Time-varying autoregressive parameter estimation of cauchy processes by particle filters

In this work, a new method is proposed in order to sequentially estimate the time-varying parameters of a Cauchy distributed process. For this purpose, particle filters, which are used in non-Gaussian and nonlinear Bayesian applications, are utilised. The proposed method forms a basis for the possible future applications of the -stable distributions with timevarying autoregressive coefficients, since it is the first general method that can be used for the estimation of such coefficients without using any restrictions on the parameters. The method is tested both for abruptly and slowly changing autoregressive parameters and observed to be performing very well.