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

A time series {e_t} is described as Gaussian white noise with mean zero and variance sigma squared. Which statement about this process is correct?

Gaussian white noise consists of independent, identically distributed normal terms with constant mean and variance. Autocovariance is zero at all non-zero lags, so the process is strictly stationary. Growing variance or unit roots belong to random walks, not white noise.

  1. AThe terms are independent and identically distributed normal variables, so the process is strictly stationary with zero autocovariance at every non-zero lagCorrect
  2. BThe terms have autocovariance sigma squared at lag 1, so the process is stationary but has a persistent memory
  3. CThe variance grows linearly with t, so the process is non-stationary
  4. DThe autocorrelation at lag k equals 0.5 raised to the power k
  5. The process has a unit root and must be differenced to become stationary

Explanation

Gaussian white noise has uncorrelated, independent, identically distributed N(0, sigma^2) terms. Its mean and variance are constant and gamma_k = 0 for k >= 1, so it is stationary. Growing variance and unit roots describe a random walk, not white noise.

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