QUESTION 1 Consider the following ARMA model for {y,}: ',=a,+ 2 j=1 +E,+ l=1 where {e) is the residual. Which of the following assumption(s) on the residuals {ɛ } is needed to enable forecasting with this model in practice? O a. e is normally distributed. O b. e, is mean-independent of y,-1,-2"** and e,-1€,-2"**** and e are stochastically independent for all + s- O d. All of the above. QUESTION 2 How can the validity of the assumption(s) identified in Question 1 be examined in practice? O a. Use the Breusch-Pagan test, where the null hypothesis is that the distribution is normal. O B- Use the Ljung-Box test, where the null hypothesis is that the first K autocorrelations are zero. O C. Examine the SACF and SPACF of the estimated residuals O d. Both (b) and (c).
QUESTION 1 Consider the following ARMA model for {y,}: ',=a,+ 2 j=1 +E,+ l=1 where {e) is the residual. Which of the following assumption(s) on the residuals {ɛ } is needed to enable forecasting with this model in practice? O a. e is normally distributed. O b. e, is mean-independent of y,-1,-2"** and e,-1€,-2"**** and e are stochastically independent for all + s- O d. All of the above. QUESTION 2 How can the validity of the assumption(s) identified in Question 1 be examined in practice? O a. Use the Breusch-Pagan test, where the null hypothesis is that the distribution is normal. O B- Use the Ljung-Box test, where the null hypothesis is that the first K autocorrelations are zero. O C. Examine the SACF and SPACF of the estimated residuals O d. Both (b) and (c).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:QUESTION 3
What conditions on the parameters a, a, ...
b are necessary for the process to be stable?
= a = 0.
Ob.
´a (z) # 0 for all 1z1 < 1. where a (L) =1+a,L+ ..+a_LP.
b(z) #0 for all Izl<1, where b ( L) =1+b,L+...+b
O d. Both (b) and (c).
QUESTION 4
Consider the 2-period ahead forecast ,,=E (y,,,| y,…..y,)· Which of the following statements is not true?
=E(y7+2! '1•…7).
T+2
å. If the ARMA(p,q) is invertible, then ŷ.can be reasonably approximated by a linear function of y,....y.
T+2
O b. The forecast error variance o
F.T+2
= Var (y,4-ŷ, ,) is finite only if the ARMA(p,q) is stable.
OC. Predictive intervals for y
account for uncertainty due to unobserved e41 €742 as well as parameter estimation.
O d. All of the above are true.
QUESTION 5
Consider the following information for a set of three ARMA models: ARMA(1,0), ARMA(1,1) and ARMA(3,2).
AIC
1
-4.204
1
1
-6.819
3
2
-6.847
Based on this, how would you proceed with model specification?
a. Eliminate the ARMA(1,0) because it has a clearly inferior fit versus parsimony tradeoff according to the AIC.
b.
O D: Choose the ARMA(3,2) only because it has the best fit versus parsimony tradeoff according to the AIC.
O C. Choose the ARMA(1,1) only because it has a better fit than the ARMA(1,0) but it is more parsimonious than the ARMA(3,2).
d.
Eliminate all the models in this set because they have a negative AIC value.
Transcribed Image Text:QUESTION 1
Consider the following ARMA model for {y,}:
y,=a,+
j=1
a
+
- E,+
1=1
where {e} is the residual.
Which of the following assumption(s) on the residuals {E} is needed to enable forecasting with this model in practice?
Oa.
a. ɛ ̟ is normally distributed.
O b.e
E, is mean-independent of y,y,-2…….. and e
Oc.
and e are stochastically independent for all +s
O d. All of the above.
QUESTION 2
How can the validity of the assumption(s) identified in Question 1 be examined in practice?
O d. Use the Breusch-Pagan test, where the null hypothesis is that the distribution is normal.
O D.Use the Ljung-Box test, where the null hypothesis is that the first K autocorrelations are zero.
O C. Examine the SACF and SPACF of the estimated residuals
O d. Both (b) and (c).
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