Colloquium Speaker - Dr. Mohamedou Ould Haye, Carleton University

Abstract:

Time series analysis typically assumes that observations are collected at equally spaced time points. In practice, however, data may be recorded at random times or only when the underlying process crosses a specified threshold. These two sampling mechanisms differ fundamentally: in the first, observation times are independent of the process, whereas in the second, they are determined by the values of the process itself. In this talk, we investigate how these sampling schemes affect the statistical properties of dependent time series, with particular emphasis on long-range dependence. We examine the asymptotic behaviour of sampled processes and related statistics, showing how the sampling mechanism can influence the dependence structure and the resulting limiting distributions. We also discuss implications for statistical inference, including challenges arising when the underlying process is nonstationary.