Forecasting with Regression

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Forecasting with Regression

• Kelloggs stock price

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data

• 35 quarters
• nine years
• 1969-1973

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Variables

• Kelloggs stock price (dependent variable)
• Dow Jones Industrial Average
• Kelloggs earnings growth
• Kelloggs dividend
• Book value of company

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Y a b1 Dow b2 Growth b3 Dividend b4
Book
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Estimated coefficients

• stand. error t-stat
• a -7.8 ----- -----
• b1 0.0096 .0024 3.91
• b2 2.68 2.83 0.95
• b3 16.18 22.7 0.71
• b4 4.84 1.47 3.29
• R-squared .95

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To forecast

• Put values for Dow, Growth, Dividend, and Book
  value into equation
• Y -7.8 .0096 Dow 2.68 Growth 16.18 Dividend
  4.84 Book
• result is predicted Y (forecast stock price)

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Forecast versus Actual

• Predicted True Price
• 26.32 24.38
• 27.37 22.38
• 27.19 23.00
• 27.13 21.88

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Large errors in prediction

• Short run forecast
• actual values of X variables
• Good fit to equation
• If you bought stock based on this forecast
• You would lose money

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This forecast used known values of X to predict Y

• Future values for X variables arent usually
  known
• Estimate or Predict X
• Conditional forecast
• if X is this, then Y would be that
• Systems of Equations

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A simple system

• Price f(Dow, Earnings, Book)
• Dow f(GDP, interest rate, consumer
  confidence)
• Earnings f(sales, costs, . . .)
• Book Value f(Bookt-1, investment,
  depreciation)

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• Estimate coefficients
• Find forecasting equation
• Use new values of independent variables to
  predict dependent variables
• reduced form
• identification issues
• two-stage least squares

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• Equation to predict GDP
• Equation to predict interest rates
• Equation to predict growth
• . . .

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Large systems

• Equation to predict GDP
• predict consumption
• predict investment
• predict government spending
• Equation to predict interest rates
• Equation to predict growth
• and more . . .

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simple Time Series models often out-perform large
macro-models
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source

• Using Econometrics
• Studenmund and Cassidy
• Little Brown Co. 1987
• p 371-373