Cointegration Analysis with Mixed-Frequency Data

38 Pages Posted: 28 Mar 2007

See all articles by Byeongchan Seong

Byeongchan Seong

Chung-Ang University

Sung K. Ahn

Washington State University

Peter A. Zadrozny

U.S. Bureau of Labor Statistics - Department of Labor; CESifo (Center for Economic Studies and Ifo Institute)

Date Written: March 2007


We develop a method for directly modeling cointegrated multivariate time series that are observed in mixed frequencies. We regard lower-frequency data as regularly (or irregularly) missing and treat them with higher-frequency data by adopting a state-space model. This utilizes the structure of multivariate data as well as the available sample information more fully than the methods of transformation to a single frequency, and enables us to estimate parameters including cointegrating vectors and the missing observations of low-frequency data and to construct forecasts for future values. For the maximum likelihood estimation of the parameters in the model, we use an expectation maximization algorithm based on the state-space representation of the error correction model. The statistical efficiency of the developed method is investigated through a Monte Carlo study. We apply the method to a mixed-frequency data set that consists of the quarterly real gross domestic product and the monthly consumer price index.

Keywords: missing data, Kalman filter, expectation maximization algorithm, forecasting, error correction model, smoothing, maximum likelihood estimation

JEL Classification: C13, C22, C32

Suggested Citation

Seong, Byeongchan and Ahn, Sung Keuk and Zadrozny, Peter A., Cointegration Analysis with Mixed-Frequency Data (March 2007). CESifo Working Paper Series No. 1939. Available at SSRN:

Byeongchan Seong

Chung-Ang University ( email )

221 Heuksuk-dong
Seoul, 156-756
Korea, Republic of (South Korea)

Sung Keuk Ahn

Washington State University ( email )

Dept. of Finance and Management Science
Pullman, WA 99164-4746
United States
509-335-6819 (Phone)


Peter A. Zadrozny (Contact Author)

U.S. Bureau of Labor Statistics - Department of Labor ( email )

2 Massachusetts Avenue, NE
Washington, DC 20212
United States

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679

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