We develop inference methods about long-run comovement of two time series. The parameters of interest are defined in terms of population second-moments of lowfrequency trends computed from the data. These trends are similar to low-pass filtered data and are designed to extract variability corresponding to periods longer than the span of the sample divided by q/2, where q is a small number, such as 12. We numerically determine confidence sets that control coverage over a wide range of potential bivariate persistence patterns, which include arbitrary linear combinations of I(0), I(1), near unit roots and fractionally integrated processes. In an application to U.S. economic data, we quantify the long-run covariability of a variety of series, such as those giving rise to the “great ratios”, nominal exchange rates and relative nominal prices, unemployment rate and inflation, money growth and inflation, earnings and stock prices, etc.
The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. Support was provided by the National Science Foundation through grant SES-1627660.