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					Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

FORECASTING AND MODEL SELECTION
Anurag Prasad
Department of Mathematics and Statistics Indian Institute of Technology Kanpur, India

REACH Symposium, March 15-18, 2008

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Outline

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Modeling and Forecasting

2

Forecasting Methods

3

Measuring the Accuracy of Forecast

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Assumptions of Forecasting

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Element of Uncertainty Blind Spots Change in Forecast Accuracy

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3

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Framework of a Forecast System

Model−Building Phase
Theory and/or Historical Data

Forecasting Phase

Model Specification

Model Estimation

No Diagnostic Checking Yes

No Forecast Generation Stability Checking Yes New Observations Forecast Updation

Data

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Choice of a Particular Forecast Model

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Degree of Accuracy Required Cost of Producing Forecasts Forecast Horizon Degree of Complexity Required Available Data

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5

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Classification of Estimation Methods

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Time Series Methods Causal Methods Judgemental Methods

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3

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Time Series Methods
• Use historical data as a basis • Underlying patterns are fairly stable
1 2 3 4 5 6 7

Autoregressive Moving Average (ARMA) Exponential Smoothing Extrapolation Linear Prediction Trend Estimation Growth Curve Box-Jenkins Approach

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Causal Methods

• Belief that some other time series can be useful • Assumption that it is possible to identify the underlying factors
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Regression Analysis * Linear Regression * Non-Linear Regression Econometrics

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Judgemental Methods
• Incorporate intuitive judgements, opinions and probability estimates
1 2 3 4 5 6

Composite Forecasts Surveys Delphi Method Scenario Building Technology Forecasting Forecast by Analogy

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Forecast Error
For t = 1, . . . , N, y (t) : Actual value at period t, y(t) : Forecast value at period t; e(t) : Forecast error at period t;

e(t) = y (t) − y (t)

y(t)

^ ) y(t i y(t ) i t t i

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Graphical Measures of Forecast Accuracy

Plot of y (t) versus y (t) • Keep the same scale for both the axes. • Departure of points from the 450 line through origin indicates imperfect forecasts.

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

y(t)

y(t)

^ y(t) Correct Model Form

^ y(t) Incorrect Model Form

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Plot of e(t) versus t • Reveals patterns of variability which the model has failed to explain. • For a good model, the forecast errors should vary in a horizontal band around zero.

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

e(t)
0

e(t)
0

t Correct Model Form

t Incorrect Model Form

e(t)
0

e(t)
0

t Incorrect Model Form

t Incorrect Model Form

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Descriptive Measures of Forecast Accuracy

Descriptive Measures of Forecast Accuracy are used to...
1

Provide a single, easily interpreted measure of model’s reliability Compare the accuracy of two different models Search for an optimal model Monitor a model’s performance

2 3 4

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Descriptive Measures of Forecast Accuracy

Mean Absolute Deviation (MAD) MAD =
|forecast error| number of forecasts

=

N t=1
 

|e(t)| N

Mean Square Error (MSE) MSE = =
 

(forecast error)2 number of forecasts
 

Root Mean Square Error (RMSE) √ RMSE = MSE

 

N t=1

e(t)2 N

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Descriptive Measures of Forecast Accuracy
Mean Absolute Percent Error (MAPE) MAPE = =
N t=1
      ¢

|forecast error/actual value| .100% number of forecasts

|e(t)/y (t)| .100% N

Pearson’s Correlation Coefficient (r ) between y (t) and y (t)
¡ ¡   ¢

r=

N ¯ ¯ t=1 (y (t)−y )(y (t)−y) N N ¯ 2 ¯ 2 t=1 (y (t)−y ) t=1 (y (t)−y)
¡ ¡  

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Descriptive Measures of Forecast Accuracy

"No Change" model is : y (t + 1) = y (t) Theil’s Inequality Coefficient (U) U=
RMSE("new" model) RMSE("no change" model)

U>1 U=1 U<1

⇒ ⇒ ⇒

worse than "no change" model as good as "no change" model better than "no change" model

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Further Readings

Quantitative Forecasting Methods, N.R. Farnum and L.W. Stanton, 1989, PWS-KENT Publishing Co. Statistical Methods for Forecasting, B. Abraham and J. Ledolter, 1983, John Wiley & Sons Introduction to Time Series and Forecasting, P.J. Brockwell and R.A. Davis, 2002 (Second Edition) , Springer-Verlag Time Series Analysis and Forecasting, R. Yaffee, 2000, Academic Press

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Forecasting and Model Selection

Modeling and Forecasting Forecasting Methods Measuring the Accuracy of Forecast

Thank You

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Forecasting and Model Selection


				
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