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a) Consider an ARMA(1,1) process given by x₁ = 0.5x₁_₁+z₁ − 0.3z₁_1 Find the first four weights.

a) Consider an ARMA(1,1) process given by x₁ = 0.5x₁_₁+z₁ − 0.3z₁_1 Find the first four weights.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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a) Consider an ARMA(1,1) process given by x₁ = 0.5x-₁ + z — 0.3z_₁ Find the first four weights. b) Classify each of the SARIMA(p, d, q)x(P, D,Q),. (i) x₁ = 0.7 X₁-12 + Z₁ +0.5Z₁-12. (ii) x₁ = Z₁ -1.3z₁-4 +0.4Z₁-8. (iii) (1 – 1.3B + 0.5B² )|1 − B¹² )x₁ = (1 + 0.5B)z, . c) Let {Y} be a stationary process with mean zero and let a and b be constants. If x₁ = a + bt + S₁ + Y, where s, is a seasonal component with period 12, show that following models as 12 VV ₁2 x₁ = (1-B)(1 – B¹²)x, is stationary. 12 (Hint: Use the fact that the seasonal effect is the same for all times, i.e. s₁ St-12, for all t.) =
Transcribed Image Text:a) Consider an ARMA(1,1) process given by x₁ = 0.5x-₁ + z — 0.3z_₁ Find the first four weights. b) Classify each of the SARIMA(p, d, q)x(P, D,Q),. (i) x₁ = 0.7 X₁-12 + Z₁ +0.5Z₁-12. (ii) x₁ = Z₁ -1.3z₁-4 +0.4Z₁-8. (iii) (1 – 1.3B + 0.5B² )|1 − B¹² )x₁ = (1 + 0.5B)z, . c) Let {Y} be a stationary process with mean zero and let a and b be constants. If x₁ = a + bt + S₁ + Y, where s, is a seasonal component with period 12, show that following models as 12 VV ₁2 x₁ = (1-B)(1 – B¹²)x, is stationary. 12 (Hint: Use the fact that the seasonal effect is the same for all times, i.e. s₁ St-12, for all t.) =
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