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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Core concepts of time series models

Which feature of the sample partial autocorrelation function (PACF) would suggest that an AR(2) model is appropriate for a stationary series?

An AR(2) model is suggested when the partial autocorrelation function cuts off after lag 2 while the autocorrelation function decays gradually. The reverse pattern, an ACF cutting off with a decaying PACF, indicates a moving average process instead.

  1. APACF cuts off after lag 2 while the ACF decays graduallyCorrect
  2. BPACF decays geometrically while the ACF cuts off after lag 2
  3. CBoth ACF and PACF cut off after lag 2
  4. DPACF is significant only at lag 1
  5. PACF is zero at all lags

Explanation

For an AR(p) process the PACF is zero beyond lag p, while the ACF tails off gradually. So an AR(2) shows a PACF cutting off after lag 2 with a decaying ACF. The reverse pattern indicates an MA(2).

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