Time Series Analysis of S&P 500 Stocks: A Comparative Study of ARIMA and GARCH Methods

Abstract

The primary aim of this thesis is to analyse stock prices using time series methods, specifically the classical ARIMA model, and the GARCH models that developed by Bollerslev (1986). By comparing these two models, we aim to determine whether GARCH provides more accurate outcomes by detecting and modelling changes in variance over time. The fundamental methodology for GARCH modelling is described in a recent book by Francq and Zakoian (2019) titled ”GARCH Models: Structure, Statistical Inference, and Financial Applications”. An analysis and modelling were conducted on the detrended closing prices of three stocks that show the highest average log returns during 2013 and 2018. The detrended values were derived from the returns of eliminating the linear regression models that fit the trends. The results indicate that the GARCH model was statistically significant for two out of the three stocks with longer data durations, namely NVDA and NFLX. However, the third stock, DXC, which was added to the market in 2017, did not provide more improved and accurate results when analysed using the GARCH model compared to sole usage of ARIMA.