective

• Perfection? Forecasts that are without error? A
  naïve and unproductive view. Fails to properly
  manage expectations about the forecasting
  process. Preoccupation with being right is
  unhealthy and only serves to stifle the process.
• Objective Minimize Forecast Errors
• (and associated costs)
• It is sufficient to develop forecasts that
  systematically reduce uncertainty (and thereby
  reduce the risks and costs associated with
  forecast errors.)

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A Brief Taxonomy of Forecasting Methods

• Subjective
• Expert Opinion
• Survey Research
• Historical Analogy

• Objective/Data-Based
• Associative
• Multiple Regression
• Econometric Models
• Projective
• Decomposition Smoothing
• Time-Series Regrn
• Box-Jenkins/ARIMA

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Subjective Methods

• Methods based primarily on judgment/expert
  opinion
• Generally little or no data to directly support
  forecast requirement
• Historical analogy may rely upon data from a
  comparable process
• Best for long-range forecasts
• More than two years out

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Data-Based Forecasting

• In God we trust, all others bring data.
• W. Edwards Deming

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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

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Associative Models
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Econometric Models
http//egov.oregon.gov/DAS/OEA/docs/revenue/pit_fo
recastmethod.pdf

• LOG(GIwages) 20.7 0.93LOG(PIwages
  PIother_lab) AR(1)0.85
• LOG(GIdividends) 16.7 0.49LOG(PIdir)
  0.30LOG(MKTw5000)
• LOG(GIinterest) 19.6 0.34LOG(PIwages)
  0.04 IR3mo_tbill 0.039 IR3mo_tbill (-1)
  AR(1)0.65
• LOG(GIcapgains) 11.5 1.14LOG(MKTw5000)
  MA(4) -0.86
• LOG(GIretirement) -0.12 1.24LOG(POP_OR65)
  0.97LOG(PItotal PIwages) 0.32LOG(MKTw5000)
  AR(1)-0.50
• LOG(GIproprietors) -304.7 0.72LOG(PIproprieto
  rs) 2.10LOG(EMPretail) AR(1)1.0
• LOG(GIschedule_e) 14.4 1.1LOG(CORP_PROFIT)
  AR(1)0.78
• LOG(GIother) -2.1 4.14LOG(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

Personal Income Tax Model Office of Economic
Analysis Department of Administrative Services
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Projection/Extrapolation

• I have seen the future and it is very much like
  the present, only longer.
• Kehlog Albran, The Profit

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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

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Projective Models
Winters Seasonal Exponential Smoothing
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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_ToolsHand_OutsForecastingNNG_Paper.p
  df)

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Example Oregon Personal Income Taxes, 1996 2005
Data Understanding
Note dramatic shift in level and nature of
seasonal variation
(see Class Tools resource Hand_OutsForecastingMu
ltDecompPITFull.xls)
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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 resource Hand_OutsForecastingMu
ltDecompPIT.xls)
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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
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Example Classical Multiplicative Decomposition
Conceptual Decomposition
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Example Classical Multiplicative Decomposition
Visual Representation
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Example Classical Multiplicative Decomposition,
Model Interpretation
Model Interpretation Initial, time-zero
(1995Q4) 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
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Example Classical Multiplicative Decomposition,
Forecasts
Forecasts
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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.

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Example Classical Multiplicative Decomposition,
Residuals/Errors
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Example Classical Multiplicative Decomposition,
Time Series Plot of Residuals
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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.

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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
• Proportion (or percentage) of variation
  explained by (or attributable to) forecast
  model
• Prediction Intervals

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Example Classical Multiplicative Decomposition,
Measures of Forecast Accuracy

• Error Summary Measures
• Mean Squared Error, MSD
• Std Deviation of Residuals, s vMSD
• Mean Absolute Deviation, MAD
• Mean Absolute Pct Error, MAPE
• Mean Pct Error, MPE (Bias)
• R2 (SSTO SSE)/SSTO

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Conclusion

• Forecasting process can be about far more than
  mere forecasts, it can also provide for essential
  Knowledge Acquisition
• Data Understanding
• Model Interpretation
• Model Assessment

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Basic Forecasting References

• Armstrong. Long-Range Forecasting From Crystal
  Ball to Computer. Wiley-Interscience, 1978.
• (Also available in .pdf form at
• http//www-marketing.wharton.upenn.edu/forecast/Lo
  ng-Range20Forecasting/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