Maximum likelihood estimation of the Cox-Ingersoll-Ross model using particle filters

I show that the QML procedure, used in many papers in the current literature to estimate the CIR model from time series data, is based on an approximation of the latent factors' density that becomes very inaccurate for typical parameter values. I also argue that this issue is not addressed by the Monte Carlo experiments carried out to support the conclusion that the QML bias is negligible. The second part of the paper describes a computationally efficient maximum likelihood estimator based on particle filters. The advantage of this estimator is that it takes into account the exact likelihood function while avoiding the huge computational burden associated with MCMC methods. The proposed methodology is implemented and tested on a sample of simulated data