Suppose a time series of returns r, follows the following recursive formula: = (1 — αL)(1 — BL³) at where a, is a normal white noise series with variance 6₂. The integer constant S>3 models the seasonal effect. What type of model is r, and what is its order? Calculate the mean and variance of r,. Calculate the covariance of r, and r₁-, as well as the covariance of r, and r₁-2. Calculate the lag s-1, s and s + 1 autocorrelation of r,.
Suppose a time series of returns r, follows the following recursive formula: = (1 — αL)(1 — BL³) at where a, is a normal white noise series with variance 6₂. The integer constant S>3 models the seasonal effect. What type of model is r, and what is its order? Calculate the mean and variance of r,. Calculate the covariance of r, and r₁-, as well as the covariance of r, and r₁-2. Calculate the lag s-1, s and s + 1 autocorrelation of r,.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please provide a derivation of the results. Thank you!
![Suppose a time series of returns r, follows the following recursive formula:
= (1 — αL)(1 – BL³) at
where a, is a normal white noise series with variance 6₂. The integer constant S> 3 models the seasonal
effect.
-
What type of model is r, and what is its order?
Calculate the mean and variance of r,.
Calculate the covariance of r, and r₁-, as well as the covariance of r, and r₁-2.
Calculate the lag s-1, s and s + 1 autocorrelation of r, .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3414f6b8-acb6-4d57-a5de-a971cbe05261%2F4340adcd-6307-4b22-bd7e-be20bbe38d84%2Fqrtgroc_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose a time series of returns r, follows the following recursive formula:
= (1 — αL)(1 – BL³) at
where a, is a normal white noise series with variance 6₂. The integer constant S> 3 models the seasonal
effect.
-
What type of model is r, and what is its order?
Calculate the mean and variance of r,.
Calculate the covariance of r, and r₁-, as well as the covariance of r, and r₁-2.
Calculate the lag s-1, s and s + 1 autocorrelation of r, .
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