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

An analyst fits an AR(1) model y_t = 2 + 0.6 y_{t-1} + e_t to a covariance-stationary series. What is the unconditional mean of the series?

The unconditional mean is 5.0. For a covariance-stationary AR(1), the mean equals the intercept divided by one minus the autoregressive coefficient, so 2 divided by 0.4 gives 5.0. The intercept alone is not the mean because persistence feeds past values into the level.

  1. A2.0
  2. B3.2
  3. C5.0Correct
  4. D1.2

Explanation

The unconditional mean of a stationary AR(1) is c/(1-phi) = 2/(1-0.6) = 2/0.4 = 5.0. Choosing 2.0 ignores the persistence term, and 3.2 results from dividing by 1 - 0.6 incorrectly (2 x 1.6).

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