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I estimated a GARCH(1,1) model and the sum of the ARCH paramter alpha and GARCH paramter beta equals 1.7. This points to an undefined unconditional variance and it follows that the conditional variance is a non-stationary and explosive process (Cuthbertson and Nitzsche, 2004).
However, Groenendijk et al. (1995) argue that the conditional variance process is still stationary, though not covariance-stationary.

Now, I am wondering what is meant by stationary. I assumed that stationarity (strict stationarity) implies covariance-stationarity (weak stationarity). And besides, which implications has a stationary conditional variance as opposed to a non-stationary conditional variance in this context?

Any help would be much appreciated!!!

References:

Cuthbertson, K. and Nitzsche, D. (2004). Quantitative Financial Economics: Stocks, Bonds and Foreign Exchange. John Wiley & Sons, Ltd.

Groenendijk, P. A., Lucas, A. and de Vries, C. G. (1995). A note on the relation- ship between GARCH and symmetric stable processes. Journal of Empirical Finance, 2 (3), 253–264.

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