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BU.232.630.W1.SP25 Quiz 3

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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 The Maximum Likelihood estimates and standard errors of the parameters are in the following table. Estimates Std. error ๐›ผ 0.0911 0.1233 ๐›ฝ 0.9222 0.0655 ๐œ‡ 0.0112 0.1212 ๐›ฟ 0.9132 0.2231 ๐œ™ 0.0611 0.0013 Using this information compute the test statistic for the null hypothesis ๐ป 0 : ๐›ผ = 0.2 . (Please round the result to the 4th decimal place.)

้€‰้กน
A.โˆ’ 0.8832 .
B.โˆ’ 7.1631 .
C.0.7388 .
D.5.9923 .
E.There is not enough information to compute the value of the test statistic.
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Question restatement: Given a GARCH(1,1) model and ML estimates with standard errors for the parameters, compute the test statistic for H0: ฮฑ = 0.2 (rounded to 4 decimals). Option 1: โˆ’0.8832. - Calculation: The standard z statistic is z = (ฮฑฬ‚ โˆ’ 0.2) / SE(ฮฑฬ‚). Here ฮฑฬ‚ = 0.0911 and SE(ฮฑฬ‚) = 0.1233. So z = (0.0911 โˆ’ 0.2) / 0.1233 = (โˆ’0.1089) / 0.1233 โ‰ˆ โˆ’0.8832. This matches the shown value and follows the standard approach of testing a single paramete......Login to view full explanation

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