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

A time series ε_t is described as a white noise process. Which of the following sets of properties must hold for ε_t under the basic (not necessarily Gaussian) definition used in the FRM curriculum?

A white noise process has zero mean, constant finite variance, and zero autocorrelation at every non-zero lag. Normality and full independence are additional assumptions that define special cases such as Gaussian white noise, but are not required in the basic definition.

  1. AMean zero, constant finite variance, and zero autocorrelation at all non-zero lagsCorrect
  2. BMean zero, constant variance, and normally distributed, independent observations
  3. CConstant mean, variance that declines with the lag, and zero autocorrelation
  4. DMean zero, constant variance, and a first-order autocorrelation equal to the autoregressive coefficient

Explanation

Basic white noise requires zero mean, a constant finite variance, and no serial correlation at any lag. Normality and independence are extra conditions defining Gaussian or independent white noise, so option B is too strong. Variance must be constant, not declining, so C is wrong.

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