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

Which statement best describes the effect of ignoring a structural break in the mean of a stationary series when applying a Dickey-Fuller test?

Ignoring a mean shift biases the Dickey-Fuller test toward not rejecting the unit root. The shift makes the series look persistent, so a series that is actually stationary around a changed mean may be wrongly classified as nonstationary.

  1. AThe test is biased toward failing to reject the unit-root null, so a series that is stationary around a shifted mean may be wrongly judged nonstationaryCorrect
  2. BThe test is biased toward rejecting the unit-root null, so a random walk is wrongly judged stationary
  3. CThe test statistic is unaffected because it is invariant to shifts in the mean
  4. DThe test becomes invalid only if the break occurs in the first 5% of the sample

Explanation

A level shift makes a series look highly persistent, so the estimated autoregressive coefficient is biased toward one. Dickey-Fuller tests then have low power and tend not to reject the unit-root null even though the series is stationary around a shifted mean. The other statements reverse the bias or deny any effect.

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