In Hamilton's paper "What is real about business cycles?" (2005) I have three questions: 1) How do we calculate C(p; theta) on page 451 if we do not know "nuisance" parameter values of p? 2) What was the logic behind setting p(gamma) = 0.2 + 0.6 (|gamma|/sqrt((1+gamma^2)) on the page 451? 3) I tried to read Carrasco, Hu, and Ploberger paper about this test -- does anyone understand why (in Hamilton's notation) gamma_t(p;theta) has such particular formula? How it got derived?
Thank you to anyone who spares time to respond if knows the answers..