This paper describes how the notion of cointegration came about, and discusses some generalizations to indicate where the topic may go next. In particular, some issues in the analysis of possibly cointegrated quantile time series are discussed.

Realized volatilities observed across several assets show a common secular trend and some idiosyncratic pattern which we accommodate by extending the class of Multiplicative Error Models (MEMs). In our model, the common trend is estimated nonparametrically, while the idiosyncratic dynamics are...