From Long-memory to Non-negativity in Time Series Analysis

Abstract

This talk consists of two parts. In the first part, I will introduce two long-memory processes: (1) a regression model with continuous-time long-memory errors, and (2) a long-memory limiting aggregate model. Applications of these models, as well as maximum likelihood and quasi-likelihood estimations, and their large sample properties will be discussed. The second part of my talk is about inequality parametric constraints for non-negative processes, which is mainly motivated by the needs for modeling volatility in financial time series data. I will talk about recent advances in the derivation of necessary and sufficient parametric conditions for non-negative processes.