Zero-non-zero Patterned Vector Error Correction Modelling for I(2) Cointegrated Time-Series with Applications in Testing PPP and Stock Market Relationships

Vector error-correction models (VECMs) have become increasingly popular in their applications to financial markets. Standard VECM models assume that the cointegrating vectors are of full rank such that they contain no zero elements. However, applications of VECM models to financial market data have revealed that zero entries are indeed possible. The existence of zero entries has not been fully discussed in cointegration theory. In such cases, the use of standard VECM models may lead to incorrect inferences. Specifically, if the underlying yes VECM and the associated cointegrating and loading vectors contain zero entries, the resultant specifications can produce different conclusions concerning the cointegrating relationships among the variables. In this paper, we provide a new efficient and effective algorithm to select cointegrating and loading vectors that can contain zero entries in the context of a VECM framework for time-series of integrated order I(2). We employ two case studies to demonstrate the usefulness of the alogrithm in tests of purchasing power parity and a three-variable system concerning the stock market.