Answer-first summary for fast verification
Answer: $\alpha = 0.075637$ and $\beta = 0.923363$
For a GARCH(1,1) process to be stable, the sum of the parameters $\alpha$ and $\beta$ needs to be less than 1.0. Let's verify each option: - **Option A**: $\alpha + \beta = 0.073637 + 0.927363 = 1.001000$ (slightly greater than 1.0) - **Option B**: $\alpha + \beta = 0.075637 + 0.923363 = 0.999000$ (less than 1.0) - **Option C**: $\alpha + \beta = 0.084637 + 0.916363 = 1.001000$ (slightly greater than 1.0) - **Option D**: $\alpha + \beta = 0.086637 + 0.914363 = 1.001000$ (slightly greater than 1.0) Only Option B satisfies the stability condition where $\alpha + \beta < 1.0$. This ensures that the GARCH(1,1) process is mean-reverting and stationary over time.
Author: LeetQuiz Editorial Team
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A risk analyst is estimating the variance of stock returns on day n, given by , using the equation,
where and represent the return and volatility on day , respectively.
If the values of and are as indicated below and the expected value of the return is constant over time, which combination of values is correct for a GARCH(1,1) process?
A
and
B
and
C
and
D
and
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