GARCHGeneralized Autoregressive Conditional Heteroskedasticity
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The GARCH model (Generalized Autoregressive Conditional Heteroskedasticity), proposed by Bollerslev (1986) is a generalization of the ARCH process created by Engle (1982), in which the conditional variance is not only the function of lagged random errors, but also of lagged conditional variances.
Further, the results from GARCH (1, 1) showed that exchange rate, interest rate, and money supply affected the stock return volatility in Nigerian markets.
Ling and McAleer (2002a, 2002b) derived the regularity conditions of a GARCH model as follows: E[[[epsilon].sup.2.sub.t]] = [omega]/1-[alpha] - [beta] < [infinity] if [alpha] + [beta] < 1, and E [[[epsilon].sup.4.sub.t]] < [infinity] if k[[alpha].sup.2] + 2[alpha][beta] + [[beta].sup.2] < 1, where k is the conditional fourth moment of [z.sub.t].
As stock market volatility is one of the most interesting topics in finance, different models have been utilized to measure it (e.g., autoregressive conditional heteroskedastic (ARCH) model of Engle 1982, generalized ARCH (GARCH) model of Bollerslev 1986, the exponential GARCH (EGARCH) model of Nelson 1991).
However, a big bias still exists in traditional GARCH option pricing model.
With regard to the remaining commodities, the T-GARCH model collapses into the standard GARCH form, where the [alpha] and [beta] coefficients are following the [alpha] + [beta] < 1 relation that guarantees stationarity of the variance.
So it's surprising (Garch calls him a breath of fresh air) when he came out to introduce each dish, to see a young, short, tattoed Pinoy who could very well be mistaken for a Pinoy hip hop/rock artist.
For the said purpose, pair wise tests of equality of variances, ARCH-LM tests and multivariate dynamic conditional correlations (DCC) GARCH models are applied.
We use the TGARCH model for analyzing spillover dynamics which has an additional advantage over the GARCH model in capturing asymmetric effects.