Skip to content

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

A time series process {X_t} is defined as weakly (second-order) stationary. Which set of conditions describes this correctly?

A weakly stationary process has a constant mean and an autocovariance between X_t and X_{t+k} that depends only on the lag k, not on t. Strict stationarity is a stronger condition on whole joint distributions.

  1. AThe mean is constant over time and the covariance between X_t and X_{t+k} depends only on the lag kCorrect
  2. BThe joint distribution of any collection of values is unchanged by a time shift, but the mean may vary with time
  3. CThe mean and variance are constant but the covariance may depend on t as well as on the lag
  4. DThe process has zero mean and the autocorrelation at every non-zero lag is zero
  5. The process has finite variance and a mean that changes linearly with t

Explanation

Weak stationarity needs a constant mean and autocovariance that depends only on the lag (which makes the variance constant too). Option 1 describes strict stationarity and does not allow a varying mean. Option 2 wrongly lets the covariance depend on t.

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