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

A researcher runs a Dickey-Fuller regression of the change in Y_t on Y_{t-1} and obtains a coefficient estimate of gamma = -0.04 with standard error 0.025, using 500 observations. The 5% Dickey-Fuller critical value (constant, no trend) is about -2.86. What should the researcher conclude, and what is the implied AR(1) coefficient?

The researcher fails to reject the unit root, and the implied AR(1) coefficient is 0.96. The test statistic is -0.04/0.025 = -1.60, which is above the critical value of -2.86, and the coefficient equals one plus gamma.

  1. AReject the unit root; implied coefficient 0.96
  2. BFail to reject the unit root; implied coefficient 0.96Correct
  3. CFail to reject the unit root; implied coefficient 1.04
  4. DReject the unit root; implied coefficient 1.04

Explanation

The t-statistic is -0.04/0.025 = -1.60, which is not below -2.86, so we fail to reject the unit root null. The AR(1) coefficient equals 1 + gamma = 0.96. Using the normal critical value of -1.96 would still not reject, but the key error is the sign in 1 + gamma giving 1.04.

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