TS Module 11: simulated and actual time series HW

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NEAS	NEAS posted 16 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 (1.9K views, 36.00 KB) 0
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chrisdacoolman	chrisdacoolman posted 12 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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