Question

In: Math

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.

Solutions

Expert Solution

TOPIC:Mean,variance and ACF of MA(1) model.


Related Solutions

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
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 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 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.
1. Consider the process {Xt} in which Xt = Zt + 0.5Zt-1 - 2Zt-2. Investigate the...
1. Consider the process {Xt} in which Xt = Zt + 0.5Zt-1 - 2Zt-2. Investigate the stationarity of the process under the following conditions. Calculate the ACF for the stationary models. (a) Zt ~ WN(0,(sigma)2) ; (sigma)2 < infinity (b) {Zt } is a sequence of i.i.d random variables with the following distribution: fzt(z) = 2/z3 ; z > 1
{Zt} is a Gaussian White Noise in time series. Yt = Zt^2. Can we conclude Yt...
{Zt} is a Gaussian White Noise in time series. Yt = Zt^2. Can we conclude Yt as a non-Gaussian White Noise distribution by the definition of White Noise? Why?
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...
We have a solution of H2O (0.1 wt%) and H2SO4 (0.9 wt%). Find the mass density...
We have a solution of H2O (0.1 wt%) and H2SO4 (0.9 wt%). Find the mass density (Ibm/ft3) and molar concentration (Ib-mole/ft3) of water in this mixture?
Consider a regression model of monthly time series data where we model the price of petrol...
Consider a regression model of monthly time series data where we model the price of petrol which is dependent on the Crude Oil price and Exchange rate (against US$). Data for the three variables were collected over a 50 month period. Suppose the estimation results showed that the Durbin-Watson (DW) test value d is 1.38. Perform the DW test for first order positive autocorrelation of the error terms at the 5% level of significance.               Model: et = r...
Consider a process where 15% of the parts produced have a defect. If we have a...
Consider a process where 15% of the parts produced have a defect. If we have a sample of 250 parts, we want to find the probability that there are between 30 and 45 defective parts in this sample. i) Calculate the probability that there are exactly 30 defective parts in the sample. ii) Write out (but don't calculate) the expression for finding the probability that between 30 and 45 parts are defective. Hint: use the binomial distribution. iii) use the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT