Unstable Multiple Cointegration Relations in the Term Structure of Interest Rates

Although the literature has theoretically shown that multiple cointegration relations are not uniquely defined, many empirical analyses report and make use of such multiple cointegrations. This paper shows that four long- maturity interest rates in the United States contain two common factors and cointegration rank is thus two. Multiple cointegration relations among four interest rates are unstable and sensitive to small changes in the number of observations. Through Monte Carlo sampling experiments, the nature and the extent of instability are established. Instead of multiple cointegration relations, stable irreducible cointegration relations among three interest rates are presented.