A1264
Title: Predictive inference for discrete-valued time series
Authors: Maxime Faymonville - TU Dortmund University (Germany) [presenting]
Carsten Jentsch - TU Dortmund University (Germany)
Efstathios Paparoditis - University of Cyprus (Cyprus)
Abstract: For discrete-valued time series, predictive inference cannot be implemented by constructing prediction intervals to some pre-determined coverage level. Although prediction sets rather than intervals respect the discrete nature of the time, they are generally unable to retain the desired coverage. To address this, reversing the construction principle is proposed by considering pre-defined sets of interest, and the conditional probability is estimated that a future observation falls in these sets, given the time series at hand. The accuracy of the corresponding prediction procedure is evaluated by quantifying the uncertainty associated with the estimation of the corresponding conditional probabilities. For this purpose, (non-)parametric approaches are considered, and asymptotic theory is derived for the estimators of the conditional probabilities focusing on the case of INAR and INARCH models. Since the established limiting distributions are typically cumbersome to apply in practice, suitable bootstrap approaches are proposed to evaluate the distribution of the estimators. Additionally, the problem of model misspecification is addressed, and a bootstrap is proposed based on the robustification of the procedure. Simulations investigate the finite sample performance of the methods developed by considering different (non-)parametric bootstrap implementations to account for the various sources of randomness and variability. Applications to real-life data sets also are presented.
