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

A risk analyst tests a log equity index for a unit root. The index trends upward over time with no tendency to revert. She runs a Dickey-Fuller regression that includes only a constant, but the series clearly contains a deterministic time trend. What is the most appropriate response?

She should include a time trend in the Dickey-Fuller regression and use the critical values for the constant-plus-trend specification. Omitting a clear deterministic trend distorts the test, and standard normal critical values remain invalid because the statistic has a nonstandard distribution under the unit root null.

  1. AKeep the constant-only test, since adding a trend always biases the test toward rejection
  2. BUse the normal distribution critical values because the sample is large
  3. CInclude a time trend term in the test regression and use the corresponding Dickey-Fuller critical valuesCorrect
  4. DDifference the series twice before running any test

Explanation

When a series has a deterministic trend, the test regression should include a time trend, and critical values for that specification (more negative than for constant-only) must be used. Omitting the trend lowers the power and distorts inference. Normal critical values are never appropriate.

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