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

A series shows a clear upward trend and a sample ACF that decays very slowly from values near 1. The first differences of the series have an ACF that is negligible beyond lag 1, with a decaying PACF. Which model is most appropriate for the original series?

The appropriate model is ARIMA(0,1,1). The slowly decaying ACF indicates one difference is needed, and the differenced series shows an MA(1) pattern, with ACF cutting off after lag 1 and a decaying PACF.

  1. AARMA(1,1)
  2. BARIMA(0,1,1)Correct
  3. CARIMA(1,1,0)
  4. DAR(1) with phi near 0.5
  5. ARIMA(0,2,1)

Explanation

The slowly decaying ACF suggests non-stationarity, so difference once (d=1). The differenced series has ACF cutting off after lag 1 and decaying PACF, which is an MA(1). The model is ARIMA(0,1,1).

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