Locally stationary vector processes and adaptive multivariate modeling

The assumption of strict stationarity is too strong for observations in many financial time series applications; however, distributional properties may be at least locally stable in time. We define multivariate measures of homogeneity to quantify local stationarity and an empirical approach for robustly estimating time varying windows of stationarity. Finally, we consider bivariate series that are believed to be cointegrated locally, assess our estimates, and discuss applications in financial asset pairs trading.