The Value-Line Dow-Jones Model: Does It Have Predictive Content?

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The Value-Line Dow-Jones Model Does It Have
Predictive Content?

• Tom Fomby and Limin Lin
• Department of Economics
• SMU, Dallas, TX
• ISF 2004

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A USEFUL RULE OF THUMB

• Data Mining by Michael Lovell (1983, RES) The
  Lovell Pretesting Rule for Coefficient
  Significance
• Start MLR with c candidate variables.
• Use A Best Subset Method to obtain
• A MLR with k final variables
• P-Value(actual) (c/k)P-Value(stated)

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A MLR PREDICTIONRULE OF THUMB

• On the Usefulness of Macroeconomic Forecasts as
  Inputs to Forecasting Models Richard Ashley Jo.
  of Forecasting. 1983
• Var(x(hat))/Var(x) versus 1
• Ratio greater than one, x generally not useful
• Ratio less than one, x possibly useful
• It seems a lot of practitioners ignore this rule
  at their peril

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The Value-Line Dow Jones Stock Evaluation Model

• Regression model used by the Value-Line
  Corporation in its end-of-year report (Value Line
  Investment Survey) to provide its readers a
  forecast range for the Dow-Jones Index in the
  coming years. (Model builder Samuel Eisenstadt)
• DJ Dow Jones Industrial Average,
• EP Earnings Per Share on the Dow Jones,
• DP Dividends Per Share on Dow Jones, and
• BY Moodys AAA Corporate Bond Yield
• logarithm transformation linear form

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Motivation

• No evaluation of the model in existing
  literature, although the model is in use for over
  twenty years and possibly by millions of readers
  who may have made decisions upon forecasting
  results from the model. It would be interesting
  and useful to see how precise and reliable these
  forecasts are.
• Arguments in the literature about the forecasting
  competence of regression model vs. univariate
  models, eg. Ashley (1983). Accuracy of the model
  depends on the accuracy of the forecasts of the
  independent variables. Are the independent
  variables making the forecast better or worse?

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Outline of Presentation

• Data
• Stability Analysis
• Out-of-Sample Forecast Evaluation
• (Predictive Content of Input Variables)
• Conclusions

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Data

• Annual observations (1920-2002) on
• DJ Dow Jones Industrial Average, annual
  averages
• EP Earnings Per Share on the Dow (data point
  1932 adjusted
• for convenience of log
  transformation)
• DP Dividends Per Share on the Dow
• BY Moodys AAA Corporate Bond Yield
• Data source Long Term Perspective chart of the
  Dow Jones Industrial Average, 1920-2002,
  published by the Value Line Publishing, Inc. in
  Value Line Investment Survey
• Logarithm transformation used to obtain linear
  regression
• Comparisons are made among forecasts of DJ

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Stability Analysis for VLDJ Model Recursive
Coefficients Diagrams
As reported in end of year ValueLine Investment
Survey, coefficients are estimated as follows
2002 (1.030, 0.210, 0.350, -0.413)
1999 (1.034, 0.217, 0.332, -0.468) 2001
(1.032, 0.218, 0.336, -0.463)
1998 (1.032, 0.216, 0.335, -0.473), and so
on. 2000 (1.033, 0.214, 0.340, -0.480)
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Stability Analysis for VLDJ ModelCUSUM and
CUSUMSQ Test Results
The CUSUM test is based on the statistic
The CUSUMSQ test is based on the statistic
Where is recursive residual defined
as
S is the standard error of the regression fitted
to all T sample points.
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Test for Structural Change of Unknown Timing
Wald Test Sequence as a Function of Break Date
Andrews (1993, 2003) critical values
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The Models for DLDJ (specified using in-sample
data only)

• Transfer function model (in same form as the
  Value-Line Model) DLDJ at time t is a function
  of DLEP, DLDP and DLBY at time t where
• DLEP MA(2) , DLDP MA(1) and DLBY AR
  (1)
• Box-Jenkins univariate model DLDJ MA(1).
• Note Transform Predictions for DLDJ to DJ in two
  steps
• Step 1
• Step 2

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Ex-Ante Forecast AccuracyTransfer Function vs.
Box-Jenkins(Imperfect Foresight)
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Usefulness of Explanatory Variables in the
Transfer Function Model
Ashley(1983 )
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Forecast Accuracy--RMSFE Assuming Perfect
Foresight for Leading Indicators in Transfer
Function Model
Disadvantage Loss of forecast accuracy relative
to TF-Perfect
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Value Line Forecasts vs. TF and BJ Forecasts
The MAFE and RMSFE are computed based on years
1983-2002 except 1993-1995
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Combination Forecasts of TF and BJ

• Simple Average (CF1)
• Nelson Combination (CF2)
• Granger-Ramanathan Combination (CF3)
• Fair-Shiller Combination (CF4)
• Note We apply dynamic weights

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Forecast Accuracy (RMSFE)Box-Jenkins vs.
Combinations
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Ways of Combating Weak Input Variables

• Drop input variables that dont satisfy Ashleys
  Criterion (Forecast could have bias but less
  variance)
• Use improved input variables Combination of
  sample mean and forecasts of input variable
• -- Simple average
• -- Ashley (1985) combination

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Forecast AccuracyDropping Inadequate Input
Variables
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Forecast AccuracyInput Variables From
Combination Forecasts
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Conclusions

• In the absence of perfect foresight, TF (Value
  Line) forecasts are less accurate than the BJ
  benchmark forecasts for any forecast horizons.
• Ashley (1983) criterion shows that the leading
  indicators are very noisy and inhibit ex ante
  forecasting accuracy of TF model.
• If future values of leading indicator variables
  are assumed known, (perfect foresight), TF
  forecasts improve considerably--beat the BJ
  forecast for 2-6 step-ahead forecast horizons,
  but do not for the 1-step-ahead forecast horizon.

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Conclusion (cont.)

• With respect to Ex Ante combination forecasting,
  BJ forecasts perform better for short horizons
  and combinations of the TF and BJ are best for
  longer horizons.
• For Ex Ante forecasts, differences in accuracy
  between TF forecasts and the most accurate
  forecasts are not statistically significant.
  Ashley (2003)
• Dynamic Combination forecasts perform better than
  combinations with fixed weights.
• Dropping inadequate input variables did not
  improve forecast accuracy. Using combination
  forecasts for the input variables only improved
  the forecast accuracy of some horizons.

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Conclusion (cont.)

• Evidently, the Value Line personnel have been
  pretty astute with respect to choosing future
  values of the independent variables of their
  model. Their published 1-step-ahead forecasts
  have smaller MAFE than the ex ante TF model and
  the BJ model. With respect to the RMSFE, however,
  the BJ model provides a more accurate
  1-step-ahead-forecast.
• Remember forecasting accuracy is only one way to
  evaluate the VLDJ model. Irrespective of its
  forecasting powers, it should be recognized that
  the VLDJ model is potentially quite useful for
  examining what if scenarios and understanding
  historical causal factors in the stock market.
• It would be interesting to compare competing
  models based on interval forecast accuracy and
  density forecast accuracy.

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Thank you!
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References

• Andrews, D. W. K. (1993) Tests for Parameter
  Instability and Structural Change with Unknown
  Change Point, Econometrica, 61, 821-856.
• Andrews, D. W. K. (2003) Tests for Parameter
  Instability and Structural Change with Unknown
  Change Point A Corrigendum, Econometrica, 71
  (1), 395-397.
• Ashley, R. (1983) On the Usefulness of
  Macroeconomic Forecasts as Inputs to Forecasting
  Models, Journal of Forecasting, 2, 211-223.
• Ashley, R. (2003) Statistically Significant
  Forecasting Improvements How Much Out-of-Sample
  Data Is Likely Necessary? International Journal
  of Forecasting, 19(2), 229-239.
• Bai, J. (1997) Estimation of A Change Point in
  Multiple Regression Models, Review of Economics
  and Statistics, 79 (4), 551-563.

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References (cont.)

• Brown, R. L., J. Durbin, and J. M. Evans (1975)
  "Techniques for Testing the Constancy of
  Regression Relationships Over Time," Journal of
  the Royal Statistical Society, Series B, 37,
  149-192.
• Diebold, F. X. and R. S. Mariano (1995)
  Comparing Predictive Accuracy, Journal of
  Business and Economic Statistics, 13 (3),
  253-263.
• Fair, R. C. and R. J. Shiller (1990) Comparing
  Information in Forecasts from Econometric
  Models, American Economic Review, 80 (3),
  375-389.
• Nelson, C. R. (1972) The Prediction Performance
  of the FRB-MIT-PENN Model of the U.S. Economy,
  American Economic Review, 62 (5), 902-917.

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Combinations of the TF and BJ models

• Naïve combination simple average (weight0.5)

In-sample (obs. 1-53)
Out-of-sample (obs. 54-83)
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Combinations of the TF and BJ models (dynamic
weights applied)

• Dynamic Nelson combination (weights sum to 1)
• where weight is obtained from LS regression

15 obs.
Test Data (Out-of-sample)
Training
Validation
15 obs.
Validation

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Combinations of the TF and BJ models (dynamic
weights applied)

• Dynamic Granger-Ramanathan combination (weights
  obtained from unrestricted regression)
• where weights are obtained from regression
• Dynamic Fair and Shiller Combination
• where weights are obtained from
  regression

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Data --LDJ
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Data --LEP
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Data --LDP
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Data --LBY
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