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