Suppose Yt = 1 + 10t + t2 + Xt where {Xt} is a zero-mean stationary...

Suppose Yt = 1 + 10t + t2 + Xt where {Xt} is a zero-mean stationary series with autocovariance function γk. Show that {Yt} is not stationary but that Zt = Wt − Wt−1 where Wt = Yt − Yt−1 is stationary.

Solutions

Expert Solution

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A stationary time series Xt follows (1 + 0.7B − 0.3B2 )Xt = 0.4 + (1...

A stationary time series Xt follows (1 + 0.7B − 0.3B2 )Xt = 0.4 + (1 + 0.6B4 )Zt. What is the mean of Xt?

Suppose we have the process (time series) xt = 0.5wt-1 + wt; where wt is white...

Suppose we have the process (time series) xt = 0.5wt-1 + wt; where wt is white noise with mean zero and variance sigma squared w. Find the mean, variance, autocovariance, and ACF of xt.

EvaluateRC F·dr where F = hyzexz,exz,xyexzi and C : r = ht2 + 1,t2 −1,t2 −2ti,...

EvaluateRC F·dr where F = hyzexz,exz,xyexzi and C : r = ht2 + 1,t2 −1,t2 −2ti, 0 ≤ t ≤ 2. Hint: Check whether F is conservative. If so, the Fundamental Theorem for Line Integrals might be useful

Suppose that xt = wt + kwt−1 + kwt−2 + kwt−3 + · · · +...

Suppose that xt = wt + kwt−1 + kwt−2 + kwt−3 + · · · + kw0, for t > 0, k constant, and wi iid N(0, σ2w). (a) Derive the mean and autocovariance function for {xt}. Is {xt} stationary? (b) Derive the mean and autocovariance function for {∇xt}. Is {∇xt} stationary?

Suppose T1 and T2 are iid Exp(1). What is the probability density function of T1+T2? What...

Suppose T1 and T2 are iid Exp(1). What is the probability density function of T1+T2? What is the probability that T1+T2 ≥ 3?

1. Let Ct be consumption and Xt be a predictor of consumption. Suppose you have quarterly...

1. Let Ct be consumption and Xt be a predictor of consumption. Suppose you have quarterly data on C and X. Let D1t , D2t , D3t , and D4t be dummy variables such that D1t takes the value 1 in quarter 1 and 0 otherwise, D2t takes the value 1 in quarter 2 and 0 otherwise, etc. Which of the following, if any, suffer from perfect multicollinearity and why? a) Ct = α + βXt + γ1XtD1t + γ2XtD2t...

Consider the time series Xt = 4t + Wt + 0.9Wt−1, where Wt ∼ N(0, σ2...

Consider the time series Xt = 4t + Wt + 0.9Wt−1, where Wt ∼ N(0, σ2 ). (i)What are the mean function and the variance function of this time series? Is this time series stationary? Justify your answer (ii). Consider the first differences of the time series above, that is, consider Yt = Xt − Xt−1. What are the mean function and autocovariance function of this time series? Is this time series stationary? Justify your answer

Consider the time series given by yt = a1yt-1 + a2yt-2 + εt. Where εt is...

Consider the time series given by yt = a1yt-1 + a2yt-2 + εt. Where εt is independent white noise and yt is stationary. A. Compute the mean of yt. E(yt) B. Compute the variance of yt. E[yt − E(yt)]2 C. Compute the first three autocovariances for yt. (E[(yt −E(yt))(yt−i −E(yt−i))] i=1,2,3).

Consider the model Yt = ΦYt−3 + et − θet−1, where et has variance σ 2...

Consider the model Yt = ΦYt−3 + et − θet−1, where et has variance σ 2 . (a) Identify Yt as a certain SARIMA(p, d, q) × (P, D, Q)s model. That is, specify each of p, d, q, P, D, Q, and s. You may assume that Φ < 1. (b) Find the variance of Yt . (c) What are the forecasts for Yt+1 and Yt+4? (d) What are the error variances for your forecasts above? (e) If σ...

Suppose X is a normal with zero mean and standard deviation of $10 million. a) Find...

Suppose X is a normal with zero mean and standard deviation of $10 million. a) Find the value at risk for X for the risk tolerances h=0.01, 0.02, 0.05, 0.10, 0.50, 0.60, and 0.95. b) Is there a relation between VaR for values of h <= 0.50 and values for h>= 0.50?

Subjects