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

A sample ACF of a monthly premium series decays very slowly from a value near 0.95 at lag 1 and stays large for many lags. What is the most reasonable conclusion?

The series is probably non-stationary, so differencing should be considered. A sample ACF that starts near 0.95 and decays very slowly signals a trend or unit root, whereas white noise or a low-order MA process would show correlations dying out quickly.

  1. AThe series is white noise
  2. BThe series is likely non-stationary and differencing should be consideredCorrect
  3. CThe series is a pure MA(1) process
  4. DThe series has a seasonal component of period 1
  5. The series is stationary with a short memory

Explanation

A slowly decaying sample ACF with high values at many lags is typical of a non-stationary series with a trend or unit root. White noise and MA(1) would show little or no correlation beyond lag 1. Differencing is the usual remedy.

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