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FRM Part I · FRM Exam Part I · Nonstationary Time Series

Two series X_t and Y_t are each I(1). An analyst regresses Y_t on X_t in levels and tests the residuals with an Engle-Granger procedure, rejecting a unit root in the residuals. Which action is most appropriate next?

Conclude the series are cointegrated and use an error-correction model. Stationary residuals from the levels regression of two I(1) series indicate a genuine long-run equilibrium. Differencing alone would discard that long-run information, so the error-correction term should be retained.

  1. AConclude the series are cointegrated and use an error-correction model rather than only differencingCorrect
  2. BDifference both series and discard the levels relationship entirely
  3. CConclude the regression is spurious because both series are I(1)
  4. DAdd a deterministic time trend to both series and rerun the levels regression

Explanation

If residuals from a levels regression of I(1) series are stationary, the series are cointegrated and the levels regression is not spurious. Differencing alone would lose the long-run information, so an error-correction model is preferred. The fact both are I(1) does not by itself imply spuriousness.

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