GARCH modelheteroskedasticAn integer-valued analogue of the classical generalized autoregressive conditional heteroskedastic (GARCH) ( p , q ) model with Poisson deviates is proposed and a condition for the existence of such a process is given. For the case p = 1, q = 1, it is explicitly ...
We consider the integer valued GARCH(1,1) process defined by the two equation system Yn similar to dPoisson(lambda n) and lambda(n + 1) = omega + alpha Y-n + beta lambda(n). When alpha + beta < 1 this process has a stationary solution and properties are well understood. In this...
PortugalWeproposeaninteger-valuedstochasticprocesswithconditionalmarginaldistributionbelongingtotheclassofinfinitelydivisiblediscreteprobabilitylaws.Withthisproposal,weintroduceawideclassofmodelsforcounttimeseriesthatincludesthePoissoninteger-valuedgeneralizedautoregressiveconditionalheteroscedastic(INGARCH)model(Ferlandetal.,...
The advantage of Bayesian inference for INGARCHX models is that it provides a method of estimation and forecasts that fully take into account parameter uncertainty and prior knowledge about a random process. One can thus impose parameter constraints appropriately as a part of the prior distribution....
MCMC based Estimation of MS-ARMA-GARCH Models They can account for sudden changes in the structure of the mean or the variance of a process and give a straightforward interpretation of these shifts. Such shifts would cause regular ARMA-GARCH models to imply non-stationary processes... J. Henne...
tosenselessresultssincetheasymptoticbehaviorofthecorrespondingstatisticalparametersordistributionsisnotavail-able.Amongtheinteger-valuedmodelspresentedinliteratureinthelastdecade(e.g.,[11]),wehighlighttheINGARCHone,[4],analogoustoGARCHmodels[2]butwithPoissondeviates,thatis,theprocessattimetgivenitspastfollowsa...
To fill this gap, we introduce a new class of beta-binomial integer-valued GARCH models, establish the geometric moment contracting property of its conditional mean process, discuss the stationarity and ergodicity of the observed process and its conditional mean process, and give some stochastic ...
Periodically correlated integer-valued processThis article deals with some probabilistic and statistical properties of a periodic integer-valued GARCH(1,1) model. Necessary and sufficient conditions for the periodical stationary, both in mean and second order, are established. The closed-forms of the ...
We give conditions under which the proposed integer-valued GARCH process is stationary, ergodic, and has _nite moments. We consider maximum likelihood estimation for model parameters, and we give the limiting distribution for these estimators when the true parameter vector is in the interior of its...
In particular, the mean of this model can be constant, while the variance depends on time as in an ordinary GARCH model. This feature is not possible to be accommodated by the standard INGARCH. Hence, they refer to the model as a pure INGARCH process to highlight the degree of ...