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.

We have to use definition of stationary time series.

Answered: Yt = €t – 0.5ɛt–1 + 0.5€t-2 Et ~ WN (0,…

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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Given the estimated linear model shown below, complete the following computations. y = 15+ 2x1 + 6x2 + 4x3 a. Compute y when x, = 29, x2 = 32, and x3 = 33. %3D b. Compute y when x, = 23, x2 = 12, and x3 = 14. c. Compute y when x, = 27, x2 = 18, and x3 = 24. d. Compute y when x, = 33, x, = 20, and x3 = 18. а. у 3D
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Kindly show me complete work clearly.
i want Solution Part 1, 2,3
Given the estimated linear model shown below, complete the following computations. y = 13 + 5x, + 3x2 + 4X3 a. Compute y when x4 16, x2 = 14, and x3 = 11. b. Compute y when x, = 27, x2 = 18, and x3 = 14. c. Compute y when x, = 31, xX, = 27, and x3 = 22. d. Compute y when x, = 11, x2 = 25, and X3 = 31. а. a. y = 179 b. ý =]
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Given the estimated linear model shown below, complete the following computations. y = 13+ 5x, + 3x2 + 4x3 a. Compute y when x, = 16, x2 = 14, and x3 = 11. %3D %3D b. Compute y when x, = 27, x2 = 18, and x3 = 14. c. Compute y when x, = 31, x2 = 27, and x3 =22. d. Compute y when x, = 11, x, = 25, and | X3 = 31. a. y = 179 b. у %3

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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?