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Autoregressive Conditional Heteroskedasticity

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Autoregressive Conditional Heteroskedasticity (ARCH)
A nonlinear stochastic process, where the variance is time-varying, and a function of the past variance. ARCH processes have frequency distributions which have high peaks at the mean and fat-tails, much like fractal distributions. The ARCH model was invented by Robert Engle. The Generalized ARCH (GARCH) model is the most widely used and was pioneered by Tim Bollerslev. See: Fractal Distributions.

Autoregressive Conditional Heteroskedasticity
A statistical measure of the average error between a best fit line and actual data that uses past data to predict future performance. General Autoaggressive Conditional Heteroskedasticity is the most common way of doing this. See also: Fractal Distribution.


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We propose three alternative specifications of expected future beta based on the past information on realized beta using autoregressive, moving average, and generalized autoregressive conditional heteroskedasticity (GARCH)-in-mean models to obtain time-varying conditional betas for each stock.
Finally, we jointly model the impact of the expiration of these contracts on the returns to the market index and the volatility of these returns, using generalised autoregressive conditional heteroskedasticity (GARCH) models.
Secondly, as a check on these results, we will employ a generalized autoregressive conditional heteroskedasticity (GARCH) (1) model.
 
 
 
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