Modelling persistent stationary processes in continuous time

This paper presents a novel approach to model continuous time processes that capture two countervailing features of many financial time series: persistency and long term stationarity. The processes introduced by our models exhibit persistent behaviors observed typically in non-stationary time series, but they remain stationary instead of tending towards explosive paths. We provide a relevant statistical theory and its implications on inference and forecasting, presenting both simulation evidence and empirical backing for the existence of, as well as the characteristic behavior for, such a series in real financial time series data.

Automated summary

This paper presents a novel approach to model financial time series that captures both persistency and long term stationarity. The provided statistical theory and empirical evidence support the existence and characteristic behavior of such series in real financial data.