Inference for infinite variance circular time series models via Estimating Functions

Recently there has been a growing interest in stochastic processes with infinite variance circular time series. This is due to the inherent challenge and theoretical interest provided by the non-normal stable laws as well as the possibility that the processes constructed from these laws may be appropriate models for many diverse phenomena. In practice, any time series which exhibits sharp spikes or occasional bursts of outlying observations suggests the possible use of a model with stable errors having infinite variance. For time series models with infinite variance stable errors and for circular time series time series with wrapped stable errors, closed form expressions for the density are not available and hence the maximum likelihood estimate cannot be obtained, Merkouris (2007) and Thavaneswaran et al. (2013) have used combined sine and cosine estimating functions to study estimation and recursive estimation. In this paper, we propose to discuss recursive estimation and filtering for infinite variance circular time series models using estimating functions.