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

An AR(1) model Y_t = 0.2 + phi Y_{t-1} + e_t is estimated. In the Dickey-Fuller regression of the first difference on the lagged level, the estimated coefficient on Y_{t-1} is -0.04 with standard error 0.02. The 5% Dickey-Fuller critical value (with constant) is about -2.86. Which conclusion is correct?

The test statistic is -0.04 divided by 0.02, or -2.0, which is above the -2.86 critical value, so you fail to reject the unit root null. Normal critical values do not apply, and non-rejection does not prove the series is a random walk.

  1. ATest statistic is -2.0; fail to reject the unit root nullCorrect
  2. BTest statistic is -2.0; reject the unit root null because |-2.0| exceeds 1.96
  3. CTest statistic is -0.5; reject the unit root null
  4. DTest statistic is -2.0; the series is shown to be a random walk with drift

Explanation

The statistic is -0.04/0.02 = -2.0, which is not below -2.86, so the unit root null is not rejected. Using the normal critical value of 1.96 is wrong because the statistic has a nonstandard distribution. Failing to reject does not prove a random walk.

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