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Some unresolved issued in non-linear population dynamics.

Joe N. Perry (1997)

Qüestiió

The Lyapunov exponent is a statistic that measures the sensitive dependence of the dynamic behaviour of a system on its initial conditions. Estimates of Lyapunov exponents are often used to characterize the qualitative population dynamics of insect time series. The methodology for estimation of the exponent for an observed, noisy, short ecological time series is still under development. Some progress has been made recently in providing measures of error for these exponents. Studies that do not account...

Spatial prediction of the mark of a location-dependent marked point process: How the use of a parametric model may improve prediction

Tomáš Mrkvička, François Goreaud, Joël Chadoeuf (2011)

Kybernetika

We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory...

Spatial structure analysis using planar indices.

José Miguel Albert, Jorge Mateu, J. C. Pernías (2000)

Qüestiió

Spatial planar indices have become a useful tool to analyze patterns of points. Despite that, no simulation study has been reported in literature in order to analyze the behaviour of these quantities under different pattern structures. We present here an extensive Monte Carlo simulation study focused on two important indices: the Index of Dispersion and the Index of Cluster Size, usually used to detect lack of homogeneity in a spatial point model. Finally, an application is also presented.

Spatio-temporal modelling of a Cox point process sampled by a curve, filtering and Inference

Blažena Frcalová, Viktor Beneš (2009)

Kybernetika

The paper deals with Cox point processes in time and space with Lévy based driving intensity. Using the generating functional, formulas for theoretical characteristics are available. Because of potential applications in biology a Cox process sampled by a curve is discussed in detail. The filtering of the driving intensity based on observed point process events is developed in space and time for a parametric model with a background driving compound Poisson field delimited by special test sets. A...

Spectral density estimation for stationary stable random fields

Rachid Sabre (1995)

Applicationes Mathematicae

We consider a stationary symmetric stable bidimensional process with discrete time, having the spectral representation (1.1). We consider a general case where the spectral measure is assumed to be the sum of an absolutely continuous measure, a discrete measure of finite order and a finite number of absolutely continuous measures on several lines. We estimate the density of the absolutely continuous measure and the density on the lines.

Spectrum of randomly sampled multivariate ARMA models

Amina Kadi (1998)

Kybernetika

The paper is devoted to the spectrum of multivariate randomly sampled autoregressive moving-average (ARMA) models. We determine precisely the spectrum numerator coefficients of the randomly sampled ARMA models. We give results when the non-zero poles of the initial ARMA model are simple. We first prove the results when the probability generating function of the random sampling law is injective, then we precise the results when it is not injective.

State-space realization of nonlinear control systems: unification and extension via pseudo-linear algebra

Juri Belikov, Ülle Kotta, Maris Tõnso (2012)

Kybernetika

In this paper the tools of pseudo-linear algebra are applied to the realization problem, allowing to unify the study of the continuous- and discrete-time nonlinear control systems under a single algebraic framework. The realization of nonlinear input-output equation, defined in terms of the pseudo-linear operator, in the classical state-space form is addressed by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials. This allows...

Stationarity and invertibility of a dynamic correlation matrix

Michael McAleer (2018)

Kybernetika

One of the most widely-used multivariate conditional volatility models is the dynamic conditional correlation (or DCC) specification. However, the underlying stochastic process to derive DCC has not yet been established, which has made problematic the derivation of asymptotic properties of the Quasi-Maximum Likelihood Estimators (QMLE). To date, the statistical properties of the QMLE of the DCC parameters have purportedly been derived under highly restrictive and unverifiable regularity conditions....

Stationary distribution of absolute autoregression

Jiří Anděl, Pavel Ranocha (2005)

Kybernetika

A procedure for computation of stationary density of the absolute autoregression (AAR) model driven by white noise with symmetrical density is described. This method is used for deriving explicit formulas for stationary distribution and further characteristics of AAR models with given distribution of white noise. The cases of Gaussian, Cauchy, Laplace and discrete rectangular distribution are investigated in detail.

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