We propose a simple stochastic model for time series which is analytically tractable,  easy to simulate and which captures some relevant stylized facts of financial indexes , including scaling properties. We show that the model fits the Dow Jones Industrial Average timeseries in the period 1935-2009 with a remarkable accuracy . Despite its simplicity , the model has several interesting features . The volatility is not constant and displays high peaks. The empirical distribution of the log-returns (increments of the logarithm of the index) is non-Gaussian and may exhibit heavy tails. Log-returns corresponding to disjoint time intervals are uncorrelated but not independent: the correlation of their absolute values decays exponentially fast in the distance between the time intervals for large distances, while it has a slower decay for moderate distances. Finally, the distribution of the log-returns obeys scaling relations that are detected on real time series, but are not satisfied by most available models .
We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of financial assets , including scaling properties. In particular, the model displays a crossover in the log-return distribution from power-law tails (small time) to a Gaussian behavior (large time), slow decay in the volatility autocorrelation and multiscaling of moments . Despite its few parameters , the model is able to fit several key features of the time series of financial indexes, such as the Dow Jones Industrial Average, with a remarkable accuracy .
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model for time series
volatility model
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very
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indexes
assets
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We show that the model fits the Dow Jones Industrial Average timeseries in the period 1935-2009 with a remarkable accuracy
In particular, the model displays a crossover in the log-return distribution from power-law tails (small time) to a Gaussian behavior (large time), slow decay in the volatility autocorrelation and multiscaling of moments
R
simplicity
few parameters
R
has several interesting features . The volatility is not constant and displays high peaks. The empirical distribution of the log-returns (increments of the logarithm of the index) is non-Gaussian and may exhibit heavy tails. Log-returns corresponding to disjoint time intervals are uncorrelated but not independent: the correlation of their absolute values decays exponentially fast in the distance between the time intervals for large distances, while it has a slower decay for moderate distances. Finally, the distribution of the log-returns obeys scaling relations that are detected on real time series, but are not satisfied by most available models
is able to fit several key features of the time series of financial indexes, such as the Dow Jones Industrial Average, with a remarkable accuracy