9.7 Using Monte Carlo Simulation to Understand Hypothesis Testing

In chapter 7 we used Monte Carlo simulation to understand the statistical properties of estimators. Now, we will use Monte Carlo Simulation to understand hypothesis testing. To fix ideas, let $R_{t}$ be the return on a single asset described by the GWN model, let $\theta$ denote some parameter of the GWN model we are interested in testing an hypothesis about, let $\hat{\theta}$ denote an estimator for $\theta$ based on a sample of size $T$, and let $\widehat{\mathrm{se}}(\hat{\theta)}$ denote the estimated standard error for $\hat{\theta}$. Suppose we are interested in testing $H_{0}:\theta=\theta_{0}$ against $H_{1}:\theta\neq\theta_{0}$ using the z-score $z_{\theta=\theta_{0}}=\frac{\hat{\theta}-\theta_{0}}{\widehat{\mathrm{se}}(\hat{\theta)}}$.

To be completed