Density forecasting of the Dow Jones share index

Öller, L-E and Stockhammar, P (2009): Density forecasting of the Dow Jones share index.

Abstract

The distribution of differences in logarithms of the Dow Jones share index is compared to the normal (N), normal mixture (NM) and a weighted sum of a normal and an Assymetric Laplace distribution (NAL). It is found that the NAL fits best. We came to this result by studying samples with high, medium and low volatility, thus circumventing strong heteroscedasticity in the entire series. The NAL distribution also fitted economic growth, thus revealing a new analogy between financial data and real growth.

• Item Type: MPRA Paper
• Language: English
• Keywords: Density forecasting, heteroscedasticity, mixed Normal- Asymmetric Laplace distribution, Method of Moments estimation, connection with economic growth.
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C20 - General

References

Aghion, P. and Howitt, P. (1992) A model of growth through creative destruction. Econometrica, 60, 323-351.

Bao, Y. and Lee, T-H. (2006) Asymmetric predictive abilities of nonlinear models for stock returns: evidence from density forecast comparison. Econometric Analysis of Financial and Economic Time Series / Part B, Advances in Econometrics, 20, 41-62.

Diebold, F. X., Gunther, T. A. and Tay. A. S. (1998) Evaluating density forecasts with applications to financial risk management. International Economic Review, 39, 863-883.

Hodrick, R. J. and Prescott, E. C. (1980) Postwar U.S. business cycles: An empirical investigation. Discussion paper 451, Carnegie-Mellon University.

Hyndman, R. J., Koehler, A. B., Ord, J. K. and Snyder, R. D. (2008) Forecasting with exponential smoothing. Springer Verlag, Berlin.

Kozubowski, T. J. and Podgorski, K. (1999) A class of asymmetric distributions. Actuarial Research Cleraring House,1, 113-134.

Kozubowski, T. J. and Podgorski, K. (2000) Asymmetric Laplace distributions. The Mathematical Scientist, 25, 37-46.

Madan, D. B. and Senata, E. (1990) The Variance Gamma (V.G.) model for share market returns. Journal of Business, 63, 511-524.

Madan, D. B., Carr, P. and Chang, E. C. (1998) The variance gamma process and option pricing. European Finance Review, 2, 74-105.

Reed, W. J. and Jorgensen, M. A. (2004) The double Pareto-lognormal distribution - A new parametric model for size distributions. Communications in Statistics: Theory and Methods, 33(8), 1733-1753.

Rosenblatt, M. (1952) Remarks on a multivariate transformation. Annals of Mathematical Statistics, 23, 470-472.

Shepard, N. (1994) Partial non-gaussian state space. Biometrika, 81, 115-131.

Stockhammar, P. and Öller, L-E. (2008) On the probability distribution of economic growth. Research Report 2008:5, Department of Statistics, Stockholm University.

Wallis, K. F. (1999) Asymmetric density forecasts of inflation and the Bank of England´s fan chart. National Institute Economic Review, 167, 106-112.