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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).

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 8E
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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 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.
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).
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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