Event-induced variance

Suppose the event multiplies the disturbance variance by $k$ in the event window but there is no mean effect. Ignore estimation error and treat $L_1$ as large. (a) Show that $Z_{\text{Patell}}\approx N(0,k)$. (b) Compute the true rejection rate of a nominal 5% two-sided Patell test for $k=2$ and $k=4$. (c) Explain why BMP is unaffected, and what assumption about $k$ BMP still needs.