2. Let {X} be a moving average process of order q (usually written as MA(q)) defined ontЄ Z aswhere {et} is a white noise process with variance 1.(1)(a) Show that for any MA(1) process with B₁ 1 there exists another MA(1) pro-cess with the same autocorrelation function, and find the lag 1 moving averagecoefficient (say) of this process.(b) For an MA(2) process, equation (1) becomesX=&t+B₁et-1+ B2ɛt-2-(2)i. Define the backshift operator B, and write equation (2) in terms of a polyno-mial function B(B), giving a clear definition of this function.ii. Hence show that equation (2) can be written as an infinite order autoregressiveprocess under certain conditions on B(B), clearly stating these conditions.

Part (a): Show equivalence of two MA(1) processes with the same autocorrelation functionProblem…

Answered: 2. Let {X} be a moving average process…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

See similar textbooks

Similar questions

Suppose that { Y,} is Moving average process with Y, = 0.25(e, + e,-1+e-2+ej_3) %3D where {e,} is zero mean white noise with var(e,) = o². For {Y,}, find mean, variance, %D auto covariance function and autocorrelation function.
Indicate True or False for the following statements: (a) A random (RP) process is a time varying random variable - True or False (b) A random (RP) process is a randomly chosen function of time - True or False (c) A stationary RP depends on time - True or False (d) The mean of a stationary RP depends on time - True or False (e) The autocorrelation of a stationary RP depends on time – True or False (f) The PSD of a WSS random process is always nonnegative and even – True or False (g) White noise is realizable in practice – True or False
Derive that the variance of the forecasted error using Exponential Smoothing (ES) method is given by 20² Var(et) 2 – α Where o² is the variance of individual observation and a is the parameter in the ES method. =
Show that the mean of a random sample of size n from an exponential population is a minimum variance unbi-ased estimator of the parameter θ.
8. Similar to Question 6, consider a portfolio with w invested in asset X and 1- w invested in asset Y for w€ (0,1). The volatilities of asset X and Y are 0.2 and 0.3, respectively. Suppose that the correlation coefficient between the two assets is zero. Express the portfolio variance as a function of w and find the value w* that yields the minimum portfolio variance, i.e. o(w*). Select the best answer that corresponds to the minimum portfolio volatility, op(w*): (a) 16.64% (b) 2% (c) 2.77% (d) 14.14% 9. Stock J has a beta of 1, an expected return of 15%. The equity risk premium is 10%, and the risk-free rate is 2.5%. Calculate Jensen's alpha measure for Stock J. (a) -2.5% (b) 0% (c) 2.5% (d) -7.5% 10. Currently, shares of MJ Corp. trade at $100. The probability of the price increasing by $10 in one day is 30% and the probability of the price decreasing by $10 in one day is 70%. Let R₂ denote log-return on the asset over two days, i.e. R₂ = In (a) 12.96% (b) 13.69% (c) 7.69% (d) 20.96%…
Show that the mean of a random sample of size n from an exponential population is a minimum variance unbiased estimator of the parameter 0.
Suppose that f(x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.
Suppose that f (x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.
In N(5,4): Round Z-scores to 2 places after the decimal and use rounded value to find the data value in N(5,4). If P(X a) = .02, then the z-score for a = If P(b
4, 12. How Call v. 13. Suppose that two raters (Rater A and Rater B) each assign pirysica attractiveness scO = not at all attractive to 10 = extremely attractive) to a set of seven facial photogranhe 21 %3D Pearson's r can be used as an index of interrater reliability or agreement on quantitative ratings. A correlation of +1 would indicate perfect rank-order agreement between rate while an r of 0 would indicate no agreement about judgments of relative attractiveness An r of .8 to .9 is considered desirable when reliability is assessed. For this example, Rater A's score is the X variable and Rater B's score is the Y variable. The ratings are as followe F follows: Photo Rater A Rater B 1 3. 5. 8. 6. 7. 8. 6. 4. 6. 10 6. 7. 5. 4. a. Compute the Pearson correlation between the Rater A and Rater B attractiveness ratings. What is the obtained r value? b. Is your obtained r statistically significant (using a =.05, two tailed)? Are the Rater A and Rater B scores "reliable"? Is there good or…
Suppose that X and Y are unknown 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 .6. Then what is the variance of X + Y?
Suppose employers care about overall productivity Z, which is made up of two components, X and Y, such that Z=X+Y (and employers know this productivity function). Suppose there are two groups (male and female) whose average Zs are the same (i.e. Z_M =Z_F), but X_M < X_F and Y_M > Y_F (and again, employers know these population averages). (Averages are given by bold font.) Researchers decide to run a resume-based audit study where they randomize names based on gender (using typically male or female names) but hold constant Y. They provide no information on X. Which of the following results would provide suggestive evidence of statistical discrimination? A. The call-back rate is the same for both sexes. B. We can't use differences in call-back rates to find evidence of statistical discrimination.C. The call-back rate is higher for women than for men. D. The call-back rate is higher for men than for women.

SEE MORE QUESTIONS

Recommended textbooks for you

Big Ideas Math A Bridge To Success Algebra 1: Stu…

Algebra

ISBN:

9781680331141

Author:

HOUGHTON MIFFLIN HARCOURT

Publisher:

Houghton Mifflin Harcourt