Parameter Estimation for the GARCH-t Model

Parameter estimation for the GARCH-t model is conducted based on existing stock data. In this process, multiple factors must be considered, such as stock market volatility, market reactions to different stocks, and market conditions across various time periods. To achieve accurate estimation results, various statistical tools and methods are commonly employed for data analysis. Common approaches include Maximum Likelihood Estimation (MLE), Bayesian estimation, and Monte Carlo simulations. These methods help improve the understanding and prediction of stock market trends, thereby providing investors with more reliable decision-making foundations. In code implementation, this typically involves optimizing likelihood functions using numerical methods like the Newton-Raphson algorithm or gradient descent, handling fat-tailed distributions with Student's t-density functions, and implementing volatility recursion equations through iterative loops in programming environments such as MATLAB, R, or Python.