Methodology
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.
Verified MATLAB Simulation Code Demonstration
Syntax-highlighted executable code demonstration for Tesla Shares & GARCH Model Analysis using R:
% MATLAB Constrained Numerical Optimization
clc; clear; close all;
obj_fun = @(x) (x(1)-2)^2 + (x(2)-3)^2;
x0 = [0, 0]; A = [1, 2]; b = 4; lb = [0, 0];
options = optimoptions('fmincon', 'Display', 'off', 'Algorithm', 'sqp');
[x_opt, fval] = fmincon(obj_fun, x0, A, b, [], [], lb, [], [], options);
fprintf('Optimization Solved: Minimum Value = %.4f\n', fval);