Robust Fitting of Inarch Models

Abstract

We discuss robust M‐estimation of INARCH models for count time series. These models assume the observation at each point in time to follow a Poisson distribution conditionally on the past, with the conditional mean being a linear function of previous observations. This simple linear structure allows us to transfer M‐estimators for autoregressive models to this situation, with some simplifications being possible because the conditional variance given the past equals the conditional mean. We investigate the performance of the resulting generalized M‐estimators using simulations. The usefulness of the proposed methods is illustrated by real data examples.

tscount: An R Package for Analysis of Count Time Series Following Generalized Linear Models

“…Elsaied and Fried (2014) and Kitromilidou and Fokianos (2016) develop M -estimators for the linear and the log-linear model, respectively. Fried, Liboschik, Elsaied, Kitromilidou, and Fokianos (2014) compare robust estimators of the (partial) autocorrelation (see also Dürre, Fried, and Liboschik 2015) for time series of counts, which can be useful for identifying the correct model order.…”

On robust estimation of negative binomial INARCH models

“…We propose another variant of robust M-estimation for NBINARCH( p) models, combining the M-estimation approaches developed by [10] for the limiting Poisson INARCH model and by [1] for the negative binomial regression model. We robustify the CML estimator along the same lines as in [10] in the Poisson case, applying M-estimation to the Pearson residuals r…”

“…, s t, p (y t , ω)) , and ω (0) = (θ (0) , κ (0) ) being the true parameter vector. The matrices A(ω (0) ) and B(ω (0) ) can be estimated using their empirical counterparts as in [10], replacing the unknown parameters by their robust estimations and the expectations by the corresponding averages across the realizations; the arising estimate inherits some robustness when using a bounded ψ-function with a bounded derivative.…”

Robust Fitting for the Number of Defects as a Measure of Product Quality

“…They construct new Mestimators based on the Tukey function as modified versions of maximum likelihood estimators to fit count data robustly, where the Poisson model provides a standard framework for the analysis of this type of data. Elsaied and Fried (2014) build some functions in R-programming language for these estimators and perform some simulation experiments to compare the performance of them. They compare the following procedures:…”

“…The package includes methods for model fitting, prediction and intervention analysis. In this paper, we compare the performance of the CML, the best function (Tukeycorr), which is given above in Elsaied and Fried (2014), for the Tukey M-estimators in the case of the Poisson INARCH(1) model and the tsglm function in the tscount package, which is given in Liboschik et al (2017) via simulations in case of outlier-contaminated Poisson time series data. Section 2 defines the defects count data.…”