An asymmetric ARCH model and the non-stationarity of Clustering and Leverage effects

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We propose a new volatility model based on two stylized facts of the volatility in the stock market: clustering and leverage effect. We calibrate our model parameters, in the leading order, with 77 years Dow Jones Industrial Average data. We find in the short time scale (10 to 50 days) the future volatility is sensitive to the sign of past returns, i.e. asymmetric feedback or leverage effect. However, in the long time scale (300 to 1000 days) clustering becomes the main factor. We study non-stationary features by using moving windows and find that clustering and leverage effects display time evolutions that are rather nontrivial. The structure of our model allows us to shed light on a few surprising facts recently found by Chicheportiche and Bouchaud.