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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@willamette.edu , 503.370.6056.

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principles of forecasting applications in revenue and expenditure forecasting

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

presentation overview
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

example project oregon personal income tax revenue
Example: Project Oregon Personal Income Tax Revenue

Atkinson Graduate School of Management

Willamette University

challenges
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

why forecast
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

why forecast6
Why Forecast?

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

Atkinson Graduate School of Management

Willamette University

why forecast7
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

forecast risks costs
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

forecast objective
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

example project oregon personal income tax revenue10
Example: Project Oregon Personal Income Tax Revenue

Atkinson Graduate School of Management

Willamette University

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 Regr’n

Box-Jenkins/ARIMA

A Brief Taxonomy of Forecasting Methods

Atkinson Graduate School of Management

Willamette University

subjective methods
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

data based forecasting
Data-Based Forecasting

In God we trust, all others bring data.

W. Edwards Deming

Atkinson Graduate School of Management

Willamette University

associative methods
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

associative models
Associative Models

Atkinson Graduate School of Management

Willamette University

econometric models
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

projection extrapolation
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

projective methods
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

projective models
Projective Models

Winters’ Seasonal Exponential Smoothing

Atkinson Graduate School of Management

Willamette University

forecasting process
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

example oregon personal income taxes 1996 2005
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

example oregon personal income taxes 1996 2001
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

example classical multiplicative decomposition
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

example classical multiplicative decomposition24
Example: Classical Multiplicative Decomposition

Conceptual Decomposition:

Atkinson Graduate School of Management

Willamette University

example classical multiplicative decomposition25
Example: Classical Multiplicative Decomposition

Visual Representation

Atkinson Graduate School of Management

Willamette University

example classical multiplicative decomposition model interpretation
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

example classical multiplicative decomposition forecasts
Example: Classical Multiplicative Decomposition, Forecasts

Forecasts

Atkinson Graduate School of Management

Willamette University

forecast model assessment
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

example classical multiplicative decomposition residuals errors
Example: Classical Multiplicative Decomposition, Residuals/Errors

Atkinson Graduate School of Management

Willamette University

example classical multiplicative decomposition time series plot of residuals
Example: Classical Multiplicative Decomposition, Time Series Plot of Residuals

Atkinson Graduate School of Management

Willamette University

desirable properties of residuals
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

measures of forecast accuracy
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

example classical multiplicative decomposition measures of forecast accuracy
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

conclusion
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

basic forecasting references
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