This phenomena is common with financial time series as the sum of GARCH alpha and beta values approaches one (very close, but not exact). There is no issue with the GARCH_CHECK function implementation as the sum does not equal to 1 (slightly smaller). The interpretation of this phenomena (i.e. sum of alpha and beta approaches 1) is that volatility reverts very slowly to its long-run mean.

This phenomena had many practitioners and academics to advocate an alternative model - IGARCH - to account for the integration in the conditional variance process. The IGARCH brings its own challenges as conditional volatility value does not revert to the a long-run mean, thus it can go to infinity.

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