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Consistency of linear and quadratic least squares estimators in regression models with covariance stationary errors

František Štulajter (1991)

Applications of Mathematics

The least squres invariant quadratic estimator of an unknown covariance function of a stochastic process is defined and a sufficient condition for consistency of this estimator is derived. The mean value of the observed process is assumed to fulfil a linear regresion model. A sufficient condition for consistency of the least squares estimator of the regression parameters is derived, too.

Contiguity and LAN-property of sequences of Poisson processes

Friedrich Liese, Udo Lorz (1999)

Kybernetika

Using the concept of Hellinger integrals, necessary and sufficient conditions are established for the contiguity of two sequences of distributions of Poisson point processes with an arbitrary state space. The distribution of logarithm of the likelihood ratio is shown to be infinitely divisible. The canonical measure is expressed in terms of the intensity measures. Necessary and sufficient conditions for the LAN-property are formulated in terms of the corresponding intensity measures.

Convergence model of interest rates of CKLS type

Zuzana Zíková, Beáta Stehlíková (2012)

Kybernetika

This paper deals with convergence model of interest rates, which explains the evolution of interest rate in connection with the adoption of Euro currency. Its dynamics is described by two stochastic differential equations – the domestic and the European short rate. Bond prices are then solutions to partial differential equations. For the special case with constant volatilities closed form solutions for bond prices are known. Substituting its constant volatilities by instantaneous volatilities we...

Copula approach to residuals of regime-switching models

Anna Petričková, Magda Komorníková (2012)

Kybernetika

The autocorrelation function describing the linear dependence is not suitable for description of residual dependence of the regime-switching models. In this contribution, inspired by Rakonczai ([20]), we will model the residual dependence of the regime-switching models (SETAR, LSTAR and ESTAR) with the autocopulas (Archimedean, EV and their convex combinations) and construct improved quality models for the original real time series.

Covariance structure of wide-sense Markov processes of order k ≥ 1

Arkadiusz Kasprzyk, Władysław Szczotka (2006)

Applicationes Mathematicae

A notion of a wide-sense Markov process X t of order k ≥ 1, X t ∼ W M ( k ) , is introduced as a direct generalization of Doob’s notion of wide-sense Markov process (of order k=1 in our terminology). A base for investigation of the covariance structure of X t is the k-dimensional process x t = ( X t - k + 1 , . . . , X t ) . The covariance structure of X t ∼ W M ( k ) is considered in the general case and in the periodic case. In the general case it is shown that X t ∼ W M ( k ) iff x t is a k-dimensional WM(1) process and iff the covariance function of x t has the triangular property....

Criteria for optimal design of small-sample experiments with correlated observations

Andrej Pázman (2007)

Kybernetika

We consider observations of a random process (or a random field), which is modeled by a nonlinear regression with a parametrized mean (or trend) and a parametrized covariance function. Optimality criteria for parameter estimation are to be based here on the mean square errors (MSE) of estimators. We mention briefly expressions obtained for very small samples via probability densities of estimators. Then we show that an approximation of MSE via Fisher information matrix is possible, even for small...

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