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

A researcher regresses one random walk on an independent random walk and finds R² = 0.85 and a t-statistic of 14 on the slope, with a Durbin-Watson statistic near 0.1. What is the most appropriate conclusion?

This is most likely a spurious regression. Independent random walks regressed on each other commonly give high R², huge t-statistics and highly autocorrelated residuals. The remedy is to difference the series, or to test properly for cointegration, rather than trust the reported significance.

  1. AThe relationship is genuine because the t-statistic is very large
  2. BThe result is likely a spurious regression, and the regression should be run on first differencesCorrect
  3. CThe high R² confirms the two series are cointegrated
  4. DThe low Durbin-Watson statistic indicates the series are stationary

Explanation

Regressing independent unit-root series often yields high R², large t-statistics and strongly autocorrelated residuals (low DW). These signal spurious regression. Cointegration would require testing that the residuals are stationary, which a DW near 0.1 contradicts. Differencing the series is the standard remedy.

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