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

A risk analyst runs a Dickey-Fuller test on a bond yield series by regressing the change in y_t on y_{t-1}. The estimated coefficient on y_{t-1} is -0.02 with a test statistic that does not fall below the critical value. What is the correct conclusion?

The analyst fails to reject the null hypothesis of a unit root, so the series is consistent with being nonstationary. The test statistic did not fall below the critical value. Failing to reject does not prove a unit root, but stationarity is not supported.

  1. AReject the null; the series is stationary
  2. BFail to reject the unit-root null; the series is consistent with being nonstationaryCorrect
  3. CAccept that the series is a white noise process
  4. DConclude that the series is trend-stationary with certainty

Explanation

The Dickey-Fuller null is that the coefficient on y_{t-1} equals zero (a unit root). A statistic not below the critical value means failing to reject, so nonstationarity cannot be ruled out. Failing to reject does not prove the null or establish white noise.

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