  Cointegration analysis is used to estimate the long-run equilibrium relations
between several time series. The coefficients of these long-run equilibrium
relations are the cointegrating vectors. In this paper, we provide a sparse
estimator of the cointegrating vectors. The estimation technique is sparse in
the sense that some elements of the cointegrating vectors will be estimated as
zero. For this purpose, we combine a penalized estimation procedure for vector
autoregressive models with sparse reduced rank regression. The sparse
cointegration procedure achieves a higher estimation accuracy than the
traditional Johansen cointegration approach in settings where the true
cointegrating vectors have a sparse structure, and/or when the sample size is
low compared to the number of time series. We also discuss a criterion to
determine the cointegration rank and we illustrate its good performance in
several simulation settings. In a first empirical application we investigate
whether the expectations hypothesis of the term structure of interest rates,
implying sparse cointegrating vectors, holds in practice. In a second empirical
application we show that forecast performance in high-dimensional systems can
be improved by sparsely estimating the cointegration relations.
