<> "The repository administrator has not yet configured an RDF license."^^ . <> . . . "Time evolution of stochastic processes with correlations in the variance: stability in power-law tails of distributions "^^ . "We model the time series of the S&P500 index by a combined process, the AR+GARCH process, where {AR} denotes the autoregressive process which we use to account for the short-range correlations in the index changes and {GARCH} denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long-range correlations in the variance. We study the AR+GARCH process with an initial distribution of truncated Lévy form. We find that this process generates a new probability distribution with a crossover from a Lévy stable power law to a power law with an exponent outside the Lévy range, beyond the truncation cutoff. We analyze the sum of n variables of the AR+GARCH process, and find that due to the correlations the AR+GARCH process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n—a feature which is observed in the probability distribution of the S&P500 index. We find that this power-law stability depends on the characteristic scale in the correlations. We also find that inclusion of short-range correlations through the {AR} process is needed to obtain convergence to a limiting Gaussian distribution for large n as observed in the data. "^^ . "2001" . "300" . "1–2" . . "Elsevier"^^ . . . "Physica A: Statistical Mechanics and its Applications"^^ . . . "03784371" . . . . . . . . . . . . . . . . . . . . . . "H. Eugene"^^ . "Stanley"^^ . "H. Eugene Stanley"^^ . . "Plamen Ch."^^ . "Ivanov"^^ . "Plamen Ch. Ivanov"^^ . . "Youngki"^^ . "Lee"^^ . "Youngki Lee"^^ . . "Alessandro"^^ . "Chessa"^^ . "Alessandro Chessa"^^ . . "Kaushik"^^ . "Matia"^^ . "Kaushik Matia"^^ . . "Boris"^^ . "Podobnik"^^ . "Boris Podobnik"^^ . . . . . "HTML Summary of #1876 \n\nTime evolution of stochastic processes with correlations in the variance: stability in power-law tails of distributions \n\n" . "text/html" . . . "QC Physics"@en . .