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We consider a stable Cox--Ingersoll--Ross process driven by a standard Wienerprocess and a spectrally positive strictly stable L\'evy process, and we studyasymptotic properties of the maximum likelihood estimator (MLE) for its growthrate based on continuous time observations. We distinguish three cases:subcritical, critical and supercritical. In all cases we prove strongconsistency of the MLE in question, in the subcritical case asymptoticnormality, and in the supercritical case asymptotic mixed normality are shownas well. In the critical case the description of the asymptotic behavior of theMLE in question remains open.

Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations