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ๅ้กน้ๆฉ้ข
Consider the following GARCH(1,1) model for the volatility of asset returns ๐ ๐ก : ๐ ๐ก = ๐ ๐ก ๐ ๐ก = โ ๐ก ๐ข ๐ก โ ๐ก = ๐ + ๐ฟ โ ๐ก โ 1 + ๐ ๐ ๐ก โ 1 2 ๐ผ ๐ก โ 1 ( ๐ข ๐ก ) = 0 ๐ผ ๐ก โ 1 ( ๐ข ๐ก 2 ) = 1 You estimated the following values for the parameters Parameters Estimates MLE ๐ 0.0112 ๐ฟ 0.932 ๐ 0.0811 and the variance-covariance matrix is ๐ ( ๐ ฬ ) = [ 0.0012 โ 0.012 0.001 โ 0.012 0.102 โ 0.003 0.001 โ 0.003 0.003 ] Assume the last observation in your sample has โ ๐ = 1.5056 . What is the value of the conditional variance ๐ ๐ โ 1 ( ๐ ๐ ) ?
้้กน
A.๐
๐
โ
1
(
๐
๐
)
=
2.266831
B.๐
๐
โ
1
(
๐
๐
)
=
0
C.There is not enough data to compute
๐
๐
โ
1
(
๐
๐
)
.
D.๐
๐
โ
1
(
๐
๐
)
=
1.227029
E.๐
๐
โ
1
(
๐
๐
)
=
1.5056
F.๐
๐
โ
1
(
๐
๐
)
=
1
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We are asked to determine the conditional variance of r_T given information up to time Tโ1, denoted V_{Tโ1}(r_T). In a GARCH(1,1) model, the conditional variance at time T given the information set F_{Tโ1} 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_{Tโ1}(r_T) = 2.266831
This value would imply a much larger conditional varia......Login to view full explanation็ปๅฝๅณๅฏๆฅ็ๅฎๆด็ญๆก
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According to the GARCH model ฯTHURSDAY2=ฯ+ฮฑRBLANK12+ฮฒฯBLANK22\sigma_{THURSDAY}^2 = \omega + \alpha R_{BLANK1}^2 +\beta \sigma_{BLANK2}^2 (Hint: fill in day of the week like Monday, Tuesday...) BLANK1:[Fill in the blank], BLANK2:[Fill in the blank],
Consider the following GARCH(1,1) model for the volatility of asset returns ๐ ๐ก : ๐ ๐ก = ๐ผ + ๐ฝ ๐ ๐ก โ 1 + ๐ ๐ก ๐ ๐ก = โ ๐ก ๐ข ๐ก โ ๐ก = ๐ + ๐ฟ โ ๐ก โ 1 + ๐ ๐ ๐ก โ 1 2 ๐ผ ๐ก โ 1 ( ๐ข ๐ก ) = 0 ๐ผ ๐ก โ 1 ( ๐ข ๐ก 2 ) = 1 You estimated the following values for the parameters Estimates Parameters ๐ผ ๐ฝ ๐ ๐ฟ ๐ Estimates 0.1911 0.9722 0.0011 0.9321 0.0821 Assume that the last 2 observations of the return process are ๐ ๐ = 0.07 and ๐ ๐ โ 1 = 0.03 , and the value of the conditional variance in the last period of your sample is โ ๐ = 0.55 . Then what is the predicted value of the conditional variance โ ๐ + 1 in period ๐ + 1 ?
Consider the following GARCH(1,1) model for the volatility of asset returns ๐ ๐ก : ๐ ๐ก = ๐ผ + ๐ฝ ๐ ๐ก โ 1 + ๐ ๐ก ๐ ๐ก = โ ๐ก ๐ข ๐ก โ ๐ก = ๐ + ๐ฟ โ ๐ก โ 1 + ๐ ๐ ๐ก โ 1 2 ๐ผ ๐ก โ 1 ( ๐ข ๐ก ) = 0 ๐ผ ๐ก โ 1 ( ๐ข ๐ก 2 ) = 1 You estimated the following values for the parameters ๐ผ ๐ฝ ๐ ๐ฟ ๐ 0.5911 0.9222 0.0112 0.9132 0.0611 Assume that the last 2 observations of the return process are ๐ ๐ = 0.04 and ๐ ๐ โ 1 = 0.05 , and the value of the conditional variance in the last period of your sample is โ ๐ = 0.5 . Then what is the predicted value of the conditional variance โ ๐ + 1 in period ๐ + 1 ?
Consider the following GARCH(1,1) model for the volatility of asset returns ๐ ๐ก : ๐ ๐ก = ๐ผ + ๐ฝ ๐ ๐ก โ 1 + ๐ ๐ก ๐ ๐ก = โ ๐ก ๐ข ๐ก โ ๐ก = ๐ + ๐ฟ โ ๐ก โ 1 + ๐ ๐ ๐ก โ 1 2 ๐ผ ๐ก โ 1 ( ๐ข ๐ก ) = 0 ๐ผ ๐ก โ 1 ( ๐ข ๐ก 2 ) = 1 You estimated the following values for the parameters ๐ผ ๐ฝ ๐ ๐ฟ ๐ 0.5911 0.9222 0.0112 0.9132 0.0611 Assume that the last 2 observations of the return process are ๐ ๐ = 0.04 and ๐ ๐ โ 1 = 0.05 , and the value of the conditional variance in the last period of your sample is โ ๐ = 0.5 . Then what is the predicted value of the conditional variance โ ๐ + 1 in period ๐ + 1 ?
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