Abstract
We discuss robust estimation of INARCH models for count time series, where each observation conditionally on its past follows a negative binomial distribution with a constant scale parameter, and the conditional mean depends linearly on previous observations. We develop several robust estimators, some of them being computationally fast modifications of methods of moments, and some rather efficient modifications of conditional maximum likelihood. These estimators are compared to related recent proposals using simulations. The usefulness of the proposed methods is illustrated by a real data example.
Highlights
Let Y1, . . . , Yn be a time series of counts like the weekly number of people falling ill in epidemiology, the number of transactions per minute in finance, or jobs sent to a server during an hour
Zhu [28] extends the Poisson integer valued GARCH model, which has been put forward by [12,14], among others, to scenarios where the conditional distribution of Yt given the past of the process exhibits overdispersion
The Poisson and the negative binomial distributions do not form location-scale families and the tail behaviour depends on the parameters, so that suitable choices of the tuning constant in principle depend on the parameters
Summary
Let Y1, . . . , Yn be a time series of counts like the weekly number of people falling ill in epidemiology, the number of transactions per minute in finance, or jobs sent to a server during an hour. A first approach for robust fitting of NBINGARCH( p, q) models has been published by [27] Like these authors we parameterize the negative binomial distribution in terms of the conditional mean μt ≥ 0 and the parameter κ = 1/r ≥ 0. Βq measuring the effects of unobserved past conditional means becomes very difficult We avoid the latter and focus on the simpler class of NBINARCH( p) models, where we regress on past observations, only. Xiong and Zhu recommend the MCD [24] for dealing with outlying past observations, the MCD has been designed for multivariate elliptically symmetric continuous measurements [17] This may eliminate observations from the estimating equations just a single preceding value is spurious.
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