Application of Computational Models in Forecasting Stock Prices Using ARCH and GARCH Models: A Case of Apple Stock Prices

This study undertook the rigorous task of forecasting Apple Inc.'s stock prices using sophisticated econometric models: the ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models. These models are renowned for their capacity to capture volatility clustering, a ubiquitous phenomenon in financial time series data. The historical stock return data that were used in the analysis covers a period of August 23, 2022, to 23, 2023, to determine the stock prices in the following week. Diagnostic tests (Linear Regression test, and Engle Lagrange Multiplier Test) were also done to ascertain that the models chosen are appropriate. A high degree of volatility in the data was found based on the tests and this confirmed the existence of the ARCH effects as well as the practicality of the ARCH and GARCH models. Subsequent analysis using the ARCH (1) GARCH (1) model provided insights but showed non-significant GARCH effects, prompting a shift to the ARCH (1) GARCH (2) model. The latter model proved to be robust since each coefficient was significant. Besides, the study proposes a new method since it incorporates an innovative model by using AI/ML techniques and modified conventional econometric models, that is, ARCH and GARCH models, to predict stock prices. The most important findings indicate increased levels of predictive accuracy of this hybrid approach, which offers important information on stock market volatility.