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

An analyst regresses the level of one trending stock index on the level of an unrelated trending commodity price index and obtains a high R-squared, a very large t-statistic on the slope, and a Durbin-Watson statistic close to 0.1. Both series contain unit roots and are not cointegrated. Which conclusion is most appropriate?

The regression is likely spurious. When two unrelated series each contain a unit root and are not cointegrated, regressing levels produces misleadingly high R-squared and t-statistics, with very low Durbin-Watson values from highly autocorrelated residuals. Standard inference is invalid in this setting.

  1. AThe regression is likely spurious, so the high R-squared and t-statistic are unreliableCorrect
  2. BThe regression is valid because a high R-squared confirms a true long-run relationship
  3. CThe regression is valid because the large t-statistic shows the slope is highly significant
  4. DThe regression shows cointegration because the Durbin-Watson statistic is low

Explanation

Regressing independent unit-root series on each other typically gives high R-squared, inflated t-statistics and highly autocorrelated residuals (low Durbin-Watson). These are classic signs of spurious regression. Low Durbin-Watson signals nonstationary residuals, not cointegration.

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