FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
In estimating a GARCH(1,1) model, an analyst obtains alpha = 0.12 and beta = 0.90. What is the correct interpretation?
Because alpha plus beta equals 1.02, which exceeds one, the GARCH(1,1) model is not mean-reverting and has no finite long-run variance. Stationarity requires the sum of the parameters to be below one, not each parameter separately.
- AThe model is non-stationary because alpha plus beta exceeds one, so no finite long-run variance existsCorrect
- BThe model is stationary because each parameter is below one
- CThe long-run variance equals omega divided by 1.02
- DThe model is valid only if omega is negative
Explanation
Alpha + beta = 1.02 > 1, so the process is not covariance stationary and the long-run variance omega/(1-alpha-beta) would be negative or undefined. Stationarity requires the sum below one, not each parameter individually.
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