Long-Run Covariability

66 Pages Posted: 21 Feb 2017 Last revised: 9 May 2022

See all articles by Ulrich K. Müller

Ulrich K. Müller

Princeton University - Department of Economics

Mark W. Watson

Princeton University - Princeton School of Public and International Affairs; National Bureau of Economic Research (NBER)

Date Written: February 2017

Abstract

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.

Suggested Citation

Müller, Ulrich K. and Watson, Mark W., Long-Run Covariability (February 2017). NBER Working Paper No. w23186, Available at SSRN: https://ssrn.com/abstract=2920403

Ulrich K. Müller (Contact Author)

Princeton University - Department of Economics ( email )

Princeton, NJ 08544-1021
United States
609-258-3216 (Phone)
609-258-4026 (Fax)

HOME PAGE: http://www.princeton.edu/~umueller

Mark W. Watson

Princeton University - Princeton School of Public and International Affairs ( email )

Princeton University
Princeton, NJ 08544-1021
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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