## Statistics for Long-Memory ProcessesStatistical Methods for Long Term Memory Processes covers the diverse statistical methods and applications for data with long-range dependence. Presenting material that previously appeared only in journals, the author provides a concise and effective overview of probabilistic foundations, statistical methods, and applications. The material emphasizes basic principles and practical applications and provides an integrated perspective of both theory and practice. This book explores data sets from a wide range of disciplines, such as hydrology, climatology, telecommunications engineering, and high-precision physical measurement. The data sets are conveniently compiled in the index, and this allows readers to view statistical approaches in a practical context. Statistical Methods for Long Term Memory Processes also supplies S-PLUS programs for the major methods discussed. This feature allows the practitioner to apply long memory processes in daily data analysis. For newcomers to the area, the first three chapters provide the basic knowledge necessary for understanding the remainder of the material. To promote selective reading, the author presents the chapters independently. Combining essential methodologies with real-life applications, this outstanding volume is and indispensable reference for statisticians and scientists who analyze data with long-range dependence. |

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basic book for long rang dependence

### Contents

Stationary processes with long memory | 41 |

Limit theorems | 67 |

heuristic approaches | 81 |

time domain MLE | 100 |

frequency domain | 116 |

Robust estimation of long memory | 124 |

Estimation of location and scale forecasting | 148 |

Regression | 172 |

Goodness of fit tests and related topics | 197 |

Miscellaneous topics | 211 |

Programs and data sets | 218 |

Bibliography | 262 |

Author index | 302 |

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### Common terms and phrases

analysis applications approximate assume assumptions asymptotic behavior Beran calculation called Chapter consider constant contrast converges correlations covariance decay defined definition denote dependence derived deviations discussed distribution effect efficiency equal equation error estimate example exists expected Figure finite fitted Fourier fractional Gaussian noise frequencies function given hand holds illustrates increases independent infinite influence instance integral interested interval known lags least limit linear log-log log-scale long memory long-range dependence matrix measurements methods needs Note observations obtained parameter particular periodogram plot polynomial positive practice prediction probability properties question random variables regression respectively sample mean scale self-similarity simple simulated slope slowly spectral density spectrum squares stationary process statistical Suppose Table tends Theorem tion trend values variance vector zero

### Popular passages

Page 284 - Lovejoy, S., and Schertzer, D., 1986, Scale invariance, symmetries, fractals, and stochastic simulations of atmospheric phenomena: Bull.

### References to this book

Time Series Analysis and Its Applications Robert H. Shumway,David S. Stoffer No preview available - 2000 |