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
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 6E
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Question
![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.)
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c17a710-26d7-4116-b1b9-95b1f447e8a0%2Fd25ef976-497c-4635-ac6a-651626dac04d%2F0hi1p8_processed.jpeg&w=3840&q=75)
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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