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

A monthly price series has been tested and is found to contain a unit root. Which approach is most appropriate before fitting an ARMA model to it?

Take first differences, or log differences for prices, and model the differenced series. A unit root series is integrated of order one, so differencing makes it stationary and suitable for ARMA modeling. Demeaning or transforming levels leaves the stochastic trend in place.

  1. AFit the ARMA model directly to the levels, since ARMA handles any persistence
  2. BTake first differences (or log differences) and then model the differenced seriesCorrect
  3. CRemove only the sample mean from the levels
  4. DSquare the series to stabilize its variance

Explanation

A unit root series is integrated of order one, so differencing yields a stationary series suitable for ARMA modeling. Fitting to levels violates stationarity and risks spurious results. Demeaning does not remove the stochastic trend, and squaring does not remove a unit root.

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