## Long-Memory Processes: Probabilistic Properties and Statistical MethodsLong-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant. |

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### Contents

1 | |

43 | |

Mathematical Concepts | 107 |

Limit Theorems | 209 |

Statistical Inference for Stationary Processes | 385 |

Statistical Inference for Nonlinear Processes | 529 |

Statistical Inference for Nonstationary Processes | 555 |

Forecasting | 733 |

Function Spaces | 797 |

Regularly Varying Functions | 799 |

Vague Convergence | 801 |

Some Useful Integrals | 802 |

Glossary | 806 |

References | 807 |

855 | |

867 | |

### Other editions - View all

Long-Memory Processes: Probabilistic Properties and Statistical Methods Jan Beran,Yuanhua Feng,Sucharita Ghosh,Rafal Kulik No preview available - 2016 |

Long-Memory Processes: Probabilistic Properties and Statistical Methods Jan Beran,Feng Yuanhua,Sucharita Ghosh,Rafal Kulik No preview available - 2013 |

### Common terms and phrases

antipersistence Appell polynomials approximation assume assumption asymptotic distribution autocovariance bandwidth Beran bias bootstrap change point coefficients consider constant covariance defined definition denotes derived Example formula Fourier fractional Brownian motion Furthermore fx(x fy(X Gaussian process Giraitis given Hermite polynomials Hermite rank Hurvich implies independent instance integral Lemma Lévy process limit theorem linear process long memory long-memory processes long-range dependence M-estimators martingale matrix mean squared error methods nonparametric Note observations obtain optimal parameter partial sums particular periodogram point process quantiles random variables rate of convergence Recall regression Robinson sample mean second-order Sect self-similarity semiparametric sequence short memory spectral density standard normal stationary process statistic stochastic volatility Surgailis Taqqu tion trend function vector wavelet Whittle estimator zero mean