Regularised Estimators for ARFIMA Processes

Stochastic processes with long-range dependence are found in many applications. ARFIMA models can be used to characterise both their short-term correlations and the phenomenon of long-range dependence. Maximum likelihood estimates of the model parameters have nice statistical properties but are ill-conditioned and hard to compute. Whittle's approximation has the same asymptotic properties and yet is easier to compute. We propose a regularisation of Whittle's approximation that overcomes the problem of ill-conditioning. Good results are demonstrated in numerical simulations.