Questions
Single choice
Consider the following GARCH(1,1) model for the volatility of asset returns 𝑟 𝑡 : 𝑟 𝑡 = 𝜀 𝑡 𝜀 𝑡 = ℎ 𝑡 𝑢 𝑡 ℎ 𝑡 = 𝜇 + 𝛿 ℎ 𝑡 − 1 + 𝜙 𝜀 𝑡 − 1 2 𝔼 𝑡 − 1 ( 𝑢 𝑡 ) = 0 𝔼 𝑡 − 1 ( 𝑢 𝑡 2 ) = 1 You estimated the following values for the parameters Parameters Estimates MLE 𝜇 0.0112 𝛿 0.932 𝜙 0.0811 and the variance-covariance matrix is 𝑉 ( 𝜃 ̂ ) = [ 0.0012 − 0.012 0.001 − 0.012 0.102 − 0.003 0.001 − 0.003 0.003 ] Assume the last observation in your sample has ℎ 𝑇 = 1.5056 . What is the value of the conditional variance 𝑉 𝑇 − 1 ( 𝑟 𝑇 ) ?
Options
A.𝑉
𝑇
−
1
(
𝑟
𝑇
)
=
2.266831
B.𝑉
𝑇
−
1
(
𝑟
𝑇
)
=
0
C.There is not enough data to compute
𝑉
𝑇
−
1
(
𝑟
𝑇
)
.
D.𝑉
𝑇
−
1
(
𝑟
𝑇
)
=
1.227029
E.𝑉
𝑇
−
1
(
𝑟
𝑇
)
=
1.5056
F.𝑉
𝑇
−
1
(
𝑟
𝑇
)
=
1
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Step-by-Step Analysis
We are asked to determine the conditional variance of r_T given information up to time T−1, denoted V_{T−1}(r_T). In a GARCH(1,1) model, the conditional variance at time T given the information set F_{T−1} is h_T. The problem provides the last estimated conditional variance h_T = 1.5056, which is precisely this quantity.
Option by option analysis:
Option 1: V_{T−1}(r_T) = 2.266831
This value would imply a much larger conditional varia......Login to view full explanationLog in for full answers
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