Answer: α = 0.075637 and β = 0.923363

For a GARCH (1,1) process to be stable, the parameters α (alpha) and β (beta) must be positive and their sum must be less than 1. This is because the GARCH model is a way to model financial time series data and estimate the volatility of returns. The stability condition ensures that the variance of the process does not explode or become negative, which would be unrealistic in financial contexts. In the provided options: - Option A: α = 0.073637 and β = 0.927363, the sum is 1.000000, which violates the stability condition. - Option B: α = 0.075637 and β = 0.923363, the sum is 0.999000, which satisfies the stability condition. - Option C: α = 0.084637 and β = 0.916363, the sum is 1.001000, which violates the stability condition. - Option D: α = 0.086637 and β = 0.914363, the sum is 1.001000, which also violates the stability condition. Therefore, the correct answer is B, as it is the only combination where the sum of α and β is less than 1, ensuring the stability of the GARCH (1,1) process.

Author: LeetQuiz Editorial Team