Introduction to Statistical Time Series

Fuller, Wayne A.

doi:10.1002/9780470316917

Cited by 1,166 publications

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“…We have repeated a similar analysis using the same number of randomized data points. For this a random phase space was generated employing a first-order autoregression model (FULLER, 1976). Nonlinear stochastic model used here is of the form of: y t =Xy t − 1 + m 1 , t= 1, 2, 3, .…”

Section: Resultsmentioning

confidence: 99%

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Phase Space Structure, Attractor Dimension, Lyapunov Exponent and Nonlinear Prediction from Earth's Atmospheric Angular Momentum Time Series

Tiwari

Rao

1999

Pure and Applied Geophysics

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On a short time scale, Atmospheric Angular Momentum (AAM) has been demonstrated to be essentially the sole excitation source of LOD variations. The LOD variation, therefore, merely reflects the AAM variation (LOD as proxy for AAM). The study of the nonlinear nature of AAM variability (e.g., its orbital complexity, dimensionality and extreme sensitivity to the initial conditions) may provide a physical premise for theoretical modelling of the earth-atmosphere-ocean system. Analysis of the high quality of detailed daily LOD/AAM variations time series, spanning the period of 1962-1992, reveals a non-zero and low positive Lyapunov exponent value which suggests possible evidence of deterministic chaos in the underlying dynamics. Application of modern nonlinear prediction techniques capable of distinguishing chaos and random fractals to the data set, further support the above findings and render a predictive time limit of approximately 12 -15 days. A low dimensional strange attractor and a low average Lyapunov exponent suggest a low level of unpredictability and stability in the system dynamics. It is argued here that a possible source of the raised entropy in LOD/AAM systems possibly stems from a conceivable nonlinear interaction between the seasonal cycle and inter-or intra-annual fluctuations due to thermodynamics properties of the atmosphere-ocean system.

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Section: Resultsmentioning

confidence: 99%

“…, N where m is the normal independent random variables uniformly distributed from the interval 0 to 1. The maximum likelihood estimator is calculated from the data (FULLER, 1976). Figure 6 illustrates the comparison of the results of original, filtered (tidal frequencies) and random data (see the figure caption).…”

Section: Resultsmentioning

confidence: 99%

Phase Space Structure, Attractor Dimension, Lyapunov Exponent and Nonlinear Prediction from Earth's Atmospheric Angular Momentum Time Series

Tiwari

Rao

1999

Pure and Applied Geophysics

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“…Whitenoise tests (Fisher's Kappa, Kolmogorov-Smirnov) were conducted to determine if the biomass time series in each case could be distinguished from a series randomly distributed in time. For 1500 observations, critical values showing significant periodicity at p < 0.01 were: Fisher's Kappa > 12.0 and Kolmogorov-Smirnov statistic > 0.042 (Fuller 1976).…”

Section: Resultsmentioning

confidence: 99%

Response of North American ecosystem models to multi-annual periodicities in temperature and precipitation

et al. 1994

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Ecosystem models typically use input temperature and precipitation data generated stochastically from weather station means and variances. Although the weather station data are based on measurements taken over a few decades, model simulations are usually on the order of centuries. Consequently, observed periodicities in temperature and precipitation at the continental scale that have been correlated with largescale forcings, such as ocean-atmosphere dynamics and lunar and sunspot cycles, are ignored. We investigated how these natural climatic fluctuations affect aboveground biomass in ecosystem models by incorporating some of the more pronounced continental-scale cycles in temperature (4, 11, 80, 180 year periods) and precipitation (11 and 19 year periods) into models of three North American forests (using LINKAGES) and one North American grassland (using STEPPE). Even without inclusion of periodicities in climate, long-term dynamics of these models were characterized by internal frequencies resulting from vegetation birth, growth and death processes. Our results indicate that long-term temperature cycles result in significantly lower predictions of forest biomass than observed in the control case for a forest on a biome transition (northern hardwoods/boreal forest). Lower-frequency, higher-amplitude temperature oscillation caused amplification of forest biomass response in forests containing hardwood species. Shortgrass prairie and boreal ecosystems, dominated by species with broad stress tolerance ranges, were relatively insensitive to climatic oscillations. Our results suggest periodicities in climate should be incorporated within long-term simulations of ecosystems with strong internal frequencies, particularly for systems on biome transitions.

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“…Since the Fourier transform of a convolution is simply the product of the Fourier transforms of its arguments (Fuller (1976), Corollary 3.4.1.1) and the autocovariance function is an even function, we have the following lemma.…”

Section: Closed Form Of Bartlett's Formulaementioning

confidence: 99%