  We study the estimation of a stable Cox-Ingersoll-Ross model, which is a
special subcritical continuous-state branching process with immigration. The
process is characterized in terms of some stochastic equations. The exponential
ergodicity and strong mixing property of the process and the heavy tail
behavior of some related random sequences are studied. We also establish the
convergence of some point processes and partial sums associated with the model.
From those results, we derive the consistency and central limit theorems of the
conditional least squares estimators and the weighted conditional least squares
estimators of the drift parameters based on low frequency observations. A
weakly consistent estimator is also proposed for the volatility coefficient
based on high frequency observations.
