Hi All, I just wanted to check on the correct degrees of freedom to be applied for the Ljung and Box ‘portmanteau’ test. The examiner's report mentions that it should be 3 as dof is "number of lags less p + q, where the null hypothesis is that Y_t is an ARMA(p, q) process. In this case p = q = 0 since the null hypothesis is that Y_t is a white noise process." So I'm very confused on this point. Why would the null hypo be that Y_t is a white noise process when in part a of the same question, it has been stated that Y_t is an ARIMA(2,0,0) process. Thanks very much for your help!
Hi Laura First thing to note is that this is an extremely hard question, the hardest on the paper in my opinion. The theme that runs through the question is "how much evidence do we need to decide that there is structure in a time series?", ie that the process is not simply white noise. For part (iv), although we know the process is ARMA(2, 0), we are assessing how many observations we would need to discover this. In other words, how many observations we would need to reject the null hypothesis that the process is white noise. So in this case H0 is that the series is white noise, and thus we are assuming ARMA(0, 0) when we set the degrees of freedom, ie p + q = 0. If it helps, I made exactly the same error as you when I attempted this paper! Hope that helps Dave
