Forecasting Tesla (TSLA) stock prices is challenging due to significant price volatility and the complexity of financial markets. Among forecasting approaches

ARIMA models are favored due to their mature theoretical foundation and easily interpretable parameters. Increased computational power and data availability have enabled more sophisticated forecasting techniques. Methods for predicting Tesla stock prices from 2019 through 2024 are systematically examined in this review. The models considered include standard ARIMA

automated ARIMA (via the forecast package's auto.arima() function)

and ARIMA-GARCH combinations that account for volatility clustering. The methodology blends literature analysis with empirical demonstrations. The principles of ARIMA modeling and their implementation in R are introduced

followed by an exploration of Tesla's stock price characteristics and preprocessing steps. The process of fitting these models and generating forecasts is demonstrated using historical price data. It is indicated that automated model selection streamlines the modeling process

while combining ARIMA with GARCH models significantly improves volatility forecasting. For instance

in one study a reduction in forecast error (RMSE) of roughly 15% was observed when using an ARIMA-GARCH model compared to a standalone ARIMA model. It is further demonstrated in comparative studies that ARIMA-GARCH models can reduce short-term forecast errors by roughly 10–20% relative to baseline methods (e.g. random walk models). Overall

ARIMA-based methods are found to be effective for short-term Tesla price forecasts when volatility is properly modeled. The findings suggest that hybrid approaches

which capture both linear trends and volatility dynamics

are shown to outperform simple ARIMA models. Future work may integrate deep learning techniques and multi-source data (such as macroeconomic indicators and sentiment analysis) to build more robust

adaptive forecasting systems.