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?

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)

A MLR PREDICTION RULE 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

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 — Moody’s AAA Corporate Bond Yield
  • logarithm transformation linear form:

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?

Outline of Presentation

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

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: Moody’s 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

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);

Stability Analysis for VLDJ Model: CUSUM 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.

Test for Structural Change of Unknown Timing: Wald Test Sequence as a Function of Break Date

  • Andrews (1993, 2003) critical values

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:

Ex-Ante Forecast Accuracy— Transfer Function vs. Box-Jenkins (Imperfect Foresight)

Usefulness of Explanatory Variables in the Transfer Function Model—

  • Ashley(1983 )

Forecast Accuracy--RMSFE: Assuming Perfect Foresight for Leading Indicators in Transfer Function Model

  • *Disadvantage: Loss of forecast accuracy relative to TF-Perfect

Value Line Forecasts vs. TF and BJ Forecasts

  • *The MAFE and RMSFE are computed based on years 1983-2002 except 1993-1995

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

Forecast Accuracy (RMSFE)— Box-Jenkins vs. Combinations

Ways of Combating Weak Input Variables

  • Drop input variables that don’t satisfy Ashley’s 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

Forecast Accuracy— Dropping Inadequate Input Variables

Forecast Accuracy— Input Variables From Combination Forecasts

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.

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.

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.

Thank you!

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.

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.

Combinations of the TF and BJ models

    • Naïve combination: simple average (weight=0.5)
  • In-sample
  • (obs. 1-53)
  • Out-of-sample
  • (obs. 54-83)

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

    • Dynamic Nelson combination (weights sum to 1)
    • where weight is obtained from LS regression
  • Training
  • Validation
  • Test Data
  • (Out-of-sample)
  • Validation
  • 15 obs.
  • 15 obs.

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

Data --LDJ

Data --LEP

Data --LDP

Data --LBY


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