Robust Estimation for Bivariate Poisson INGARCH Models

Abstract

In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we consider a robust estimation method for bivariate Poisson INGARCH models while using the minimum density power divergence estimator. We demonstrate the proposed estimator is consistent and asymptotically normal under certain regularity conditions. Monte Carlo simulations are conducted to evaluate the performance of the estimator in the presence of outliers. Finally, a real data analysis using monthly count series of crimes in New South Wales and an artificial data example are provided as an illustration.

Multivariate Count Data Models for Time Series Forecasting

“…Squared error score ses(P, x) = (x − µ p ) 2 , where µ p is the mean of P Note, that in practice, one calculates the mean score…”

“…In many applications, such count data dynamics are correlated across several data series. Examples include from correlated number of bank failures [1], number of crimes [2] to COVID-19 contagion dynamics [3]. The analysis of such correlations provides detailed information about the overall connectedness of the series, as well as the dynamics of an individual series conditional on the others.…”

Time Series Modelling

“…In many applications, such count data dynamics are correlated across several data series. Examples include from correlated number of bank failures [1], number of crimes [2] to COVID-19 contagion dynamics [3]. The analysis of such correlations provides detailed information about the overall connectedness of the series, as well as the dynamics of an individual series conditional on the others.…”

Time Series Modelling

“…The authors use a cumulative sum chart for process monitoring, discuss its performance evaluation, and apply it to a crime-counts time series. Contrary to the aforementioned papers, the articles by Kim et al [ 16 ] and Shapovalova et al [ 17 ] refer to multivariate count time series. For a bivariate count time series following an integer-valued generalized AR conditional heteroscedastic (INGARCH) model, Kim et al [ 16 ] propose a minimum density power divergence estimator being robust against outliers.…”

“…Contrary to the aforementioned papers, the articles by Kim et al [ 16 ] and Shapovalova et al [ 17 ] refer to multivariate count time series. For a bivariate count time series following an integer-valued generalized AR conditional heteroscedastic (INGARCH) model, Kim et al [ 16 ] propose a minimum density power divergence estimator being robust against outliers. The asymptotics of the estimator are investigated, and an application to bivariate crime counts is presented.…”