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

Which statement correctly describes the sample autocorrelation function (ACF) and partial autocorrelation function (PACF) pattern expected from a pure MA(2) process?

For an MA(2) the ACF cuts off after lag 2 while the PACF decays gradually. Autocorrelations vanish beyond the MA order, but the invertible MA has an infinite autoregressive form, so partial autocorrelations tail off. The opposite pattern identifies an AR(2).

  1. AACF cuts off after lag 2; PACF decays graduallyCorrect
  2. BACF decays gradually; PACF cuts off after lag 2
  3. CBoth ACF and PACF cut off after lag 2
  4. DACF is significant only at lag 1; PACF is zero at all lags

Explanation

A finite MA(q) has nonzero autocorrelations only up to lag q, so the ACF cuts off after lag 2. Because an invertible MA has an infinite AR representation, the PACF decays gradually. The reverse pattern describes an AR(2).

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