Skip to content

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

An analyst examines the sample ACF and PACF of a stationary series. Both the ACF and the PACF decay gradually toward zero with no sharp cutoff. Which model class is most consistent with this pattern?

A mixed ARMA model fits best, because gradual decay in both the ACF and PACF indicates neither a pure AR (PACF cutoff) nor a pure MA (ACF cutoff). White noise would show insignificant autocorrelation at all lags.

  1. APure AR(2)
  2. BPure MA(2)
  3. CARMA with both AR and MA componentsCorrect
  4. DWhite noise

Explanation

A pure AR has a PACF that cuts off after p lags; a pure MA has an ACF that cuts off after q lags. When both decay gradually without cutoff, a mixed ARMA is indicated. White noise would show no significant autocorrelations.

Did you get it right without looking?

One question tells you little. A timed set on Stationary Time Series shows your real accuracy, how long you take and where you lose marks.

Practise Stationary Time SeriesFree diagnostic mock

More Stationary Time Series questions