Analysis of Tesla shares returns and developing Garch Model using R programming

Abstract

MATLABSolutions demonstrate Analyzing the returns of Tesla shares and developing a GARCH (Generalized Autoregressive Conditional Heteroskedasticity) model can help in understanding and predicting the volatility of the stock's returns. Let's break down the process into several steps:
Data Collection: Obtain historical price data for Tesla shares, preferably with daily or higher frequency. The data should cover a sufficiently long period, including both up and down market conditions.

To develop a GARCH model for Tesla's stock returns, you need to follow these steps:

a) Determine the appropriate lag order: Test different lag orders for the AR and MA components using statistical criteria (e.g., Akaike Information Criterion, Bayesian Information Criterion) to select the best-fitting model.
b) Estimate the GARCH model: Fit the selected GARCH model to the historical returns data using maximum likelihood estimation. This estimation process will provide parameter estimates for the AR and MA components, as well as the volatility persistence (GARCH) parameters.
c) Model diagnostics: Assess the model's goodness of fit by examining residual plots, autocorrelation of squared residuals, and Ljung-Box tests for residual independence. If the model fails to meet the assumptions, you may need to refine the model specification.
d) Forecasting: Once you have a satisfactory GARCH model, you can use it to forecast future volatility. The model provides predictions of the conditional variance, which can be used to estimate future volatility levels and construct confidence intervals.

It's important to note that developing a GARCH model requires some statistical knowledge and expertise in time series analysis. Additionally, the accuracy of the model's forecasts depends on the quality of the historical data and the assumption that future volatility will behave similarly to the past.