TS Module 11: simulated and actual time series HW

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NEAS	NEAS posted 15 Years Ago #8693 #
Supreme Being Group: Administrators Posts: 4.5K, Visits: 1.6K	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 TS Module 11 partial autocorrelations HW.pdf (1.8K views, 36.00 KB) 0
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benjaminttp	benjaminttp posted 14 Years Ago #9532 #
Forum Newbie 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? 0
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RayDHIII	RayDHIII posted 14 Years Ago #9544 #
Forum Member 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 0
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CalLadyQED	CalLadyQED posted 13 Years Ago #10401 #
Forum Guru 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.] 0
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minnie53053	minnie53053 posted 13 Years Ago #10713 #
Junior Member 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. 0
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moo5003	moo5003 posted 13 Years Ago #11139 #
Junior Member 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. 0
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chrisdacoolman	chrisdacoolman posted 11 Years Ago #12728 #
Forum Newbie 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. 0
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