GARCH Model Fitting For IBM

Introduction:
Nowadays, many econometric studies have documented that financial return time series tend to be highly heteroskedastic, with varying variability or volatility and thick-tailed marginal distribution. Volatility is the conditional variance, which is unobservable and tends to be clustered together. Clustering is referred to as the phenomenon that large price changes of either signs tend to be followed by large changes, and similarly small changes follow small changes. Sudden bursts of volatility in financial returns exhibit strong dependence on the return time series, and a period of tranquility alternates with a period of volatility bursts. A popular ARCH, which is called Autoregressive Conditional Heteroscedasticity, modeling was introduced to capture the predictability of volatility ad the volatility clustering as well as the thick-tailed marginal distribution of the return time series. The tremendous success of GARCH modeling in empirical work makes may econometricians to treat it as the benchmark model for financial time series.
Data Description:
In this GARCH model fitting report, I use the history of stock price of IBM from January 2nd, 2013, to December 31th, 2013, collecting the data of “High”, “Low”, “Close”, and so on. At the beginning, I run the ACF for the log return and squared log return of IBM to get the autocorrelation for them. Then, by assuming that the model is normal distribution, we use the R to fit a GARCH model (1, 1) for the returns and analyzing the data output. If the GARCH model doesn’t fit well for the data, I will try T distribution or EGARCH instead in order to find a better model. After having a mostly fitted model, I plot the volatility of the model and forecast the possible trend or output for the next 5 days.

Model Fitting:
By fitting the model to GARCH (1, 1) and assuming it is