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

A Dickey-Fuller test is applied to a series that follows a stationary AR(1) with coefficient 0.95 in a sample of only 60 observations. Which statement best describes the likely outcome and the reason?

The test has low power in this situation and will often fail to reject the unit root null, even though the series is stationary. A highly persistent AR(1) with a short sample is hard to distinguish from a random walk.

  1. AThe test will almost surely reject the unit root null, since 0.95 is below 1
  2. BThe test has low power and will often fail to reject, so a stationary but highly persistent series may be mistaken for a unit rootCorrect
  3. CThe test is biased toward rejection because small samples inflate the t-statistic
  4. DThe test is invalid because it requires the AR coefficient to be exactly 1

Explanation

With a root close to one and a short sample, the data look very similar to a random walk, so the Dickey-Fuller test has low power. Failure to reject therefore does not prove a unit root. The test does not require the coefficient to equal 1; that is only the null.

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