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A spectral characterization of the behavior of discrete time AR–representations over a finite time interval

E. N. Antoniou, Antonis I. G. Vardulakis, Nikolas P. Karampetakis (1998)

Kybernetika

In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also gived.

A uniform central limit theorem for dependent variables

Konrad Furmańczyk (2009)

Applicationes Mathematicae

Niemiro and Zieliński (2007) have recently obtained uniform asymptotic normality for the Bernoulli scheme. This paper concerns a similar problem. We show the uniform central limit theorem for a sequence of stationary random variables.

A zero-inflated geometric INAR(1) process with random coefficient

Hassan S. Bakouch, Mehrnaz Mohammadpour, Masumeh Shirozhan (2018)

Applications of Mathematics

Many real-life count data are frequently characterized by overdispersion, excess zeros and autocorrelation. Zero-inflated count time series models can provide a powerful procedure to model this type of data. In this paper, we introduce a new stationary first-order integer-valued autoregressive process with random coefficient and zero-inflated geometric marginal distribution, named ZIGINAR RC ( 1 ) process, which contains some sub-models as special cases. Several properties of the process are established....

Adaptive density estimation under weak dependence

Irène Gannaz, Olivier Wintenberger (2010)

ESAIM: Probability and Statistics

Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue's measure. [Donoho et al. Ann. Stat.24 (1996) 508–539] propose near-minimax estimators f ^ n based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim of the present work is to extend these results to general weak dependent contexts. Weak dependence assumptions are expressed as decreasing bounds of covariance terms and are...

Algunas características de los modelos agregados MC-MN de modelos MA.

Andrés Carrión García (1988)

Qüestiió

Se estudian algunas propiedades de los modelos agregados de mínimos cuadrados y mínima norma de procesos MA. Dichos agregados MC-MN se obtienen mediante una metodología matricial desarrollada por el autor, que es aquí brevemente esbozadas. Las características analizadas se refieren a la multiplicatividad de las estructuras componentes del modelo y la invertibilidad del modelo agregado.

An estimator for parameters of a nonlinear nonnegative multidimensional AR(1) process

Jiří Anděl (1998)

Applications of Mathematics

Let 𝕖 t = ( e t 1 , , e t p ) ' be a p -dimensional nonnegative strict white noise with finite second moments. Let h i j ( x ) be nondecreasing functions from [ 0 , ) onto [ 0 , ) such that h i j ( x ) x for i , j = 1 , , p . Let 𝕌 = ( u i j ) be a p × p matrix with nonnegative elements having all its roots inside the unit circle. Define a process 𝕏 t = ( X t 1 , , X t p ) ' by X t j = u j 1 h 1 j ( X t - 1 , 1 ) + + u j p h p j ( X t - 1 , p ) + e t j for j = 1 , , p . A method for estimating 𝕌 from a realization 𝕏 1 , , 𝕏 n is proposed. It is proved that the estimators are strongly consistent.

An extreme Markovian-evolutionary (EME) sequence.

José Tiago de Oliveira (1985)

Trabajos de Estadística e Investigación Operativa

The most general sequence, with Gumbel margins, generated by maxima procedures in an auto-regressive way (one step) is defined constructively and its properties obtained; some remarks for statistical estimation are presented.

Análisis Bayesiano del modelo ARE(1) con coeficiente independiente

Demetrio López Romero (1997)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

En este trabajo se introduce el modelo ARE(I) con indicador de nivel mínimo J.l, parámetro que generaliza el modelo ARO) con errores exponenciales y se analiza desde un punto de vista bayesiano, obteniéndose una familia de distribuciones conjugadas para el hiperparámetro que describe el modelo.

Análisis de detección de raíces unitarias en series de tiempo. Un enfoque metodológico con tests no similares.

José Angel Roldán Casas, Rafaela Dios Palomares (2000)

Qüestiió

El presente artículo recoge los resultados de una investigación llevada a cabo con el fin de analizar, desde la perspectiva de la no similaridad, las distribuciones de los distintos estadísticos planteados por Dickey y Fuller para contrastar la presencia de raíz unitaria. Asimismo, se definen zonas de rechazo y aceptación de las hipótesis nulas para cada estadístico, considerando las distintas distribuciones del mismo, y se estudian las situaciones con las que nos podemos encontrar de cara a deducir...

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