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BU.232.630.W6.SP25
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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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We begin by restating the problem in our own terms and identifying the inputs we will use to forecast h_{T+1}.
- The GARCH(1,1) structure provided uses h_t = ฮผ + ฮด h_{t-1} + ฯ ฮต_{t-1}^2 (as inferred from the given parameter setup and c......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 = 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 ) ?
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 ?
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