FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility
An analyst estimates a GARCH(1,1) model with alpha = 0.12 and beta = 0.90. What is the main implication for the estimated model?
The model is nonstationary because alpha plus beta equals 1.02, above one. Stationary GARCH(1,1) requires persistence below one for a finite positive long-run variance, so the implied variance is not valid.
- AThe model is nonstationary because alpha + beta exceeds 1, so no finite long-run variance existsCorrect
- BThe model is stationary because beta exceeds alpha
- CThe long-run variance is negative but still usable
- DThe model is stationary because alpha is below 0.2
Explanation
Alpha + beta = 1.02, which is above 1. Stationarity requires alpha + beta < 1, so the unconditional variance omega/(1 - alpha - beta) would be negative and meaningless. The estimation should be constrained or the model respecified.
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