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Mean Reversion and the Distribution of United Kingdom Stock Index Returns
Author(s) -
Ashton David,
Tippett Mark
Publication year - 2006
Publication title -
journal of business finance and accounting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.282
H-Index - 77
eISSN - 1468-5957
pISSN - 0306-686X
DOI - 10.1111/j.1468-5957.2006.00637.x
Subject(s) - skewness , mean reversion , econometrics , stock market index , stock (firearms) , mathematics , index (typography) , kurtosis , statistics , goodness of fit , markov chain , normal distribution , computer science , stock market , mechanical engineering , paleontology , horse , world wide web , engineering , biology
Our purpose here is to develop the Pearson Type IV distribution as a candidate for modelling the evolution of short period stock index returns. Here, early work by Praetz (1972 and 1978) and Blattberg and Gonedes (1974) has shown that the scaled ‘ t ’ distribution, which is a particular (symmetric) interpretation of the Pearson Type IV, provides a reasonable description of the way stock index returns evolve over time. Our analysis shows this is certainly not the case for the daily stock index returns on which our empirical analysis is based. There is significant skewness in the data and this cannot be captured by symmetric distributions like the scaled ‘ t ’ and normal distributions. However, the Pearson Type IV, which is a skewed generalisation of the scaled ‘ t ’, is capable of modelling the skewness inherent in our data and in such a way that it satisfies asymptotically efficient goodness of fit criteria. Furthermore, the Pearson Type IV can be derived from a stochastic differential equation with standard Markov properties. This enables one to integrate the distributional and time series properties of the returns process and thereby, facilitates both the interpretation and understanding of the role played by the distribution's parameters in the generation of the underlying stock index returns.