Dear all,
kindly update me about the latest models on volatility check of stock market indices. Whether GARCH model are outdated?
I also want to know that While using GARCH models the reason to use the order levels like 1-1, 2-1, 2-2. etc. I mean why we use any particular order in GARCH models.
One more question is that why a long study period is considered good in GARCH model studies related to volatility. while the reality is that GARCH model can be applied to one year data also that dictates the dynamics of volatility in that particular year. if we take long period and apply GARCH model to analyse volatility dynamics then how can we say that study is good or not while the reality is that long years can or can't follow a trend.
thanks and regards....
Absolutely not! GARCH models are the most widely used tools to estimate volatility in financial markets. Actually, GARCH models are used to describe financial markets in which volatility is time-varying. You can use different forms of GARCH (EGARCH, PARCH, NGARCH, IGARCH, ...).
If an ARMA (Auto Regressive Moving Average) model is assumed for the error term variance, then we have a GARCH model. Then, GARCH(p,q) has two orders (p and q). p is the order (Number) of AR terms, and q is the order (Number) of MA terms.
I didn't fully understand your last question about sampling period!
Garch models are not at all outdated for modelling volatility of financial data. Their order can be determined by graphical methods. For the time series X, if the autocorrelation function of X-squared cuts off at lag q and the partial autocorrelation cuts off at lag p this is indicative of a Garch(p,q) model for X.
You can determine the order of GARCH model performing the goodness-of-fit tests. Your squared residuals should not exhibit any autocorrelation. If the latter is true, then you do not need to include more lags. In most empirical situations GARCH(1,1) is enough and if your squared residuals still exhibit autocorrelation you should re-specify the model either including more lags or change specification to FIGARCH, IGARCH or even regime-switching/treshold etc. - if you suspect a structural change. It is hard to say, when you do not see the data. When it comes to the period - it depends. First step is to perform Nyblom test of stability of your parameters. If the period is calm, then your GARCH model can perform well over a long period of time. If the time is hectic, and structural changes are possible, probably you will need to change the specification. Once again - after estimating the model you should perform the goodness-of-fit tests. They will show you whether your specification is OK or whether you still should work on it.
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