Parameter estimation of stochastic process with long-range dependence and intermittency (Q2759336)

This paper deals with estimation of parameters involved in a spectral density function of the form \(\phi(\omega,\theta)=\eta|\omega|^{-2\beta}(1+\omega^2)^{-\alpha}\), \(\omega\in R^1\), where \(\theta=(\alpha,\beta,\eta)\in[1/2,\infty)\times(0,1/2)\times(0,\infty)\) is a vector of unknown parameters. The authors propose an estimation procedure and the weak consistency of the Gauss-Whittle estimators for \(\alpha\) and \(\beta\). An approximation procedure is developed and a numerical scheme for the estimation procedure is provided. The resulting estimators are shown to be strongly consistent and asymptotically normal. Numerical results are presented and demonstrate that the estimation procedure can detect whether a given set of real data exhibits both long-range dependence and intermittency.