Identifying Cointegration by Eigenanalysis

ABSTRACT

We propose a new and easy-to-use method for identifying cointegrated components of nonstationary time series, consisting of an eigenanalysis for a certain nonnegative definite matrix. Our setting is model-free, and we allow the integer-valued integration orders of the observable series to be unknown, and to possibly differ. Consistency of estimates of the cointegration space and cointegration rank is established both when the dimension of the observable time series is fixed as sample size increases, and when it diverges slowly. The proposed methodology is also extended and justified in a fractional setting. A Monte Carlo study of finite-sample performance, and a small empirical illustration, are reported. Supplementary materials for this article are available online.

KEYWORDS:

• Cointegration
• Eigenanalysis
• I(d)
• Nonstationary processes
• Vector time series

Supplementary Materials

The online supplementary materials contain additional proofs and Lemmas.

Additional information

Funding

This work was partially supported by the NSFC research grants 11371318/11771390, the ZPNSFC research grant LR16A010001, the ESRC research grant ES/J007242/1, and the EPSRC research grant EP/L01226X/1.