Displaying similar documents to “Extremal (in)dependence of a maximum autoregressive process”

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

Sugata Sen Roy, Sourav Chakraborty (2006)

Applicationes Mathematicae

Similarity:

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.

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

Similarity:

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...

Relationship between Extremal and Sum Processes Generated by the same Point Process

Pancheva, E., Mitov, I., Volkovich, Z. (2009)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17. We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^d as well as for the associated with it sum and extremal processes on an open subset S . The complement of S turns out to be the explosion area of the limit Poisson point process. In order to prove our criterion for weak convergence of the sum processes we introduce and study sum processes...

Hazard rate model and statistical analysis of a compound point process

Petr Volf (2005)

Kybernetika

Similarity:

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...

Branching Processes with Immigration and Integer-valued Time Series

Dion, J., Gauthier, G., Latour, A. (1995)

Serdica Mathematical Journal

Similarity:

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes...