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

A risk analyst runs a Dickey-Fuller test on the log of an equity index price including a constant and a time trend. Compared with a test with no constant and no trend, which statement is correct about the critical values?

Critical values become more negative when a constant and a time trend are included. The statistic's null distribution shifts left, so the analyst needs a more negative t-statistic to reject the unit root null than in the no-constant, no-trend specification.

  1. AThey are more negative, so stronger evidence is needed to reject the unit root nullCorrect
  2. BThey are less negative, so rejection is easier
  3. CThey are identical because the null hypothesis is unchanged
  4. DThey become positive because the trend is deterministic

Explanation

Adding a constant and a trend changes the distribution of the t-statistic under the null, shifting the critical values further left (more negative). A given statistic is therefore less likely to reject the unit root. The null itself is unchanged but the distribution is not.

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