Comparison of different statistical models in financial time series analysis

The main purpose of this study is to investigate the use of Box-Jenkins models and ARCH (autoregressive conditional heteroskedasticity), GARCH (generalized autoregressive conditional heteroskedasticity), EGARCH (exponential GARCH) and GJR-GARCH (Glosten, Jagannathan and Runkle GARCH) from ARCH/GARCH family models for examining the returns of BIST 100, FTSE 100, NIKKEI 225 and S&P 500 indices. Predictions of conditional heteroskedasticity models constructed after the determination of suitable ARMA models are obtained under the normal distribution, the t distribution, and the generalized error distribution and their skew variants. As a result of a series of graphical and statistical evaluations performed for the models, it was seen that EGARCH and GJR-GARCH models outperformed ARCH and GARCH models. Furthermore, it was determined that the normal and skewed normal distributions performed worse than the other distributions. It has also been determined that indices were more affected by negative shocks than positive shocks. On the other hand, it was concluded that bad news affected BIST 100 index less than other indices, and shocks affected volatility in BIST 100 index longer than other indices.