3. Consider the MA(2) model y, = ɛ, + 0ɛ,-2. where < 1 and (s,) WN(0, 1).(a) Find the autocovariance functions of (y,).(b) Is this model weakly stationary?(c) Compute the variance of the sample mean (y, + y2 + ys)/3 when 0 0.5.

A Moving Averages MA(2) process takes the form (a) yt = εt+θεt-2 where θ <1 and {εt }…

Answered: 3. Consider the MA(2) model y, = E, +…

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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The variance of temperatures (Fahrenheit) in Mobile, Ala. is 165.16. What is this variance if temp is re-expressed in Celsius? [Hint: Conversion between Fahrenheit and Celsius is a linear transformation: Fahrenheit = Celsius*1.80 + 32, or Celsius = Fahrenheit*(1/1.80) - (32/1.80)]
Suppose that X and Y are unknowns with E ( X ) = 10, Var ( X ) =4, E ( Y ) = 12 and Var ( Y ) = 100. In addition, suppose that the correlation coefficient of X with Y is .8. Then what is the expected value of XY?
Define the Distributed Lag Model with Additional Lags and AR(p) Errors?
Suppose that the response y is generated by y = f(x) + €, where e is a zero-mean Gaussian noise with variance 1. a) Suppose that f(x) = x. Randomly generate 10 x's and generate the corresponding y's; you need to generate two random numbers (i.e., x and e for each of the 10 points). Fit the data with linear regression and plot the scatter points. b) Suppose that f(x) = x². Randomly generate 10 (x, y) pairs. Fit the data with linear regression and plot the scatter points. c) Suppose that f(x) = 1/x. Randomly generate 10 (x, y) pairs. Fit the data with linear regression and plot the scatter points.
In an analysis of a sample of bivariate data concerning the soil acidity x (in pH) and germination time y (in days) for tomato seeds, a linear regression model is constructed and follows the equation y^=−1.22x+5y^=−1.22x+5 Select the most appropriate statement about the linear correlation exhibited. A. The data set exhibits strong positive linear correlation. B.We cannot determine anything about the strength or direction of linear correlation from this information alone. C. The data set exhibits strong negative linear correlation. D. The linear correlation coefficient is -1.22.
There is a relationship between the following variables as y = 1 / (a * x ^ b) (x ^ b: means x over b). a) Calculate the correlation coefficient and interpret the degree of the relationship? b) Estimate the y value for x = 4.3 and the x value for y = 0.90 by obtaining the regression equation. x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10 x 1.2 1.5 2.0 3.0 4.0 5.0 y 0.58 0.50 0.32 0.18 0.15 0.10
If Linear correlation coefficient r = 0.794556 Coefficient of determination = 0.631319 Equation of regression line is y = 16.5523 + %3D 0.725938x then both variables are moving in the same direction. A True В False
For two variables X and Y, we have two regression lines 2X-7Y+3=0 and aX+bY+6=0 for some constants a and b. Suppose we know that X = 2 and Y = 1. Also the second regression line passes through (4, 5). Find the correlation coefficient of these two lines.
For the data shown to the right, determine the linear.correlation coefficient using the formulas shown below. Compare your answers in part (a) and (b). 3 5 2| 1| 0 |-1-2 y a. Use the definition r= SySy Exy - (Ex)(E»)/n b. Use the computing formula r= a. Using the definition, r= (Round to three decimal places as needed.)
Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain
Consider an MA(2) model: STEPS -Write the equation of the M(2) model-Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.
The variance of temperatures (Fahrenheit) in Las Vegas, Nev. is 327.84. What is this variance if temp is re-expressed in Celsius? [Hint: Conversion between Fahrenheit and Celsius is a linear transformation: Fahrenheit = Celsius*1.80 + 32, or Celsius = Fahrenheit*(1/1.80) - (32/1.80)]

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3. Consider the MA(2) model y, = E, + Bɛ,-2. where < 1 and (ɛ,) WN(0, 1). (a) Find the autocovariance functions of (y,). (b) Is this model weakly stationary? (c) Compute the variance of the sample mean (y, + y2 + yı)/3 when @ 0.5. %3D