Stochastic And Statistical Analysis Of Long- Range Dependent Processes With "Mathematica"
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A. Novikov & N. Kordzakhia
Stochastic and Statistical Analysis of Long- Range Dependent Processes with "Mathe- matica" A. Novikov & N. Kordzakhia of Abstract Mathematical models of stationary long-range dependent processes are more complicated then ordinary autoregressive models as they involve fractional difference equations (or, even fractional differential equations in continuous time case). The explicit representation of solutions of these equations re- quires special functions like hypergeometric or Gegenbauer polynomials. This paper demonstrates that Mathematica capability doing symbolic calculations makes both stochastic and statistical analysis of stationary processes with long memory easier. 1 Introduction A stationary process Xt with long memory, or with long-range dependence (LRD) is characterized by a slow rate of convergence of the covariance func- tion #(g) = ccw(%t,Xt+g) to zero: ][%Q |B(s)| = oo in case of discrete-time parameter; j^ |B(s