Multivariate probability density functions of returns are constructed inorder to model the empirical behavior of returns in a financial time series.They describe the well-established deviations from the Gaussian random walk,such as an approximate scaling and heavy tails of the return distributions,long-ranged volatility-volatility correlations (volatility clustering) andreturn-volatility correlations (leverage effect). The model is testedsuccessfully to fit joint distributions of the 100+ years of daily pricereturns of the Dow Jones 30 Industrial Average.
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