Yt = €t – 0.5ɛt–1 + 0.5€t-2 Et ~ WN (0, 1) (a) Find E(y) and Var(y.). (b) Find Cor(yt, Yt–1) and Cor(yt, Yt-2). (c) Is the model above covariance stationary?
Yt = €t – 0.5ɛt–1 + 0.5€t-2 Et ~ WN (0, 1) (a) Find E(y) and Var(y.). (b) Find Cor(yt, Yt–1) and Cor(yt, Yt-2). (c) Is the model above covariance stationary?
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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Question
Consider the following model:
![The text presents a time series model and asks questions regarding its statistical properties.
### Model Description:
The given time series model is:
\[
y_t = \varepsilon_t - 0.5\varepsilon_{t-1} + 0.5\varepsilon_{t-2}
\]
where \(\varepsilon_t\) is a white noise process:
\[
\varepsilon_t \sim WN(0,1)
\]
### Questions:
(a) **Find \(E(y_t)\) and \(Var(y_t)\).**
(b) **Find \(Cor(y_t, y_{t-1})\) and \(Cor(y_t, y_{t-2})\).**
(c) **Is the model above covariance stationary?**
### Explanation:
- **\(E(y_t)\)** refers to the expected value or mean of \(y_t\).
- **\(Var(y_t)\)** refers to the variance of \(y_t\), a measure of the dispersion of the series.
- **\(Cor(y_t, y_{t-1})\)** and **\(Cor(y_t, y_{t-2})\)** refer to the correlation between \(y_t\) and its lagged values, which help in understanding the temporal dependence structure of the series.
- **Covariance Stationarity** requires constant mean, constant variance, and constant autocovariance that depends only on lag for the series.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ebf2759-59a4-4687-9e64-2cf88860377f%2F3d1282c8-6b6c-4083-bf9f-d2ce5c484fcd%2Fdnwvnvp_processed.png&w=3840&q=75)
Transcribed Image Text:The text presents a time series model and asks questions regarding its statistical properties.
### Model Description:
The given time series model is:
\[
y_t = \varepsilon_t - 0.5\varepsilon_{t-1} + 0.5\varepsilon_{t-2}
\]
where \(\varepsilon_t\) is a white noise process:
\[
\varepsilon_t \sim WN(0,1)
\]
### Questions:
(a) **Find \(E(y_t)\) and \(Var(y_t)\).**
(b) **Find \(Cor(y_t, y_{t-1})\) and \(Cor(y_t, y_{t-2})\).**
(c) **Is the model above covariance stationary?**
### Explanation:
- **\(E(y_t)\)** refers to the expected value or mean of \(y_t\).
- **\(Var(y_t)\)** refers to the variance of \(y_t\), a measure of the dispersion of the series.
- **\(Cor(y_t, y_{t-1})\)** and **\(Cor(y_t, y_{t-2})\)** refer to the correlation between \(y_t\) and its lagged values, which help in understanding the temporal dependence structure of the series.
- **Covariance Stationarity** requires constant mean, constant variance, and constant autocovariance that depends only on lag for the series.
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