PERBANDINGAN MODEL VOLATILITAS RETURN MENGGUNAKAN MODEL GLOSTEN-JAGANNATHAN-RUNKLE GARCH (GJR-GARCH) DAN EXPONENTIAL GARCH (EGARCH); COMPARISON OF RETURN VOLATILITY MODELS USING GLOSTEN-JAGANNATHAN-RUNKLE GARCH (GJR-GARCH) AND EXPONENTIAL GARCH (EGARCH) MODEL

Al maidah, Firdaus, Dedi Rosadi

2015 | Skripsi | FMIPA UGM

In financial data, ARCH and GARCH models are widely used to describe the shape of the volatility of a time series data. ARCH and GARCH models assume that the positive errors and negative error will give the same effect on volatility (symmetrical). In fact, this assumption is often violated, because the time series data is usually just show the phenomenon of asymmetry between positive error value and negative error value to volatility. This problem can be solved using models GJR-GARCH and EGARCH. This study aims to perform modeling GJR-GARCH (1,1) and EGARCH (1,1). The data used is the stock S & P 500, NASDAQ Composite, and NYSE ARCA Oil and Gas Index. The data available from the period January 1968 to December 2002. This study begins with the transformation of return and selected the best mean model for each of the data return. Based on the mean of the best models of each return then formed GJR-GARCH (1,1) and EGARCH (1,1) volatility models. Then do a comparison of the two models to determine volatility models which one is better. Comparison of models GJR-GARCH (1,1) and EGARCH (1,1) conducted by the maximum value of the log likelihood with BIC and AIC values are small, and followed with a minimum RMSE values. Of the three data can be concluded that the model EGARCH (1,1) is the best volatility models.

Kata Kunci : ARCH and GARCH