TS Module 11: simulated and actual time series HW


TS Module 11: simulated and actual time series HW

Author
Message
NEAS
Supreme Being
Supreme Being (5.7K reputation)Supreme Being (5.7K reputation)Supreme Being (5.7K reputation)Supreme Being (5.7K reputation)Supreme Being (5.7K reputation)Supreme Being (5.7K reputation)Supreme Being (5.7K reputation)Supreme Being (5.7K reputation)Supreme Being (5.7K reputation)

Group: Administrators
Posts: 4.2K, Visits: 1.2K

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.


 

 

 


Attachments
benjaminttp
Forum Newbie
Forum Newbie (7 reputation)Forum Newbie (7 reputation)Forum Newbie (7 reputation)Forum Newbie (7 reputation)Forum Newbie (7 reputation)Forum Newbie (7 reputation)Forum Newbie (7 reputation)Forum Newbie (7 reputation)Forum Newbie (7 reputation)

Group: Forum Members
Posts: 6, Visits: 1
part A, so the graph is like showing rho on x-axis and phi on y-axi?
part B, what is this about?
RayDHIII
Forum Member
Forum Member (43 reputation)Forum Member (43 reputation)Forum Member (43 reputation)Forum Member (43 reputation)Forum Member (43 reputation)Forum Member (43 reputation)Forum Member (43 reputation)Forum Member (43 reputation)Forum Member (43 reputation)

Group: Forum Members
Posts: 39, Visits: 138

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.

RDH


CalLadyQED
Forum Guru
Forum Guru (66 reputation)Forum Guru (66 reputation)Forum Guru (66 reputation)Forum Guru (66 reputation)Forum Guru (66 reputation)Forum Guru (66 reputation)Forum Guru (66 reputation)Forum Guru (66 reputation)Forum Guru (66 reputation)

Group: Forum Members
Posts: 62, Visits: 2

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.]


minnie53053
Junior Member
Junior Member (13 reputation)Junior Member (13 reputation)Junior Member (13 reputation)Junior Member (13 reputation)Junior Member (13 reputation)Junior Member (13 reputation)Junior Member (13 reputation)Junior Member (13 reputation)Junior Member (13 reputation)

Group: Forum Members
Posts: 11, Visits: 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.


moo5003
Junior Member
Junior Member (11 reputation)Junior Member (11 reputation)Junior Member (11 reputation)Junior Member (11 reputation)Junior Member (11 reputation)Junior Member (11 reputation)Junior Member (11 reputation)Junior Member (11 reputation)Junior Member (11 reputation)

Group: Forum Members
Posts: 10, Visits: 60

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.


chrisdacoolman
Forum Newbie
Forum Newbie (4 reputation)Forum Newbie (4 reputation)Forum Newbie (4 reputation)Forum Newbie (4 reputation)Forum Newbie (4 reputation)Forum Newbie (4 reputation)Forum Newbie (4 reputation)Forum Newbie (4 reputation)Forum Newbie (4 reputation)

Group: Awaiting Activation
Posts: 2, Visits: 40
Using this definition I found online:

“A partial autocorrelation is the amount of correlation between a variable and a lag of itself that is not explained by correlations at all lower-order-lags. The autocorrelation of a time series Y at lag 1 is the coefficient of correlation between Y(t) and Y(t-1), which is presumably also the correlation between Y(t-1) and Y(t-2). But if Y(t) is correlated with Y(t-1), and Y(t-1) is equally correlated with Y(t-2), then we should also expect to find correlation between Y(t) and Y(t-2). (In fact, the amount of correlation we should expect at lag 2 is precisely the square of the lag-1 correlation.) Thus, the correlation at lag 1 "propagates" to lag 2 and presumably to higher-order lags. The partial autocorrelation at lag 2 is therefore the difference between the actual correlation at lag 2 and the expected correlation due to the propagation of correlation at lag 1. “

http://people.duke.edu/~rnau/411arim3.htm

And the hint given by NAES

When the correlation for lag 1 increases, more of the correlation for lag 2 is explained by the correlation for lag 1“



B) Because the partial auto correlation is the amount of correlation between a variable and a lag of itself that is NOT explained by correlations at all lower-order-lags, a low ρ1 means that less of the correlation for the lag 2 is explained by the correlation for lag 1. Thus less of the partial correlation is explained by the lower-order-lag and more is explained by the variable and a log of itself, making the partial auto correlation greater/positive at lower values of ρ1. At higher values of ρ1 the opposite is true and less correlation is explained by the variable and a log of itself, which makes the partial auto correlation negative.
GO
Merge Selected
Merge into selected topic...



Merge into merge target...



Merge into a specific topic ID...





Reading This Topic


Login
Existing Account
Email Address:


Password:


Social Logins

  • Login with twitter
  • Login with twitter
Select a Forum....











































































































































































































































Neas-Seminars

Search