In reference to modeling fitting, this means the residuals vary in magnitude. Volatility clustering means the data is auto correlated. GARCH is a statistical tool that helps predict the residuals in k data
ARCH means Autoregressive Conditional Heteroskedasiticy and is closely related to GARCH. The simplest method to predict stock volatility is an n day standard deviation, and let’s consider a rolling year with 252 trading days. If we want to predict stock prices for the next day, the mean is usually a safe starting point.
But the mean treats each day with the same weight. Giving the recent past more significance is more logical, with perhaps an exponential weighted average being a better method to predict tomorrow’s stock price.
However, this method does not capture any data older than a year, and the weighting is rather arbitrary. The ARCH model, however, varies weights on each residual such that the best fit is obtained. The GARCH (General Autoregressive Conditional Heteroscedasiticy) is similar, but gives recent data more significance.
The GARCH(p,q) model has two characteristic parameters; p is the number of GARCH terms and q is the number of ARCH terms. GARCH(1,1) is defined by the following equation.
h is variance, ε is the residual squared, t denotes time. ω, α and β are empirical parameters determined by maximum likelihood estimation. The equation tells us that tomorrow’s variance is a function of
today’s squared residual,
today’s variance,
the weighted average long-term variance
GARCH(1,1) captures only once square residual and one square variance.
This is not a magic wand, and financial analysts should be use the approach with a high degree of caution. Given the appropriate circumstance, the predicted variance can greatly differ from the actual variance. Techniques such as the Ljung box text are used to determine if any autocorrelation remains in the residuals.
发表于 2015-1-20 21:46
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