16.322 Stochastic Estimation and Control Professor Vander Velde 1. P(ABCD.=P(A)P(B A)P(C|AB)P(D 1 ABC) Derive this by letting A=CD. Then P(BCD)= P(CD)P(B ICD)= P(C)P(DIC)P(DICD) 2. If A,, A2r.. is a set of mutually exclusive and collectively exhaustive events, then
Testing for Unit roots Consider an AR(1): y=a+p +e,t Let Ho: p=1, (assume there is a unit root) Define 0=p-1 and subtract y, from both sides to obtain Ay,=a+ B+e, Unfortunately, a simple t-test is inappropriate, since this is an I(1) process ADickey-Fuller Test uses the t-statistic, but different critical values Economics 20- Prof anderson