Cointegration Analysis with Mixed-Frequency Data
38 Pages Posted: 28 Mar 2007
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
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