LONG-RANGE DEPENDENCE AND MIXING FOR DISCRETE TIME FRACTIONAL PROCESSES

type="main" xml:lang="en"> Abstract. A large class of discrete time stationary processes, an extension of the well-known fractionally integrated autoregressive moving-average models, is investigated. For a suitable choice of parameters, these processes are long-range dependent. After a detailed study of the asymptotic behaviour of their correlations, we investigate their mixing properties and then give some simulated examples.

[1]  H. Künsch.  Discrimination between monotonic trends and long-range dependence , 1986 .

[2]  M. Ichise,et al.  An analog simulation of non-integer order transfer functions for analysis of electrode processes , 1971 .

[3]  H. L. Gray,et al.  ON GENERALIZED FRACTIONAL PROCESSES , 1989 .

[4]  D. Sarason,et al.  Past and Future , 1967 .

[5]  J. Hosking.  Modeling persistence in hydrological time series using fractional differencing , 1984 .

[6]  Esmeralda Gonçalves.  Une généralisation des processus ARMA , 1987 .

[7]  Tuan Pham,et al.  Some mixing properties of time series models , 1985 .

[8]  J. Beran.  Statistical methods for data with long-range dependence , 1992 .

[9]  J. Geweke,et al.  THE ESTIMATION AND APPLICATION OF LONG MEMORY TIME SERIES MODELS , 1983 .

[10]  B. Mandelbrot,et al.  Fractional Brownian Motions, Fractional Noises and Applications , 1968 .

[11]  Laurent Baratchart,et al.  Existence and Generic Properties of L2 Approximants for Linear Systems , 1986 .

[12]  Uwe Hassler.  REGRESSION OF SPECTRAL ESTIMATORS WITH FRACTIONALLY INTEGRATED TIME SERIES , 1993 .

[13]  K. B. Oldham.  Semiintegral electroanalysis. Analog implementation , 1973 .

[14]  Uwe Hassler,et al.  MIS)SPECIFICATION OF LONG MEMORY IN SEASONAL TIME SERIES , 1994 .

[15]  C. Hurvich,et al.  ASYMPTOTICS FOR THE LOW‐FREQUENCY ORDINATES OF THE PERIODOGRAM OF A LONG‐MEMORY TIME SERIES , 1993 .

[16]  S. Porter-Hudak.  An Application of the Seasonal Fractionally Differenced Model to the Monetary Aggregates , 1990 .

[17]  P. Newbold,et al.  BIAS IN AN ESTIMATOR OF THE FRACTIONAL DIFFERENCE PARAMETER , 1993 .

[18]  C. Granger,et al.  AN INTRODUCTION TO LONG‐MEMORY TIME SERIES MODELS AND FRACTIONAL DIFFERENCING , 1980 .

[19]  V. Volkonskii,et al.  Some Limit Theorems for Random Functions. II , 1959 .

[20]  Georges Oppenheim,et al.  Continuous-time fractional ARMA processes , 1994 .