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

Two nonstationary series X_t and Y_t are each I(1). An analyst regresses Y on X in levels and finds the residuals pass a unit-root test for stationarity, so the residuals are stationary. Which statement is correct?

The series are cointegrated. A stationary residual from regressing one I(1) series on another means a linear combination is stationary, so the levels regression reflects a real long-run relation and is not spurious, while pure differencing would discard that information.

  1. AThe series are cointegrated, so the levels regression is not spurious and differencing would discard the long-run relationshipCorrect
  2. BThe series are not cointegrated, so differencing is required
  3. CThe regression is spurious because both series are I(1)
  4. DThe series must be I(0) individually

Explanation

If a linear combination of I(1) series is stationary, they are cointegrated. The levels regression then captures a genuine long-run equilibrium. Differencing alone would lose that long-run information. Being I(1) does not by itself make a regression spurious.

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