GARCH(1,1) Maximum Likelihood Estimation with Model Validation

In MATLAB, you can estimate parameters for the GARCH(1,1) model using Maximum Likelihood Estimation (MLE). The implementation typically involves defining the GARCH model structure using the garch function, specifying the optimization algorithm for MLE, and computing standard errors for parameter significance testing. To validate that your model specification is correct, you should perform simulation-based hypothesis testing to examine two types of errors: size (Type I error) and power (Type II error). This involves generating simulated data from your estimated GARCH model, then applying statistical tests to these synthetic datasets to analyze error rates. The simulation process requires creating multiple Monte Carlo paths using the filtered volatility series and random innovation terms. If you detect significant errors during testing, you should adjust model parameters accordingly and rerun the simulation analysis. This iterative refinement process continues until you identify the optimal model specification that minimizes both Type I and Type II errors. This validation framework ensures your GARCH model accurately captures volatility dynamics and provides reliable forecasts for future market trends.