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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‘Ÿ ๐‘ก : ๐‘Ÿ ๐‘ก = ๐›ผ + ๐›ฝ ๐‘Ÿ ๐‘ก โˆ’ 1 + ๐œ€ ๐‘ก ๐œ€ ๐‘ก = โ„Ž ๐‘ก ๐‘ข ๐‘ก โ„Ž ๐‘ก = ๐œ‡ + ๐›ฟ โ„Ž ๐‘ก โˆ’ 1 + ๐œ™ ๐œ€ ๐‘ก โˆ’ 1 2 ๐”ผ ๐‘ก โˆ’ 1 ( ๐‘ข ๐‘ก ) = 0 ๐”ผ ๐‘ก โˆ’ 1 ( ๐‘ข ๐‘ก 2 ) = 1 You estimated the following values for the parameters ๐›ผ ๐›ฝ ๐œ‡ ๐›ฟ ๐œ™ 0.5911 0.9222 0.0112 0.9132 0.0611 Assume that the last 2 observations of the return process are ๐‘Ÿ ๐‘‡ = 0.04 and ๐‘Ÿ ๐‘‡ โˆ’ 1 = 0.05 , and the value of the conditional variance in the last period of your sample is โ„Ž ๐‘‡ = 0.5 . Then what is the predicted value of the conditional variance โ„Ž 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 explanation

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Consider the following GARCH(1,1) model for the volatility of asset returns ๐‘Ÿ ๐‘ก : ๐‘Ÿ ๐‘ก = ๐œ€ ๐‘ก ๐œ€ ๐‘ก = โ„Ž ๐‘ก ๐‘ข ๐‘ก โ„Ž ๐‘ก = ๐œ‡ + ๐›ฟ โ„Ž ๐‘ก โˆ’ 1 + ๐œ™ ๐œ€ ๐‘ก โˆ’ 1 2 ๐”ผ ๐‘ก โˆ’ 1 ( ๐‘ข ๐‘ก ) = 0 ๐”ผ ๐‘ก โˆ’ 1 ( ๐‘ข ๐‘ก 2 ) = 1 You estimated the following values for the parameters Parameters Estimates MLE ๐œ‡ 0.0112 ๐›ฟ 0.932 ๐œ™ 0.0811 and the variance-covariance matrix is ๐‘‰ ( ๐œƒ ฬ‚ ) = [ 0.0012 โˆ’ 0.012 0.001 โˆ’ 0.012 0.102 โˆ’ 0.003 0.001 โˆ’ 0.003 0.003 ] Assume the last observation in your sample has โ„Ž ๐‘‡ = 1.5056 . What is the value of the conditional variance ๐‘‰ ๐‘‡ โˆ’ 1 ( ๐‘Ÿ ๐‘‡ ) ?

Consider the following GARCH(1,1) model for the volatility of asset returns ๐‘Ÿ ๐‘ก : ๐‘Ÿ ๐‘ก = ๐›ผ + ๐›ฝ ๐‘Ÿ ๐‘ก โˆ’ 1 + ๐œ€ ๐‘ก ๐œ€ ๐‘ก = โ„Ž ๐‘ก ๐‘ข ๐‘ก โ„Ž ๐‘ก = ๐œ‡ + ๐›ฟ โ„Ž ๐‘ก โˆ’ 1 + ๐œ™ ๐œ€ ๐‘ก โˆ’ 1 2 ๐”ผ ๐‘ก โˆ’ 1 ( ๐‘ข ๐‘ก ) = 0 ๐”ผ ๐‘ก โˆ’ 1 ( ๐‘ข ๐‘ก 2 ) = 1 You estimated the following values for the parameters Estimates Parameters ๐›ผ ๐›ฝ ๐œ‡ ๐›ฟ ๐œ™ Estimates 0.1911 0.9722 0.0011 0.9321 0.0821 Assume that the last 2 observations of the return process are ๐‘Ÿ ๐‘‡ = 0.07 and ๐‘Ÿ ๐‘‡ โˆ’ 1 = 0.03 , and the value of the conditional variance in the last period of your sample is โ„Ž ๐‘‡ = 0.55 . Then what is the predicted value of the conditional variance โ„Ž ๐‘‡ + 1 in period ๐‘‡ + 1 ?

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