TSS module 9 ARI processes

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NEAS	NEAS posted 14 Years Ago #10185 #
Supreme Being Group: Administrators Posts: 4.3K, Visits: 1.3K	TSS module 9 ARI processes. Cryer and Chan, chapter 5, show how to convert ARI (intergrated autoregressive) processes to stationary autoregressive process by taking differences. The ARI(1,1) format is shown in this illustrative test question, using equation 5.2.12 on page 97. Cryer and Chan provide the general expression for ARI(p,1) processes. Question 1.2: ARI(1,1) process Which of the following is an ARI(1,1) process? A. Y_t = Y_t-1 – (1 + ö) Y_t-2 + e_t B. Y_t = Y_t-1 + ö Y_t-2 + e_t C. Y_t = Y_t-1 – ö Y_t-2 + e_t D. Y_t = (1 + ö) Y_t-1 – ö Y_t-2 + e_t E. Y_t = (1 + ö) Y_t-1 + ö Y_t-2 + e_t Answer 1.2: D Y_t = (1 + ö) Y_t-1 – ö Y_t-2 + e_t ➾ Y_t – Y_t-1 = ö Y_t-1 – ö Y_t-2 + e_t ➾ ∇Y_t = ö ∇Y_t-1 + e_t Final exam problems give ö₁, ö₂, … and derive the underlying AR(p) process. They also test variances of Y_t given a starting point for the time series, covariances, and correlations. Question 1.3: ARI(1,1) process An ARI(1,1) process Y_t has first differences ∇ Y_t that are an AR(1) process with parameter ö = 0.5. Y_t – Y_t-1 = ö (Y_t-1 – Y_t-2) + å_t The ARI(1,1) process is written as a non-stationary ARMA process with weights øj applied to the error terms: Y_t = ø₀ å_t + ø₁ å_t-1 + ø₂ å_t-3 + ø₃ å_t-3 + … What is the value of ø₂? A. 0.25 B. 0.5 C. 0.75 D. 1 E. 1.75 Answer 1.3: E See equation 5.2.15 on page 97: For ö = 0.5 and k = 2, this gives (1 – 0.5²⁺¹) / (1 – 0.5) = ⅞ / ½ = 1.75 Intuition:* Expand the expression for the ARI(1,1) process: Y_t – Y_t-1 = ö (Y_t-1 – Y_t-2) + å_t Y_t = (1 + ö) Y_t-1 – ö Y_t-2 + å_t Y_t = (1 + ö) Y_t-1 – ö Y_t-2 + å_t Attachments TSS module 9 ARI processes df.pdf (1.9K views, 55.00 KB) 0
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CalLadyQED	CalLadyQED posted 13 Years Ago #10406 #
Forum Guru Group: Forum Members Posts: 62, Visits: 2	I thought we didn't need to know the Section 5.2 equations. Please clarify what is required as both questions above seem to require knowing or deriving equations from that section in order to solve them. EDIT: I found the answer in NEAS' response regarding the revised reading here: http://www.neas-seminars.com/discussions/shwmessage.aspx?ForumID=354&MessageID=10181 As I understand, for Jan 2011, we are not required to know the section 5.2 equations, as all questions relating to them should be readily answerable by intuition and/or first principles. After the Jan '11 final, those equations will need to be memorized and understood. 0
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