Cointegration relationships or common trends detection has been undertaken mainly by VARMA representation of stochastic processes, while the specialized literature has paid less attention to the state-space modeling, although it presents computationals and analytical advantages that justify its study. This paper will focus on the state-space analysis of nonstationarity series. The justification of the method and its algorithms will be exposed and an alternative approach to the classical Johansen or Beveridge and Nelson methods is proposed.

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