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how can I simulate/generate two non-stationary time series (with unit root) so that they can be also cointegrated (using R or Matlab).

Thanks in advance.

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See quant.stackexchange.com/a/1038 –  user508 Aug 10 at 19:18

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Two cointegrated series contain a single unit root. Each series can be formulated as the sum of a common unit root plus a stationary component. Most textbooks covering cointegration will cover such formulations - see Hamilton's (1994) discussion of Phillips' "triangular representation" of a cointegrated vector, for example.

Simulating is likely to be easy (depending on other features you may need, of course). For example, simulate one non-stationary series, and construct a second series as the sum of the first and a stationary variable. Viola! Cointegrated.

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