Financial Density Selection

Marin, J. Miguel and Sucarrat, Genaro (2012): Financial Density Selection. Published in: The European Journal of Finance , Vol. 21, No. 13-14 (2015): pp. 1195-1213.

Abstract

We propose and study simple but flexible methods for density selection of skewed versions of the two most popular density classes in finance, the exponential power distribution and the t distribution. For the first type of method, which simply consists of selecting a density by means of an information criterion, the Schwarz criterion stands out since it performs well across density categories, and in particular when the Data Generating Process is normal. For the second type of method, General-to-Specific density selection, the simulations suggest that it can improve the recovery rate in predictable ways by changing the significance level. This is useful because it enables us to increase (reduce) the recovery rate of non-normal densities by increasing (reducing) the significance level, if one wishes to do so. The third type of method is a generalisation of the second type, such that it can be applied across an arbitrary number of density classes, nested or non-nested. Finally, the methods are illustrated in an empirical application.

• Item Type: MPRA Paper
• Language: English
• Keywords: Financial returns, density selection, skewed exponential power distribution, skewed t distribution, general-to-specific density selection
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics

References

Aas, K. and D. H. Haff (2006). The Generalized Hyperbolic Skew Student’s t-Distribution. Journal of Financial Econometrics 4, 275–309.

Akaike, H. (1974). A New Look at the Statistical Model Identification. IEEE Transactions on Automatic Control 19, 716–723.

Azzalini, A. (1986). Further results on a class of distributions that includes the normal ones. Statistica 46, 199–208.

Azzalini, A. and A. Capitanio (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. Journal of the Royal Statistical Society B 65, 367–389.

Bauwens, L. and S. Laurent (2005). A new class of multivariate skew densities, with applications to garch models. Journal of Business and Economic Statistics 23, 346–354.

Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics 31, 307–327.

Bollerslev, T. and J. Wooldridge (1992). Quasi-Maximum Likelihood Estimation and Inference in Dynamic Models with Time Varying Covariances. Econometric Reviews 11, 143–172.

Campos, J., D. F. Hendry, and N. R. Ericsson (Eds.) (2005). General-to-Specific Modeling. Volumes 1 and 2. Cheltenham: Edward Elgar Publishing.

DiCiccio, T. J. and A. C. Monti (2004). Inferential Aspects of the Skew Exponential Power Distribution. Journal of the American Statistical Association 99, 439–450.

Fernandez, C., J. Osiewalski, and M. Steel (1995). Modeling and Inference with v-Spherical Distributions. Journal of the American Statistical Association 90, 1331–1340.

Fernandez, C. and M. Steel (1998). On Bayesian Modelling of Fat Tails and Skewness. Journal of the American Statistical Association 93, 359–371.

Glosten, L. R., R. Jagannathan, and D. E. Runkle (1993). On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance 48, 1779–1801.

Hannan, E. and B. Quinn (1979). The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society. Series B 41, 190–195.

Harvey, A. C. (1981). The Econometric Analysis of Time Series. London: Philip Allan.

Harvey, A. C. and T. Chakravarty (2010). Beta-t-EGARCH. Unpublished working paper.

Komunjer, I. (2007). Asymmetric power distribution: Theory and application to risk measurement. Journal of Applied Econometrics 22, 891–921.

Ljung, G. and G. Box (1979). On a Measure of Lack of Fit in Time Series Models. Biometrika 66, 265–270.

Marin, J. M. and G. Sucarrat (2011). Modelling the Skewed Exponential Power Distribution in Finance. In C. Perna and M. Sibill (Eds.), Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, in press.

Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica 59, 347–370.

Schwarz, G. (1978). Estimating the Dimension of a Model. The Annals of Statistics 6, 461–464.

Sorokin, A. (2010). Non-invertibility in Some Heteroscedastic Models. Unpublished working paper.

Straumann, D. and T. Mikosch (2006). Quasi-Maximum-Likelihood Estimation in Conditionally Heteroscedastic Time Series: A Stochastic Recurrence Equations Approach. The Annals of Statistics 34, 2449–2495.

Sucarrat, G. and A. Escribano (2010). The Power Log-GARCH Model. http://www.sucarrat.net/.

Theodossiou, P. (2000). Skewed generalized error distribution of financial assets and option pricing. SSRN working paper.

Wurtz, D. and Y. Chalabi (2009). Package fGarch. www.rmetrics.org. Downloadable via http://cran.r-project.org/web/packages/fGarch/index.html.

Zakoıan, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control 18, 931–955.

Zhu, D. and J. W. Galbraith (2010). A Generalized Asymmetric Student t Distribution with Application to Financial Econometrics. Journal of Econometrics, 297–305.

Zhu, D. and V. Zinde-Walsh (2009). Properties and estimation of asymmetric exponential power distribution. Journal of Econometrics 148, 86–99.