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

In a Dickey-Fuller regression ΔY_t = γY_{t-1} + ε_t, the estimated γ is −0.060 with a standard error of 0.030. The 5% Dickey-Fuller critical value for this specification is −1.95, and the standard normal 5% two-sided critical value is 1.96. What is the correct conclusion?

The statistic is −0.060 divided by 0.030, which equals −2.00. Because it is more negative than the Dickey-Fuller 5% critical value of −1.95, the unit root null is rejected, suggesting the series is stationary at the 5% level.

  1. AThe test statistic is −2.00; reject the unit root null at 5% using the DF critical valueCorrect
  2. BThe test statistic is −2.00; fail to reject, because |−2.00| exceeds only the normal critical value 1.96 in the wrong direction
  3. CThe test statistic is −0.50; fail to reject the unit root null
  4. DThe test statistic is −2.00; reject the null of stationarity at 5%

Explanation

t = −0.060/0.030 = −2.00. This is below (more negative than) the DF critical value of −1.95, so the unit root null is rejected at 5%. The test statistic is not −0.50, which would result from dividing incorrectly, and the null being rejected is a unit root, not stationarity.

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