Homework Answers
Solution:
Add Answer to:
4.1 Consider the model (1 B)PZ, (1 .3B - 5B2)a (a) Is the model for Z, stationary? Why? (b) Let W (1 - BYZ. Is the mode...
4.1 Consider the model (1 – B)Z, = (1 - 3B – .5B2)aş. (a) Is the model for Ze stationary? Why? (b) Let W, = (1 - B)?Zz....
4.1 Consider the model (1 – B)Z, = (1 - 3B – .5B2)aş. (a) Is the model for Ze stationary? Why? (b) Let W, = (1 - B)?Zz. Is the model for W, stationary? Why? (C) Find the ACF for the second-order differences W..
Consider the MA(1) model x5 wt 0.6W-1 with the w assumed to be jid N0,02). A....
Consider the MA(1) model x5 wt 0.6W-1 with the w assumed to be jid N0,02). A. Give a numerical value for the first lag autocorrelation. B. Give a numerical value for the second lag autocorrelation. C. Describe the appearance of the ACF for this model. D. Use R to sketch the ACF for this model. The commands are: acfprob3-ARMAacfíma-c(.6), lag max-10) plot seal0,10), acfprob3, xlm-c(1.10), lab-"lags", type-"h") (In the plot command, the type-"h" causes projections from the value to the...
QUESTION 3 (a) Consider the ARMA (1, 1) process -Bat-1-where o and θ are model parame-...
QUESTION 3 (a) Consider the ARMA (1, 1) process -Bat-1-where o and θ are model parame- are independent and identically distributed random variables with mean 0 z, oz,-1 ters, and a1, a2, and variance σ (i) Show that the variance of the process is γ,- (ii) Using (i) or otherwise, show that the autocorrelation function (ACF) of the process is: ifk=0. (b) Let Y be an AR(2) process of the special form Y-2Y-2e (i) Find the range of values of...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...
2. Consider the time series X, = 2 + 0.5t +0.8X1-1 + W, where W N(0.1). (a) (8 points) Calculate E(X2) Is this process weakly stationary? Give reasons for your answer. Hint: Find the mean function of...
2. Consider the time series X, = 2 + 0.5t +0.8X1-1 + W, where W N(0.1). (a) (8 points) Calculate E(X2) Is this process weakly stationary? Give reasons for your answer. Hint: Find the mean function of {X) and then substitute t = 20. (b) (3 points) Calculate Var(X20) Question 2 continues on the next page... Page 4 of 12 c)(4 points) Consider the first differences of the time series above, that is Is {%) a weakly stationary process. Prove...
a) Let z,w ∈ C, prove or disprove: Ln(z/w) = Lnz − Lnw b) Find all...
a) Let z,w ∈ C, prove or disprove: Ln(z/w) = Lnz − Lnw b) Find all values in C and the principal value of j^j and ln(-3) c) Find all z ∈ C such that i. tanh z = 2 ii. e^z = 0 iii. Ln(Ln(z)) = −jπ
4. Let (Yi] be a stationary process with mean zero and let a, b and c be constants. Let st be a seasonal with period 4, that is, st-st+4, t-1, 2, . . . , and Xt = a + bt + ct2 + st + Y. (i) Let (ho,...
4. Let (Yi] be a stationary process with mean zero and let a, b and c be constants. Let st be a seasonal with period 4, that is, st-st+4, t-1, 2, . . . , and Xt = a + bt + ct2 + st + Y. (i) Let (ho, do )-min( (k, d)such that k > 0, d 0, and the proces s W t ▽k▽dX,-(1 B)a Find ko and do. For W, (with k = ko and d...
6.Let W={(a +b-c,2a +3b, -a +3c,-b-2c): a,b, CER) a) For what value of n is W...
6.Let W={(a +b-c,2a +3b, -a +3c,-b-2c): a,b, CER) a) For what value of n is W isomorphic to R"?, clear answer the question and justify your answer b) Find an isomorphism T:R" W for the value of n you found in part (a).Please make it clear from your work that your function T is really an isomorphism. 7.Let T:P2(R) – P2(R) be a linear transformation such that T(x2)=x2 a) Prove that if there exist distinct linearly independent polynomials 2,9 €...
2. Let [et be a zero mean white noise process with variance 0.25. Suppose that the...
2. Let [et be a zero mean white noise process with variance 0.25. Suppose that the observed process is k = et + 0.5e-2. a. Explain why {Yt) is stationary. b. Compute yo-V(Y.) c. Compute the autocorrelation pkY, kl-0,1,2,... for Y) d. Let Wt = 3 + 4t + h. i. Find the mean of {W) ii. Is W3 stationary? Why or why not? iii. Let Z Vw, W,- W,_1. Is {Z.1 stationary? Why or why not?
3. Let Zt) be a Gaussian white noise, that is, a sequence of i.i.d. normal r.v.s...
3. Let Zt) be a Gaussian white noise, that is, a sequence of i.i.d. normal r.v.s each with mean zero and variance 1. Let Y% (a) Using R generate 300 observations of the Gaussian white noise Z. Plot the series and its acf. (b) Using R, plot 300 observations of the series Y -Z. Plot its acf. c) Analyze graphs from (a) and (b). Can you see a difference between the plots of graphs of time series Z and Y?...
4.1 Consider the model (1 – B)Z, = (1 - 3B – .5B2)aş. (a) Is the model for Ze stationary? Why? (b) Let W, = (1 - B)?Zz. Is the model for W, stationary? Why? (C) Find the ACF for the second-order differences W..
Consider the MA(1) model x5 wt 0.6W-1 with the w assumed to be jid N0,02). A. Give a numerical value for the first lag autocorrelation. B. Give a numerical value for the second lag autocorrelation. C. Describe the appearance of the ACF for this model. D. Use R to sketch the ACF for this model. The commands are: acfprob3-ARMAacfíma-c(.6), lag max-10) plot seal0,10), acfprob3, xlm-c(1.10), lab-"lags", type-"h") (In the plot command, the type-"h" causes projections from the value to the...
QUESTION 3 (a) Consider the ARMA (1, 1) process -Bat-1-where o and θ are model parame- are independent and identically distributed random variables with mean 0 z, oz,-1 ters, and a1, a2, and variance σ (i) Show that the variance of the process is γ,- (ii) Using (i) or otherwise, show that the autocorrelation function (ACF) of the process is: ifk=0. (b) Let Y be an AR(2) process of the special form Y-2Y-2e (i) Find the range of values of...
Problem 1: Let W = {p(t) € Pz : p'le) = 0}. We know from Problem 1, Section 4.3 and Problem 1, Section 4.6 that W is a subspace of P3. Let T:W+Pbe given by T(p(t)) = p' (t). It is easy to check that T is a linear transformation. (a) Find a basis for and the dimension of Range T. (b) Find Ker T, a basis for Ker T and dim KerT. (c) Is T one-to-one? Explain. (d) Is...
2. Consider the time series X, = 2 + 0.5t +0.8X1-1 + W, where W N(0.1). (a) (8 points) Calculate E(X2) Is this process weakly stationary? Give reasons for your answer. Hint: Find the mean function of {X) and then substitute t = 20. (b) (3 points) Calculate Var(X20) Question 2 continues on the next page... Page 4 of 12 c)(4 points) Consider the first differences of the time series above, that is Is {%) a weakly stationary process. Prove...
4. Let (Yi] be a stationary process with mean zero and let a, b and c be constants. Let st be a seasonal with period 4, that is, st-st+4, t-1, 2, . . . , and Xt = a + bt + ct2 + st + Y. (i) Let (ho, do )-min( (k, d)such that k > 0, d 0, and the proces s W t ▽k▽dX,-(1 B)a Find ko and do. For W, (with k = ko and d...
6.Let W={(a +b-c,2a +3b, -a +3c,-b-2c): a,b, CER) a) For what value of n is W isomorphic to R"?, clear answer the question and justify your answer b) Find an isomorphism T:R" W for the value of n you found in part (a).Please make it clear from your work that your function T is really an isomorphism. 7.Let T:P2(R) – P2(R) be a linear transformation such that T(x2)=x2 a) Prove that if there exist distinct linearly independent polynomials 2,9 €...
2. Let [et be a zero mean white noise process with variance 0.25. Suppose that the observed process is k = et + 0.5e-2. a. Explain why {Yt) is stationary. b. Compute yo-V(Y.) c. Compute the autocorrelation pkY, kl-0,1,2,... for Y) d. Let Wt = 3 + 4t + h. i. Find the mean of {W) ii. Is W3 stationary? Why or why not? iii. Let Z Vw, W,- W,_1. Is {Z.1 stationary? Why or why not?
3. Let Zt) be a Gaussian white noise, that is, a sequence of i.i.d. normal r.v.s each with mean zero and variance 1. Let Y% (a) Using R generate 300 observations of the Gaussian white noise Z. Plot the series and its acf. (b) Using R, plot 300 observations of the series Y -Z. Plot its acf. c) Analyze graphs from (a) and (b). Can you see a difference between the plots of graphs of time series Z and Y?...
Most questions answered within 3 hours.
-
What major physiological changes account for electrodermal
activity (as in during a lie-detector test)?
asked 48 minutes ago -
You are going to sell fruits & vegetables at a local
roadside market. List separately and...
asked 1 hour ago -
Hows does water affect the digestion of fats ?
asked 3 hours ago -
A buffer that contains 0.41 M of a base, B and 0.21 M of its
conjugate...
asked 3 hours ago -
Pleaaaaaaaasssssse help me please please it's more important
:((((((((((((((((((((
CASE STUDY
Nissan Company
Nissan Motor Company,...
asked 3 hours ago -
Calculate the concentration of hydronium and hyroxide ions in 1)
2.0 mol/L HNO3 2) 0.5 mol/L...
asked 4 hours ago -
In a loop-the-loop ride a car goes around a vertical, circular
loop at a constant speed....
asked 4 hours ago -
50 grams each of water (18.015 g/mol) and ethylene glycol
(C2H6O2) (62.07 g/mol) are mixed. At...
asked 4 hours ago -
The life expectancy of sport utility vehicles follows a normal
distribution with a mean of 145.8...
asked 4 hours ago -
If an object with mass of 5 kg is pushed with a force of 552 N,...
asked 4 hours ago -
Suppose your program already has a list called nums, which
contains several numbers. Write a for...
asked 4 hours ago -
A spherical shell with a finite thickness just barely floats in
water. If the shell is...
asked 4 hours ago