Time Series Analysis: Forecasting and Control
About: This article is published in The Statistician.The article was published on 1978-12-01. It has received 5341 citations till now. The article focuses on the topics: Time series.
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TL;DR: It is demonstrated that Ethernet LAN traffic is statistically self-similar, that none of the commonly used traffic models is able to capture this fractal-like behavior, and that such behavior has serious implications for the design, control, and analysis of high-speed, cell-based networks.
Abstract: Demonstrates that Ethernet LAN traffic is statistically self-similar, that none of the commonly used traffic models is able to capture this fractal-like behavior, that such behavior has serious implications for the design, control, and analysis of high-speed, cell-based networks, and that aggregating streams of such traffic typically intensifies the self-similarity ("burstiness") instead of smoothing it. These conclusions are supported by a rigorous statistical analysis of hundreds of millions of high quality Ethernet traffic measurements collected between 1989 and 1992, coupled with a discussion of the underlying mathematical and statistical properties of self-similarity and their relationship with actual network behavior. The authors also present traffic models based on self-similar stochastic processes that provide simple, accurate, and realistic descriptions of traffic scenarios expected during B-ISDN deployment. >
5,567Â citations
TL;DR: Work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.
Abstract: Complex dynamical systems, ranging from ecosystems to financial markets and the climate, can have tipping points at which a sudden shift to a contrasting dynamical regime may occur. Although predicting such critical points before they are reached is extremely difficult, work in different scientific fields is now suggesting the existence of generic early-warning signals that may indicate for a wide class of systems if a critical threshold is approaching.
3,450Â citations
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01 Feb 2006TL;DR: Wavelet analysis of finite energy signals and random variables and stochastic processes, analysis and synthesis of long memory processes, and the wavelet variance.
Abstract: 1. Introduction to wavelets 2. Review of Fourier theory and filters 3. Orthonormal transforms of time series 4. The discrete wavelet transform 5. The maximal overlap discrete wavelet transform 6. The discrete wavelet packet transform 7. Random variables and stochastic processes 8. The wavelet variance 9. Analysis and synthesis of long memory processes 10. Wavelet-based signal estimation 11. Wavelet analysis of finite energy signals Appendix. Answers to embedded exercises References Author index Subject index.
2,734Â citations
TL;DR: In this paper, the authors review emerging ways to link theory to observation, and conclude that although, field observations can provide hints of alternative stable states, experiments and models are essential for a good diagnosis.
Abstract: Occasionally, surprisingly large shifts occur in ecosystems. Theory suggests that such shifts can be attributed to alternative stable states. Verifying this diagnosis is important because it implies a radically different view on management options, and on the potential effects of global change on such ecosystems. For instance, it implies that gradual changes in temperature or other factors might have little effect until a threshold is reached at which a large shift occurs that might be difficult to reverse. Strategies to assess whether alternative stable states are present are now converging in fields as disparate as desertification, limnology, oceanography and climatology. Here, we review emerging ways to link theory to observation, and conclude that although, field observations can provide hints of alternative stable states, experiments and models are essential for a good diagnosis.
2,464Â citations
01 Mar 1991
TL;DR: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher- order statistics to practical problems is demonstrated.
Abstract: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher-order statistics to practical problems is demonstrated. Most of the results are given for one-dimensional processes, but some extensions to vector processes and multichannel systems are discussed. The topics covered include cumulant-polyspectra formulas; impulse response formulas; autoregressive (AR) coefficients; relationships between second-order and higher-order statistics for linear systems; double C(q,k) formulas for extracting autoregressive moving average (ARMA) coefficients; bicepstral formulas; multichannel formulas; harmonic processes; estimates of cumulants; and applications to identification of various systems, including the identification of systems from just output measurements, identification of AR systems, identification of moving-average systems, and identification of ARMA systems. >
1,854Â citations