Ch. 16. Discrete variate time series

Numerous time series admit weak autoregressive-moving average (ARMA) representations, in which the errors are uncorrelated but not necessarily independent nor martingale differences. The statistical inference of this general class of models requires the estimation of generalized Fisher information matrices. We give analytic expressions and propose consistent estimators of these matrices, at any point of the parameter space. Our results are illustrated by means of Monte Carlo experiments and by analyzing the dynamics of daily returns and squared daily returns of financial series.

show abstract

“…McKenzie (2003) reviews the literature on models for integer-valued time series. Let • be the thinning operator defined by…”

Section: Strong Semistrong and Weak Arma Representationsmentioning

confidence: 99%

Computing and estimating information matrices of weak ARMA models

Maïnassara

Carbon

Francq

2012

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

show abstract

“…The analysis of time series of counts has become an important area of research in the last two decades par- We refer to McKenzie (2003) for an overview of the early work in this area and to Tremayne (2006, 2010) and Weiß (2008b) for recent developments.…”

Section: Introductionmentioning

confidence: 99%

Integer-Valued Self-Exciting Threshold Autoregressive Processes

Monteiro

Scotto

Pereira

2012

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

In this paper we introduce a class of self-exciting threshold integer-valued autoregressive models driven by independent Poisson-distributed random variables. Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the least squares-type and likelihood-based ones. Their performance is compared through a simulation study.

show abstract

“…For an overview of the literature in this area refer to the review work by McKenzie (2003) and the monographs of MacDonald and Zucchini (1997) or Kedem and Fokianos (2002). Count data models may be divided into two broad categories: observation-driven and parameter driven models.…”

Section: Introductionmentioning

confidence: 99%

On the maximum of periodic integer-valued sequences with exponential type tails via max-semistable laws

Hall

Temido

2012

Journal of Statistical Planning and Inference

View full text Add to dashboard Cite

In this work we study the limiting distribution of the maximum term of periodic integer-valued sequences with marginal distribution belonging to a particular class where the tail decays exponentially. This class does not belong to the domain of attraction of any max-stable distribution. Nevertheless, we prove that the limiting distribution is max-semistable when we consider the maximum of the first k n observations, for a suitable sequence {k n } increasing to infinity. We obtain an expression for calculating the extremal index of sequences satisfying certain local conditions similar to conditions D (m) (u n ), m ∈ N, defined by Chernick et al. (1991). We apply the results to a class of max-autoregressive sequences and a class of moving average models. The results generalize the ones obtained for the stationary case.

show abstract

Ch. 16. Discrete variate time series

Cited by 149 publications

References 66 publications

Computing and estimating information matrices of weak ARMA models

Computing and estimating information matrices of weak ARMA models

Integer-Valued Self-Exciting Threshold Autoregressive Processes

On the maximum of periodic integer-valued sequences with exponential type tails via max-semistable laws

Contact Info

Product

Resources

About