Skip to content

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

An analyst fits an ARMA model to monthly claim counts for an Indian insurer and tests residuals. Which finding would most clearly indicate that the fitted model is inadequate?

A Ljung-Box statistic far above the chi-square critical value signals inadequacy. It shows the residual autocorrelations are jointly significant, so they are not white noise and the model has failed to capture the dependence structure in the data.

  1. AResidual sample autocorrelations lie within roughly plus or minus 2/sqrt(n) at all lags
  2. BA Ljung-Box (portmanteau) statistic far above the chi-square critical valueCorrect
  3. CResiduals appear to have constant variance over time
  4. DA turning point test shows a number of turning points close to its expectation
  5. A residual histogram that is approximately symmetric

Explanation

A large portmanteau statistic means the residuals have significant joint autocorrelation, so the model has not captured all the dependence. The other options are all consistent with residuals behaving like white noise.

Did you get it right without looking?

One question tells you little. A timed set on Core concepts of time series models shows your real accuracy, how long you take and where you lose marks.

Practise Core concepts of time series modelsFree diagnostic mock

More Core concepts of time series models questions