Conditional minimum density power divergence estimator for self-exciting integer-valued threshold autoregressive models

To overcome the sensitivity of maximum likelihood estimation to outliers in integer-valued time series of counts, we develop a conditional version of minimum density power divergence estimator by introducing the structure of the loss function of the original minimum density power divergence estimator. The properties of the proposed estimator, including the strong consistency and asymptotic normality, are obtained. Some simulation studies are conducted to show the performances of the conditional minimum density power divergence estimator. Finally, an application to the quarterly earthquake data is provided and prove that when outliers exist in data set, the proposed estimator has a better performance than the conditional maximum likelihood estimator, showing robustness property.