(Q7) (Theoretical/Practical Question) In this question we develop Yule-Walker estimators in AR(1) and ARMA(1, 1) models and study their numerical performance. Recall from lectures that in AR(1) model X₁ = 6X₁−1 + Z₁ the Yule-Walker estimator is ổ = ^x(0) – ^^x(1) = ^x(0) – êx(1)^x(0). ^x(1) = Px (1), 7x (0) (a) Numerical experiment for AR(1): * Load into R the file Data-AR.txt. (Just type Data=scan(file.choose()) and then copy and paste). This is data set generated from AR(1) model with = 0.8. * Type var (Data) to obtain x (0). * Type ACF<-acf (Data). Then type ACF. You will get px (h), the estimators of px (h). The second entry will be px (1). Via the formula above this is also o. * Write the final values for and ☎². * Compare your estimated with the true o. (b) Consider ARMA(1, 1) model X₁ = 6Xt-1 + Zt + 0Zt−1, |6| < 1, so that the sequence X, is causal. Apply the Yule-Walker procedure to get the estimators for o, 0 and o² = Var(Z₁). HINT: You should get 7x (2) Yx (1) (0 Yx (1) = 6Yx(0) + 0o², Yx(0) = 0² 7x (0) = 0² [1 = 0² [1 + 0 + 0)²]. 1 - (c) Numerical experiment for ARMA(1, 1): * Load into R the file Data-ARMA.txt. (Just type Data=scan(file.choose()) and then copy and paste). This is data set generated from ARMA(1, 1) model with = 0.8 and 0 = 1. * Write the final values for ô, ô and ☎². * Compare your estimated with the true . Which estimate is more accurate, for ARMA(1, 1) or for AR(1)?
(Q7) (Theoretical/Practical Question) In this question we develop Yule-Walker estimators in AR(1) and ARMA(1, 1) models and study their numerical performance. Recall from lectures that in AR(1) model X₁ = 6X₁−1 + Z₁ the Yule-Walker estimator is ổ = ^x(0) – ^^x(1) = ^x(0) – êx(1)^x(0). ^x(1) = Px (1), 7x (0) (a) Numerical experiment for AR(1): * Load into R the file Data-AR.txt. (Just type Data=scan(file.choose()) and then copy and paste). This is data set generated from AR(1) model with = 0.8. * Type var (Data) to obtain x (0). * Type ACF<-acf (Data). Then type ACF. You will get px (h), the estimators of px (h). The second entry will be px (1). Via the formula above this is also o. * Write the final values for and ☎². * Compare your estimated with the true o. (b) Consider ARMA(1, 1) model X₁ = 6Xt-1 + Zt + 0Zt−1, |6| < 1, so that the sequence X, is causal. Apply the Yule-Walker procedure to get the estimators for o, 0 and o² = Var(Z₁). HINT: You should get 7x (2) Yx (1) (0 Yx (1) = 6Yx(0) + 0o², Yx(0) = 0² 7x (0) = 0² [1 = 0² [1 + 0 + 0)²]. 1 - (c) Numerical experiment for ARMA(1, 1): * Load into R the file Data-ARMA.txt. (Just type Data=scan(file.choose()) and then copy and paste). This is data set generated from ARMA(1, 1) model with = 0.8 and 0 = 1. * Write the final values for ô, ô and ☎². * Compare your estimated with the true . Which estimate is more accurate, for ARMA(1, 1) or for AR(1)?
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Hand written plz..... Only (part c) plzzz fast pzzzz...hand written plzzzz
![(Q7) (Theoretical/Practical Question) In this question we develop Yule-Walker estimators in
AR(1) and ARMA(1, 1) models and study their numerical performance.
Recall from lectures that in AR(1) model X₁ = ¢Xt-1 + Zt the Yule-Walker estimator is
o² = 7x (0) — 7x (1) = x (0) — ēx (1) ²x (0).
^x(1)
7x (0)
= Px (1),
(a) Numerical experiment for AR(1):
* Load into R the file Data-AR.txt. (Just type Data=scan(file.choose()) and then
copy and paste). This is data set generated from AR(1) model with = 0.8.
Type var (Data) to obtain 7x (0).
Type ACF<-acf (Data). Then type ACF. You will get px (h), the estimators of
px (h). The second entry will be px (1). Via the formula above this is also o.
*Write the final values for and ².
* Compare your estimated with the true .
(b) Consider ARMA(1, 1) model X = Xt-1 + Zt +0Zt-1, || < 1, so that the sequence
Xt is causal. Apply the Yule-Walker procedure to get the estimators for ø, 0 and
o2 = Var(Zt).
HINT: You should get
7x (2)
Yx (1) '
= 0 { [ 1 + (0 = 0)²0 ]
(0+)²]
1 -
yx(1) = ¢yx(0) + 0oz, Yx(0) = 6|1+
(c) Numerical experiment for ARMA(1, 1):
* Load into R the file Data-ARMA.txt. (Just type Data=scan(file.choose()) and
then copy and paste). This is data set generated from ARMA(1, 1) model with
= 0.8 and 0 = 1.
* Write the final values for , and 2.
* Compare your estimated with the true . Which estimate is more accurate,
for ARMA(1, 1) or for AR(1)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F19585bc4-222b-4ca3-8f5c-b258e91271d3%2F996431c1-4724-44e1-b3af-38b1f61cce0a%2Fufmobc_processed.png&w=3840&q=75)
Transcribed Image Text:(Q7) (Theoretical/Practical Question) In this question we develop Yule-Walker estimators in
AR(1) and ARMA(1, 1) models and study their numerical performance.
Recall from lectures that in AR(1) model X₁ = ¢Xt-1 + Zt the Yule-Walker estimator is
o² = 7x (0) — 7x (1) = x (0) — ēx (1) ²x (0).
^x(1)
7x (0)
= Px (1),
(a) Numerical experiment for AR(1):
* Load into R the file Data-AR.txt. (Just type Data=scan(file.choose()) and then
copy and paste). This is data set generated from AR(1) model with = 0.8.
Type var (Data) to obtain 7x (0).
Type ACF<-acf (Data). Then type ACF. You will get px (h), the estimators of
px (h). The second entry will be px (1). Via the formula above this is also o.
*Write the final values for and ².
* Compare your estimated with the true .
(b) Consider ARMA(1, 1) model X = Xt-1 + Zt +0Zt-1, || < 1, so that the sequence
Xt is causal. Apply the Yule-Walker procedure to get the estimators for ø, 0 and
o2 = Var(Zt).
HINT: You should get
7x (2)
Yx (1) '
= 0 { [ 1 + (0 = 0)²0 ]
(0+)²]
1 -
yx(1) = ¢yx(0) + 0oz, Yx(0) = 6|1+
(c) Numerical experiment for ARMA(1, 1):
* Load into R the file Data-ARMA.txt. (Just type Data=scan(file.choose()) and
then copy and paste). This is data set generated from ARMA(1, 1) model with
= 0.8 and 0 = 1.
* Write the final values for , and 2.
* Compare your estimated with the true . Which estimate is more accurate,
for ARMA(1, 1) or for AR(1)?
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