In this study, we consider the problem of testing for a parameter change in general integer-valued time series models whose conditional distribution belongs to the one-parameter exponential family when the data are contaminated by outliers. In particular, we use a robust change point test based on density power divergence (DPD) as the objective function of the minimum density power divergence estimator (MDPDE). The results show that under regularity conditions, the limiting null distribution of the DPD-based test is a function of a Brownian bridge. Monte Carlo simulations are conducted to evaluate the performance of the proposed test and show that the test inherits the robust properties of the MDPDE and DPD. Lastly, we demonstrate the proposed test using a real data analysis of the return times of extreme events related to Goldman Sachs Group stock.

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.

The recently observed hydrologic extremes are unlike what has been experienced so far. Both the magnitude and frequency of extremes are important indicators that determine the flood safety design criteria. Therefore, how are design criteria updated faced with these extremes? Both a sudden increase of design rainfall by the inclusion of these extremes and complete ignorance are inappropriate. In this study, the changes in extremes were examined and an alternative way to estimate the design rainfall amounts was developed using the data from 60 stations in South Korea. The minimum density power divergence estimator (MDPDE) with the optimal value of a tuning parameter, α, was suggested as an alternative estimator instead of the maximum likelihood estimator (MLE); its performance was evaluated using the Gumbel (GUM) and the generalized extreme value (GEV) distribution. The results revealed an increase in both the frequency and magnitude of extreme events over the last two decades, which imply that the extremes are already occurring. The performance of the MDPDE was evaluated. The results revealed decreased and adjusted values of the design rainfall compared to MLE. On the other hand, the MDPDE of the GEV distribution with a positive shape parameter, ξ, does not show its advantage conditionally because the GEV distribution has a heavier right tail than the GUM distribution (ξ = 0). In contrast, the results showed the high sensitivity of the MLE to the extremes compared to MDPDE.