Questions
BU.232.630.W1.SP25 Quiz 3
Single choice
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 The Maximum Likelihood estimates and standard errors of the parameters are in the following table. Estimates Std. error ๐ผ 0.0911 0.1233 ๐ฝ 0.9222 0.0655 ๐ 0.0112 0.1212 ๐ฟ 0.9132 0.2231 ๐ 0.0611 0.0013 Using this information compute the test statistic for the null hypothesis ๐ป 0 : ๐ผ = 0.2 . (Please round the result to the 4th decimal place.)
Options
A.โ
0.8832
.
B.โ
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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Step-by-Step Analysis
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: โ0.8832.
- Calculation: The standard z statistic is z = (ฮฑฬ โ 0.2) / SE(ฮฑฬ). Here ฮฑฬ = 0.0911 and SE(ฮฑฬ) = 0.1233. So z = (0.0911 โ 0.2) / 0.1233 = (โ0.1089) / 0.1233 โ โ0.8832. This matches the shown value and follows the standard approach of testing a single paramete......Login to view full explanationLog in for full answers
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