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Series (mathematics)
About: Series (mathematics) is a research topic. Over the lifetime, 31012 publications have been published within this topic receiving 625614 citations. The topic is also known as: mathematical series.
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TL;DR: This excellent text provides a comprehensive treatment of the state space approach to time series analysis, where observations are regarded as made up of distinct components such as trend, seasonal, regression elements and disturbence terms, each of which is modelled separately.
Abstract: This excellent text provides a comprehensive treatment of the state space approach to time series analysis. The distinguishing feature of state space time series models is that observations are regarded as made up of distinct components such as trend, seasonal, regression elements and disturbence terms, each of which is modelled separately. The techniques that emerge from this approach are very flexible and are capable of handling a much wider range of problems than the main analytical system currently in use for time series analysis, the Box-Jenkins ARIMA system. The book provides an excellent source for the development of practical courses on time series analysis.
1,931 citations
TL;DR: In this paper, the authors define measures of linear dependence and feedback for multiple time series, and a readily usable theory of inference for all of these measures and their decompositions is described; the computations involved are modest.
Abstract: Measures of linear dependence and feedback for multiple time series are defined. The measure of linear dependence is the sum of the measure of linear feedback from the first series to the second, linear feedback from the second to the first, and instantaneous linear feedback. The measures are nonnegative, and zero only when feedback (causality) of the relevant type is absent. The measures of linear feedback from one series to another can be additively decomposed by frequency. A readily usable theory of inference for all of these measures and their decompositions is described; the computations involved are modest.
1,874 citations
TL;DR: An error estimate is presented for this forecasting technique for chaotic data, and its effectiveness is demonstrated by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow.
Abstract: We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we ``learn'' the induced nonlinear mapping using local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow.
1,836 citations