Testing serial dependence or cross dependence for time series with underreporting

Abstract

Abstract In practice, it is common for collected data to be underreported, an issue that is particularly prevalent in fields such as the social sciences, ecology and epidemiology. Drawing inferences from such data using conventional statistical methods can lead to incorrect conclusions. In this paper, we study tests for serial or cross dependence in time series data that are subject to underreporting. We introduce new test statistics, develop corresponding group-of-blocks bootstrap techniques and establish their consistency. The methods are shown via simulation studies to be efficient and are used to identify key factors responsible for the spread of dengue fever and the occurrence of cardiovascular disease.