We will begin by describing the theory underlying the Johansen test and then perform our usual procedure of carrying out the test on simulated data with known cointegrating properties. Such a procedure will be utilised in subsequent articles to form a mean reverting portfolio of assets for trading purposes. We will then form a stationary series by taking a linear combination of the underlying series. In this article we are going to discuss a test due to Johansen that allows us to determine if three or more time series are cointegrated. However, we can clearly imagine a set of three or more financial assets that might share an underlying cointegrated relationship.Ī trivial example would be three separate share classes on the same asset, while a more interesting example would be three separate ETFs that all track certain areas of commodity equities and the underlying commodity spot prices. In the previous article on the Cointegrated Augmented Dickey Fuller (CADF) test we noted that one of the biggest drawbacks of the test was that it was only capable of being applied to two separate time series.
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