Skip to content

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

An ARMA model is fitted to a series of 200 observations and the residual autocorrelations at lags 1 to 10 are computed. A Ljung-Box (portmanteau) test is applied. Which statement about its use is correct?

A large Ljung-Box statistic compared with the chi-squared critical value indicates the residuals still contain autocorrelation and are not white noise, so the fitted model is inadequate. The test examines residual independence, not normality, and is valid for general ARMA models.

  1. AA large test statistic relative to the chi-squared critical value suggests the residuals are not white noise, so the model is inadequateCorrect
  2. BA large test statistic indicates the model fits well because residual autocorrelations are large
  3. CThe test compares the AIC of two competing models
  4. DThe test checks whether the residuals are normally distributed
  5. The test is only valid for pure moving average models

Explanation

The Ljung-Box statistic sums squared residual autocorrelations; under the null of white noise it is approximately chi-squared with degrees of freedom reduced by the number of fitted ARMA parameters. A large value signals remaining autocorrelation, so the model is inadequate. It tests independence, not normality, and does not compare models.

Did you get it right without looking?

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

Practise Applications of time series modelsFree diagnostic mock

More Applications of time series models questions