Displaying similar documents to “Asymptotic distribution of the estimated parameters of an ARMA(p,q) process in the presence of explosive roots”

Prediction problems related to a first-order autoregressive process in the presence of outliers

Sugata Sen Roy, Sourav Chakraborty (2006)

Applicationes Mathematicae

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Outliers in a time series often cause problems in fitting a suitable model to the data. Hence predictions based on such models are liable to be erroneous. In this paper we consider a stable first-order autoregressive process and suggest two methods of substituting an outlier by imputed values and then predicting on the basis of it. The asymptotic properties of both the process parameter estimators and the predictors are also studied.

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...

Linear distribution processes.

Bel, L., Oppenheim, G., Robbiano, L., Viano, M.C. (1998)

Journal of Applied Mathematics and Stochastic Analysis

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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...

Stationary distribution of absolute autoregression

Jiří Anděl, Pavel Ranocha (2005)

Kybernetika

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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.

A counting process model of survival of parallel load-sharing system

Petr Volf, Aleš Linka (2001)

Kybernetika

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A system composed from a set of independent and identical parallel units is considered and its resistance (survival) against an increasing load is modelled by a counting process model, in the framework of statistical survival analysis. The objective is to estimate the (nonparametrized) hazard function of the distribution of loads breaking the units of the system (i. e. their breaking strengths), to derive the large sample properties of the estimator, and to propose a goodness-of-fit...

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...