TS Module 11: simulated and actual time series HW
(The attached PDF file has better formatting)
Homework assignment: Partial autocorrelations
[Partial autocorrelations are covered in Module 10, along with sample autocorrelations.]
A stationary ARMA process has ñ2 = 0.20.
ñ1 ranges from 0.2 to 0.7 in units of 0.1.
A. Graph the partial autocorrelation of lag 2 (ö22) as a function of ñ1.
B. Explain why the partial autocorrelation is positive for low ñ1 and negative for high ñ1.
ben, you are correct in your assumption for part A. For part B, examine equation 6.2.3 remembering that rho2 is a constant. The question should answer itself at this point. Let me know if you have any further questions.
I know it's obvious what's going on with phi_22 from the formula, but I'm having trouble answering in a more conceptual, intuitive way. I guess I'm thinking the question is more like, why should the Corr(Y_t, Y_t-2|Y_t-1) become negative when Corr(Y_t, Y_t-1) increases? Am I making this more complicated than it is?
[NEAS: When the correlation for lag 1 increases, more of the correlation for lag 2 is explained by the correlation for lag 1.]
what's meaning , more correltion of lag 2 is explained by lag 1? because of being explained by lag, the phi 22 becomes more negative? I couldn't figure out the relationship between these two consequences.
My guess - Since autocorrelation lag 2 is constant, as autocorrelation lag 1 increases we would expect autocorrelation lag 2 to increase since more and more of it should rely on autocorrelation lag 1. However, since autocorrelation lag 2 is constant, it must be that the autocorrelation of lag 2 removing the effect of intervening variable must be decreasing to make up the difference for the larger effect of autocorrelation lag 1.
I'm unsure if I explained my thought process very well, but that is the general idea I think they are trying to get.
Let me know if you guys come up with a more tangible answer.