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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Applications of time series models

Two series of annual rupee equity returns and bond returns for an Indian pension fund are each non-stationary, integrated of order 1. A linear combination of the two is found to be stationary. What does this indicate?

The series are cointegrated. Two I(1) series are cointegrated when a linear combination of them is stationary, showing a stable long-run relationship even though each series individually has a stochastic trend.

  1. AThe series are cointegrated, implying a long-run equilibrium relationshipCorrect
  2. BThe series are both stationary after all
  3. CThe series are independent white noises
  4. DThe series must be differenced twice before modelling
  5. The VAR model cannot be applied in any form

Explanation

Two I(1) series are cointegrated if some linear combination is I(0), that is stationary. This implies a long-run equilibrium relationship between them even though each wanders individually. Differencing both loses the long-run information, which is why option 3 is not the conclusion.

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