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

An analyst regresses the level of one stock market index on the level of an unrelated commodity price index. Both series are random walks with drift. The regression reports an R-squared of 0.92 and a very large t-statistic on the slope. Which conclusion is most appropriate?

The relationship is likely spurious. When two independent random walks are regressed on each other in levels, the regression often shows a high R-squared and significant t-statistics even though no true relationship exists, because the series are nonstationary.

  1. AThe relationship is likely spurious, because regressing independent nonstationary series can produce high R-squared and significant t-statisticsCorrect
  2. BThe relationship is confirmed as causal, because R-squared exceeds 0.90
  3. CThe result is reliable because large t-statistics offset nonstationarity
  4. DThe result is reliable provided the sample size exceeds 30 observations

Explanation

Regressing independent unit-root series on each other typically gives inflated R-squared and t-statistics, with residuals that are themselves nonstationary. This is the classic spurious regression problem. Sample size does not cure it, and a high R-squared does not show causality.

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