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Information contained in design points of experiments with correlated observations

Andrej Pázman (2010)

Kybernetika

A random process (field) with given parametrized mean and covariance function is observed at a finite number of chosen design points. The information about its parameters is measured via the Fisher information matrix (for normally distributed observations) or using information functionals depending on that matrix. Conditions are stated, under which the contribution of one design point to this information is zero. Explicit expressions are obtained for the amount of information coming from a selected...

Intelligent financial time series forecasting: A complex neuro-fuzzy approach with multi-swarm intelligence

Chunshien Li, Tai-Wei Chiang (2012)

International Journal of Applied Mathematics and Computer Science

Financial investors often face an urgent need to predict the future. Accurate forecasting may allow investors to be aware of changes in financial markets in the future, so that they can reduce the risk of investment. In this paper, we present an intelligent computing paradigm, called the Complex Neuro-Fuzzy System (CNFS), applied to the problem of financial time series forecasting. The CNFS is an adaptive system, which is designed using Complex Fuzzy Sets (CFSs) whose membership functions are complex-valued...

Investigation of periodicity for dependent observations

Tomáš Cipra (1984)

Aplikace matematiky

It is proved that Hannan's procedure for statistical test of periodicity in the case of time series with dependent observations can be combined with Siegel's improvement of the classical Fischer's test of periodicity. Simulations performed in the paper show that this combination can increase the power of Hannan's test when at least two periodicities are present in the time series with dependent observations.

Irregular sampling and central limit theorems for power variations : the continuous case

Takaki Hayashi, Jean Jacod, Nakahiro Yoshida (2011)

Annales de l'I.H.P. Probabilités et statistiques

In the context of high frequency data, one often has to deal with observations occurring at irregularly spaced times, at transaction times for example in finance. Here we examine how the estimation of the squared or other powers of the volatility is affected by irregularly spaced data. The emphasis is on the kind of assumptions on the sampling scheme which allow to provide consistent estimators, together with an associated central limit theorem, and especially when the sampling scheme depends on...

Kalman filter with a non-linear non-Gaussian observation relation.

Tomás Cipra, Asunción Rubio (1991)

Trabajos de Estadística

The dynamic linear model with a non-linear non-Gaussian observation relation is considered in this paper. Masreliez's theorem (see Masreliez's (1975)) of approximate non-Gaussian filtering with linear state and observation relations is extended to the case of a non-linear observation relation that can be approximated by a second-order Taylor expansion.

Kriging and masurement errors

István Fazekas, Alexander G. Kukush (2005)

Discussiones Mathematicae Probability and Statistics

A linear geostatistical model is considered. Properties of a universal kriging are studied when the locations of observations aremeasured with errors. Alternative prediction procedures are introduced and their least squares errors are analyzed.

LAMN property for hidden processes : the case of integrated diffusions

Arnaud Gloter, Emmanuel Gobet (2008)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process X. Our data are given by ∫01X(s+i)/n dμ(s) for i=0, …, n−1 and the unknown parameter appears in the diffusion coefficient of the process X only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood of the model, and then study the asymptotic...

Lévy Processes, Saltatory Foraging, and Superdiffusion

J. F. Burrow, P. D. Baxter, J. W. Pitchford (2008)

Mathematical Modelling of Natural Phenomena

It is well established that resource variability generated by spatial patchiness and turbulence is an important influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly,...

Likelihood for interval-censored observations from multi-state models.

Daniel Commenges (2003)

SORT

We consider the mixed dicrete-continuous pattern of observation in a multi-state model; this is a classical pattern because very often clinical status is assessed at discrete visit times while time of death is observed exactly. The likelihood can easily be written heuristically for such models. However a formal proof is not easy in such observational patterns. We give a rigorous derivation al the likelihood for the illness-death model based on applying Jacod´s formula to an observed bivariate counting...

Limit theorems for stationary Markov processes with L2-spectral gap

Déborah Ferré, Loïc Hervé, James Ledoux (2012)

Annales de l'I.H.P. Probabilités et statistiques

Let ( X t , Y t ) t ∈ 𝕋 be a discrete or continuous-time Markov process with state space 𝕏 × ℝ d where 𝕏 is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. ( X t , Y t ) t ∈ 𝕋 is assumed to be a Markov additive process. In particular, this implies that the first component ( X t ) t ∈ 𝕋 is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process ( Y t ) t ∈ 𝕋 is shown to satisfy the...

Linear approximations to some non-linear AR(1) processes

Jiří Anděl (2000)

Kybernetika

Some methods for approximating non-linear AR(1) processes by classical linear AR(1) models are proposed. The quality of approximation is studied in special non-linear AR(1) models by means of comparisons of quality of extrapolation and interpolation in the original models and in their approximations. It is assumed that the white noise has either rectangular or exponential distribution.

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