Abstract
An important research field in finance is the identification of probability distribution model that fits at the best the empirical distribution of time series returns. In this paper we propose the use of mixtures of truncated normal distributions in modelling returns. An optimization algorithm has been developed to obtain the best fit by using the minimum distance approach. Empirical results show evidence of the capability of the method to fit return distributions at a satisfactory level, completely maintaining local normality properties in the model. Moreover, the model provides a good tail fit thus improving the accuracy of Value at Risk estimates.
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Notes
- 1.
In general, the choice of the window length involves balancing two opposite factors: on the one hand a larger window could embrace changing data generating processes, whereas on the other hand a shorter period implies a smaller data set available for estimation. In our opinion, the selection of the window size depends on the specific application. For the purposes of the empirical investigation proposed in this paper, the choice of equal sized sections of 500 data points seems to be a good compromise between the two factors.
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Bramante, R., Zappa, D. (2014). Fitting Financial Returns Distributions: A Mixture Normality Approach. In: Corazza, M., Pizzi, C. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-02499-8_7
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DOI: https://doi.org/10.1007/978-3-319-02499-8_7
Publisher Name: Springer, Cham
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