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Displaying similar documents to “Prediction problems related to a first-order autoregressive process in the presence of outliers”

Hazard rate model and statistical analysis of a compound point process

Petr Volf (2005)

Kybernetika

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A stochastic process cumulating random increments at random moments is studied. We model it as a two-dimensional random point process and study advantages of such an approach. First, a rather general model allowing for the dependence of both components mutually as well as on covariates is formulated, then the case where the increments depend on time is analyzed with the aid of the multiplicative hazard regression model. Special attention is devoted to the problem of prediction of process...

Asymptotic properties of the minimum contrast estimators for projections of inhomogeneous space-time shot-noise Cox processes

Jiří Dvořák, Michaela Prokešová (2016)

Applications of Mathematics

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We consider a flexible class of space-time point process models—inhomogeneous shot-noise Cox point processes. They are suitable for modelling clustering phenomena, e.g. in epidemiology, seismology, etc. The particular structure of the model enables the use of projections to the spatial and temporal domain. They are used to formulate a step-wise estimation method to estimate different parts of the model separately. In the first step, the Poisson likelihood approach is used to estimate...

Stable-1/2 bridges and insurance

Edward Hoyle, Lane P. Hughston, Andrea Macrina (2015)

Banach Center Publications

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We develop a class of non-life reserving models using a stable-1/2 random bridge to simulate the accumulation of paid claims, allowing for an essentially arbitrary choice of a priori distribution for the ultimate loss. Taking an information-based approach to the reserving problem, we derive the process of the conditional distribution of the ultimate loss. The "best-estimate ultimate loss process" is given by the conditional expectation of the ultimate loss. We derive explicit expressions...

Extremal (in)dependence of a maximum autoregressive process

Marta Ferreira (2013)

Discussiones Mathematicae Probability and Statistics

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Maximum autoregressive processes like MARMA (Davis and Resnick, [5] 1989) or power MARMA (Ferreira and Canto e Castro, [12] 2008) have singular joint distributions, an unrealistic feature in most applications. To overcome this pitfall, absolute continuous versions were presented in Alpuim and Athayde [2] (1990) and Ferreira and Canto e Castro [14] (2010b), respectively. We consider an extended version of absolute continuous maximum autoregressive processes that accommodates both asymptotic...

Asymptotic distribution of the estimated parameters of an ARMA(p,q) process in the presence of explosive roots

Sugata Sen Roy, Sankha Bhattacharya (2012)

Applicationes Mathematicae

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We consider an autoregressive moving average process of order (p,q)(ARMA(p,q)) with stationary, white noise error variables having uniformly bounded fourth order moments. The characteristic polynomials of both the autoregressive and moving average components involve stable and explosive roots. The autoregressive parameters are estimated by using the instrumental variable technique while the moving average parameters are estimated through a derived autoregressive process using the same...

Hurwicz's estimator of the autoregressive model with non-normal innovations

Youcef Berkoun, Hocine Fellag (2011)

Applicationes Mathematicae

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Using the Bahadur representation of a sample quantile for m-dependent and strong mixing random variables, we establish the asymptotic distribution of the Hurwicz estimator for the coefficient of autoregression in a linear process with innovations belonging to the domain of attraction of an α-stable law (1 < α < 2). The present paper extends Hurwicz's result to the autoregressive model.

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

Blažena Frcalová, Viktor Beneš (2009)

Kybernetika

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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...

On cumulative process model and its statistical analysis

Petr Volf (2000)

Kybernetika

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The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator...