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

In a Dickey-Fuller regression ΔY_t = δ + γY_{t-1} + ε_t on 250 observations of a bond yield, the estimate of γ is -0.040 with a standard error of 0.020. The 5% Dickey-Fuller critical value (with constant) is -2.86. What is the test statistic and the correct conclusion?

The test statistic is -0.040 divided by 0.020, which is -2.00. This is not more negative than the Dickey-Fuller critical value of -2.86, so the unit root null cannot be rejected. Standard normal or t critical values are invalid under the null.

  1. AStatistic -2.00; reject the unit root null because it is below -1.96 in absolute terms
  2. BStatistic -0.80; fail to reject the unit root null
  3. CStatistic -2.00; fail to reject the unit root nullCorrect
  4. DStatistic -2.00; reject the null because the estimate is negative

Explanation

The statistic is -0.040/0.020 = -2.00. For rejection it must be below (more negative than) -2.86. It is not, so the unit root null is not rejected. Using the normal critical value of -1.96 is the key mistake, since the statistic does not follow a standard t distribution under the null.

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