### 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 requires 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.

Original language | English |
---|---|

Title of host publication | Innovation in mathematics |

Editors | Keranen, P Mitic, A Hietamaki |

Place of Publication | Southampton, UK |

Publisher | COMPUTATIONAL MECHANICS PUBLICATIONS LTD |

Pages | 369-376 |

Number of pages | 8 |

ISBN (Print) | 9525153029 |

Publication status | Published - 1997 |

Externally published | Yes |

Event | 2nd International Mathematica Symposium (IMS 97) - ROVANIEMI, Finland Duration: 29 Jun 1997 → 4 Jul 1997 |

### Publication series

Name | INTERNATIONAL MATHEMATICA SYMPOSIUM |
---|---|

Publisher | COMPUTATIONAL MECHANICS PUBLICATIONS LTD |

ISSN (Print) | 1239-7725 |

### Conference

Conference | 2nd International Mathematica Symposium (IMS 97) |
---|---|

Country | Finland |

City | ROVANIEMI |

Period | 29/06/97 → 4/07/97 |

## Cite this

Novikov, A., & Kordzakhia, N. (1997). Stochastic and statistical analysis of long-range dependent processes with ''Mathematica''. In Keranen, P. Mitic, & A. Hietamaki (Eds.),

*Innovation in mathematics*(pp. 369-376). (INTERNATIONAL MATHEMATICA SYMPOSIUM). Southampton, UK: COMPUTATIONAL MECHANICS PUBLICATIONS LTD.