This paper discusses the estimation of fractionally integrated processes with seasonal components. In order to estimate the fractional parameters, we propose several estimators obtained from the regression of the log-periodogram ...

This article deals with the efficiency of fractional integration parameter estimators. This study was based on Monte Carlo experiments involving simulated stochastic processes with integration orders in the range]-1,1[. ...

We provide an almost sure convergent expansion of a process with power law of fractional order by means of some known theorems from harmonic analysis and simple probability theory results.

For appropriate orthonormal wavelet basis {ψ^e_jk} j∈Zk∈Z^de∈{0,1}^d, constants p and γ , if I_γ denotes the Riesz fractional integral operator of order γ and (ηjke)j∈Zk∈Z^de∈{0,1}^d a sequence of independent identically ...

This paper presents the design and application of fractional single-input–single-output (SISO) controllers to a grinding mill circuit, which is a multiple-input–multiple-output (MIMO) process. Two kinds of controllers are ...

This paper presents the design and application of a multiple-input–multiple-output fractional order proportional-integral (MIMO FOPI) controller to a grinding mill circuit. The MIMO FOPI controller pa- rameters are tuned ...

For a fractionally integrated ARFIMA(p, d, q) model, temporal aggregation changes the order of the process to an ARFIMA(p, d,∞), while leaving the value of d unchanged. This paper analyses the effects of temporal aggregation ...