# zbMATH — the first resource for mathematics

Entropy and predictability of stock market returns. (English) Zbl 1043.62090
Summary: We examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties. We compare our results with a number of traditional measures. The metric entropy is capable of detecting nonlinear dependence within the returns series, and is also capable of detecting nonlinear ”affinity” between the returns and their predictions obtained from various models thereby serving as a measure of out-of-sample goodness-of-fit or model adequacy.
Several models are investigated, including the linear and neural-network models as well as nonparametric and recursive unconditional mean models. We find significant evidence of small nonlinear unconditional serial dependence within the returns series, but fragile evidence of superior conditional predictability (profit opportunity) when using market-switching versus buy-and-hold strategies.

##### MSC:
 62P05 Applications of statistics to actuarial sciences and financial mathematics 62B10 Statistical aspects of information-theoretic topics
bootstrap; NUMAL
Full Text:
##### References:
 [1] Abhyankar, A.; Copeland, L.; Wong, W.: Uncovering nonlinear structure in real-time stock-market indexes: the S&P 500, the dax, the nikkei 225, and the ftse-100. Journal of business and economic statistics 15, No. 1, 1-14 (1997) [2] Balvers, R.; Wu, Y.; Gilliland, E.: Mean reversion across national stock markets and parametric contrarian investment strategies. Journal of finance 55, No. 2, 745-772 (2000) [3] Brock, W.; Deckert, W.; Scheinkman, J.; Lebaron, B.: A test for independence based on the correlation dimension. Econometric reviews 15, No. 3, 197-236 (1996) · Zbl 0893.62034 [4] Cameron, A.; Windmeijer, F. A. G.: An r-squared measure of goodness of fit for some common nonlinear regression models. Journal of econometrics 77, 329-342 (1997) · Zbl 0877.62097 [5] Campbell, J. Y.; Lo, A. W.; Mackinlay, A. C.: The econometrics of financial markets. (1997) · Zbl 0927.62113 [6] Delgado, M.: Testing for serial correlation using sample distribution function. Journal of time series analysis 17, No. 3, 271-285 (1994) · Zbl 0854.62047 [7] Diebold, F. X.; Nason, J. A.: Nonparametric exchange rate prediction. Journal of international economics 28, 315-332 (1990) [8] Ebrahimi, N.; Maasoumi, E.; Soofi, E.: Comparison of entropy and variance orderings. Journal of econometrics 90, 317-336 (1999) · Zbl 1041.62501 [9] Efron, B.; Tibshirani, R.: An introduction to the bootstrap. (1993) · Zbl 0835.62038 [10] Frank, M.; Stengos, T.: Chaotic dynamics in economic time series. Journal of economic surveys 2, No. 2, 103-133 (1988) [11] Geweke, J.: Measurement of linear dependence and feedback. Journal of American statistical association 77, 304-313 (1982) · Zbl 0492.62078 [12] Gourieroux, C., Monfort, A., Renault, E., 1986. Kullback causality measures, Mimeo, Ecole Nationale de la Statistique et de l’Administration Economique. [13] Granger, C., Maasoumi, E., 1993. A metric entropy measure. Unpublished notes, Department of Economics, UCSD and SMU. [14] Granger, C., Maasoumi, E., Racine, J., 2000. A metric entropy and a new test of independence. UCSD working paper. · Zbl 1062.62178 [15] Havrda, J.; Charvat, F.: Quantification method of classification processes: concept of structural $${\alpha}$$-entropy. Kybernetika cislo I. Rocnik 3, 30-34 (1967) [16] Hirschberg, D.; Maasoumi, E.; Slottje, D.: Clusters of attributes and well-being in the US. Journal of applied econometrics 16, No. 3, 445-460 (2001) [17] Hong, Y., White, H., 2000. Asymptotic distribution theory for nonparametric entropy measures of serial dependence. Mimeo, Department of Economics, Cornell University, and UCSD. [18] Hsieh, D.: Testing for nonlinear dependence in foreign exchange rates: 1974–1983. Journal of business 62, 339-368 (1989) [19] Joe, H.: Relative entropy measures of multivariate dependence. Journal of the American statistical association 84, 157-164 (1989) · Zbl 0677.62054 [20] Lau, H. T.: A numerical library in C for scientists and engineers. (1995) · Zbl 0815.65001 [21] Liu, Z.; Stengos, T.: Nonlinearities in cross-country growth regressions: a semiparametric approach. Journal of applied econometrics 14, 527-538 (1999) [22] Ljung, G.; Box, G.: On a measure of lack of fit in time series models. Biometrica 65, 297-303 (1978) · Zbl 0386.62079 [23] Maasoumi, E.: A compendium to information theory in economics and econometrics. Econometric reviews 12, No. 2, 137-181 (1993) · Zbl 0769.62003 [24] Pagan, A.; Schwert, G.: Alternative models for conditional stock volatility. Journal of econometrics 45, 267-290 (1990) [25] Pesaran, M. H.; Timmermann, A.: Predictability of stock returns: robustness and economic significance. Journal of finance 50, 1201-1228 (1995) [26] Qi, M.: Nonlinear predictability of stock returns using financial and economic variables. Journal of business and economic statistics 17, No. 4, 419-429 (1999) [27] Racine, J.: Consistent significance testing for nonparametric regression. Journal of business and economic statistics 15, No. 3, 369-379 (1997) [28] Racine, J.: On the nonlinear predictability of stock returns using financial and economic variables. Journal of business and economic statistics 19, No. 3, 380-382 (2001) [29] Robinson, P.: Consistent nonparametric entropy based testing. Review of economic studies 58, 437-453 (1991) · Zbl 0719.62055 [30] Scheinkman, J.; Lebaron, B.: Nonlinear dynamics and stock returns. Journal of business 62, 311-337 (1989) [31] Silverman, B. W.: Density estimation for statistics and data analysis. (1986) · Zbl 0617.62042 [32] Skaug, H.; Tjøstheim, D.: Nonparametric tests of serial independence. Developments in time series analysis, 207-229 (1993) · Zbl 0880.62052 [33] Skaug, H.; Tjøstheim, D.: Testing for serial independence using measures of distance between densities. Springer lecture notes in statistics (1996) · Zbl 0880.62052 [34] Stengos, T.: Nonparametric forecasts of gold rates of return. Nonlinear dynamics and economics (1995) · Zbl 1044.91558 [35] White, H., 1988. Economic prediction using neural networks: the case of IBM daily stock returns. Paper No. 88-20, UCSD. [36] Zheng, J., 2000. A specification test of conditional parametric distribution using kernel estimation methods. Econometric Theory.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.