On the Internal Consistency of Stock Market Forecasts

Abstract

Using the Livingston survey data, we test internal consistency restrictions on short-term, medium-term, and long-term stock market forecasts of the S&P 500®. We find that neither short-term forecasts are consistent with medium-term forecasts nor that medium-term forecasts are consistent with long-term forecasts. Using a forecast formation process featuring a distributed lag structure, however, we find some weak evidence of internal inconsistency of medium-term forecasts with long-term forecasts.

Keywords:

• Stock market
• Forecasting
• Internal consistency

ACKNOWLEDGMENTS

We are grateful to an anonymous referee for helpful comments and suggestions and to Tim Meyer for copyediting the manuscript.

Notes

1. We define the change in the stock market index as rather than as in order to derive the internal consistency restrictions in a mathematically convenient way.

2. When both the intercept and the slope coefficients in Equations 2 and 3 are zero, forecasts are consistent with a random walk model of the stock market. See also Ito ([1990],Table 5). Equations 2 and 3 nest the random walk model as a special case.

3. The derivation of the internal consistency restrictions follows Pierdzioch et al. [2012].

4. Strictly speaking, the coefficients only have different signs if the short-term β-coefficients are larger than 1, and they have the same sign if the short-term β-coefficients are smaller than 1. We mention the interval -1 and 1 in the text, however, because it covers both the case of bandwagon and the case of contrarian expectations, and because empirical studies typically find coefficients in this interval. See also Figures 4 and 5.

5. Frankel and Froot [1987b] find evidence of a twisting behavior of exchange-rate forecasts across different forecast horizons. See also the analysis by Ito ([1990], p. 446).

6. In contrast to the benchmark model, the extended model features levels on the right-hand side. Alternatively, the model could be formulated entirely in first differences. Because forecasters forecast the level, not the change, of stock prices, we decided to specify the model in levels. In addition, we checked that the results of standard panel unit root tests (Im et al. [2003], Pedroni [2004]) for heterogeneous panels show that the null hypothesis of a unit root can be rejected indicating that the series can be treated as panel stationary.

7. Data and a detailed documentation are available at http://www.phil.frb.org/research-and-data/real-time-center/livingston-survey/. See also Söderlind ([2010], p. 870) for a critical discussion of the limitations of the Livingston data.

8. Standard unit root tests indicate that the change in the (expected) stock market index is stationary.

9. Because the properties of stock market forecasts may depend on the sample period being analyzed (Lakonishok [1980]), we also studied, as a robustness test, the period since June 1990 for the short-term forecasts (i.e., the period of time for which long-term forecasts are available). Results are qualitatively similar and available upon request. As a further robustness check, we studied the internal consistency of the consensus forecasts. Results showed that consistency can be rejected for all model specifications. Furthermore, results indicated that the consensus forecasts are in line with contrarian forecast formation, supporting our baseline results. To economize on journal space, we make the results for the consensus forecast available upon request.