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

A time series analyst inspects the sample ACF and PACF of a stationary series. The sample ACF decays gradually towards zero, while the sample PACF is significant at lags 1 and 2 and negligible afterwards. Which model is the most appropriate first choice?

The best first choice is AR(2). An autoregressive process of order p has a partial autocorrelation function that cuts off after lag p and an autocorrelation function that decays gradually, which matches the pattern described here.

  1. AMA(2)
  2. BAR(2)Correct
  3. CARMA(1,1)
  4. DAR(1)
  5. ARIMA(0,1,2)

Explanation

For an AR(p) process the PACF cuts off after lag p while the ACF decays gradually. A PACF significant only at lags 1 and 2 with a decaying ACF points to AR(2). An MA(2) would show the reverse pattern: ACF cut-off and PACF decay.

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