## 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