On the Estimation of Financial Risk: A Theoretical Exploration Using ARIMA-GARCH Models

This study investigates the application of advanced statistical models to analyze the Malaysian stock market, with a focus on the ARIMA-GARCH model. Traditional ARIMA models, following the Box-Jenkins approach, are designed to forecast the mean behavior of financial time series, assuming stationarity with constant or seasonally dependent variances. However, these models overlook variations in conditional variance, which are crucial for capturing the nonlinear dynamics often present in financial data. Although the statistical properties of the Malaysian financial market have been widely studied, the adoption of heteroskedastic models that account for non-constant variances remains limited. To address this gap, this research integrates GARCH with ARIMA models to capture both serial dependence and time-varying volatility in daily closing prices. The study focuses on the financial risks of three major Malaysian banks that are Maybank, Public Bank, and CIMB Bank, using a model that effectively reflects market fluctuations. Analyzing daily stock prices from 2000 to 2023, the study employs two key risk measures, namely Value at Risk (VaR) and Expected Shortfall (ES), which help estimate potential losses under adverse conditions. The findings reveal varying risk levels, with Maybank showing a $\mathbf{1 . 1 \%}$ VaR, CIMB Bank $\mathbf{1 . 7 \%}$, and Public Bank $0.7 \%$. This research offers valuable insights for enhancing risk management practices within Malaysia’s banking sector and provides a framework that can benefit other emerging markets.