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Keywords:

  • time series decomposition;
  • cointegration;
  • mean reversion;
  • spread trading;
  • Ornstein–Uhlenbeck;
  • statistical arbitrage

Abstract

This technical paper offers simple views and uses of cointegration analysis which are not often clear in textbook presentation and research literature. Decompositions of time series and derivations, usually omitted in presentation of the equilibrium correction models, are collected in a structured Appendix A. Instead of constructing a long-term forecast and entering what essentially is a trend-following strategy, the experienced arbitrageur would use the mean-reversion feature of the highly autoregressive spread generated by a cointegrated relationship. The suitability of mean-reversion is evaluated by fitting the spread to the Ornstein–Uhlenbeck process that provides a balanced fit for the features of correction to the long-term equilibrium. Conclusions formulate and address three common complaints about economic tests for cointegration and instability of the equilibrium.