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

A risk analyst fits Y_t = a + bX_t + u_t using levels of two series that each have a unit root. The Durbin-Watson statistic is 0.15 and residuals look like a random walk. Which action best addresses the problem, assuming the analyst believes there is no cointegration?

Regress the first difference of Y on the first difference of X. The low Durbin-Watson and random-walk residuals indicate spurious regression from unit roots, and when the series are not cointegrated, differencing makes them stationary and restores valid inference.

  1. ARegress the first difference of Y on the first difference of XCorrect
  2. BAdd a time trend and keep levels
  3. CTake the logarithm of both series and keep levels
  4. DUse a larger sample and keep levels

Explanation

A very low Durbin-Watson with random-walk residuals signals nonstationary errors, which is typical of spurious regression. Without cointegration, differencing both series makes them stationary and gives valid inference. A trend, logs or more data do not remove the unit roots.

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