Question
In: Math
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).
Solutions
milcah answered 1 year agoRelated Solutions
2. Consider the same model in a time series context, namely, yt = β0 + β1xt...
2. Consider the same model in a time series context, namely, yt
= β0 + β1xt + ut, t = 1, . . . , T where ut = ρut−1 + vt, |ρ| <
1, vt is i.i.d. with E(vt) = 0 and Var(vt) = σ 2 v . (a) What is
the problem in using OLS to estimate the model? Is there any
problem in hypothesis testing? (b) Show that Cov(ut, ut−τ ) = ρ
τVar(ut−τ ) for τ...
Consider the following time series data. t 1 2 3 4 5 6 7 yt 10...
Consider the following time series data. t 1 2 3 4 5 6 7 yt 10 9
7 8 6 4 4 a. Construct a time series plot. What type of pattern
exists in the data? b. Develop the linear trend equation for this
time series. c. What is the forecast for t=8?
Consider the following time series. t 1 2 3 4 5 6 7 Yt 83 61...
Consider the following time series.
t
1
2
3
4
5
6
7
Yt
83
61
45
36
29
28
36
b. Develop the quadratic trend equation for the
time series. Enter negative value as negative number.(to 3
decimals)
Tt = ______ + _______t + ________ t2
c. What is the forecast for t = 8?
Consider the following time series. t 1 2 3 4 5 6 7 yt 125 108...
Consider the following time series.
t
1
2
3
4
5
6
7
yt
125
108
102
99
94
92
86
(b)
Use simple linear regression analysis to find the parameters
for the line that minimizes MSE for this time series.
If required, round your answers to two decimal places.
y-intercept, b0 =
Slope, b1 =
MSE =
(c)
What is the forecast for t = 8?
If required, round your answer to one decimal place.
Consider the following time series. t 1 2 3 4 5 yt 6 10 8 13...
Consider the following time series. t 1 2 3 4 5 yt 6 10 8 13 15
(a) Choose the correct time series plot. (i) (ii) (iii) (iv) What
type of pattern exists in the data? (b) Use simple linear
regression analysis to find the parameters for the line that
minimizes MSE for this time series. If required, round your answers
to two decimal places. y-intercept, b0 = 4.1 Slope, b1 = 2.1 MSE =
???? (c) What is the...
{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?
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...
Consider a simple linear regression model with time series data: yt=B0+ B1xt +ut t= 1;2,.....T Suppose...
Consider a simple linear regression model with time series data:
yt=B0+ B1xt +ut t= 1;2,.....T
Suppose the error ut is strictly exogenous. That is
E(utIx1;....xt,.....xT) = 0
Moreover, the error term follows an AR(1) serial correlation
model. That is, ut= put-1 +et t= 1;2,.....T (3)
where et are uncorrelated, and have a zero mean and constant
variance.
a. [2 points] Will the OLS estimator of B1 be unbiased? Why or
why not?
b. [3 points] Will the conventional estimator of...
Econometrics Question (a) What properties must a time series {yt} have to satisfy in order for...
Econometrics Question
(a) What properties must a time series {yt} have to
satisfy in order for it to be a covariance stationary process?
Let {ut} be a sequence of i.i.d. N(0,1)
variables.
Let yt= α+βt+ut, and
yt = yt -yt-1.
(b) Is {yt} covariance stationary? Justify your
answer.
(c) Would your answer to part (b) change if {ut} were a
moving average of order 1?
(d) Is {yt} covariance stationary? Justify your
answer.
= change in, won't allow a...
Econometrics Question (a) What properties must a time series {yt} have to satisfy in order for...
Econometrics Question
(a) What properties must a time series {yt} have to
satisfy in order for it to be a covariance stationary process?
Let {ut} be a sequence of i.i.d. N(0,1)
variables.
Let yt= α+βt+ut, and
yt = yt -yt-1.
(b) Is {yt} covariance stationary? Justify your
answer.
(c) Would your answer to part (b) change if {ut} were a
moving average of order 1?
(d) Is {yt} covariance stationary? Justify your
answer.
= change in, won't allow a...
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