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FRM Part I · FRM Exam Part I · Stationary Time Series

Which set of conditions must a time series satisfy to be covariance stationary?

A covariance stationary series has a constant mean, a constant finite variance, and autocovariances that depend only on the lag between observations, not on calendar time. It need not be normal or serially uncorrelated; AR processes are stationary yet autocorrelated.

  1. AConstant mean, constant variance, and autocovariance that depends only on the lag between observationsCorrect
  2. BConstant mean and zero autocorrelation at every lag
  3. CConstant variance and a normal distribution of the shocks
  4. DA deterministic linear trend and autocovariance that grows with time

Explanation

Covariance stationarity requires a time-invariant mean, a finite time-invariant variance, and autocovariances that depend only on the displacement (lag) between observations. Zero autocorrelation is not required, since AR processes are stationary with nonzero autocorrelation. Normality is not required either.

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