Analyzing the Selective Stock Price Index Using Fractionally Integrated and Heteroskedastic Models

Stock market indices are important tools to measure and compare stock market performance. The Selective Stock Price (SSP) index reflects fluctuations in a set value of financial instruments of Santiago de Chile’s stock exchange. Stock indices also reflect volatility linked to high uncertainty or potential investment risk. However, economic shocks are altering volatility. Evidence of long memory in SSP time series also exists, which implies long-term persistence. In this paper, we studied the volatility of SSP time series from January 2010 to September 2023 using fractionally heteroskedastic models. We considered the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) innovations—the ARFIMA-GARCH model—for SSP log returns, and the fractionally integrated GARCH, or FIGARCH model, was compared with a classical GARCH one. The results show that the ARFIMA-GARCH model performs best in terms of volatility fit and predictive quality. This model allows us to obtain a better understanding of the observed volatility and its behavior, which contributes to more effective investment risk management in the stock market. Moreover, the proposed model detects the influence volatility increments of the SSP index linked to external factors that impact the economic outlook, such as China’s economic slowdown in 2012 and the subprime crisis in 2008.