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

A stationary bivariate time series (X_t, Y_t) is modelled with a vector autoregression of order 1 (VAR(1)). Which statement about the process is correct?

In a VAR(1) each series is regressed on the previous values of both series, so each depends on its own past and on the past of the other. This allows feedback between series, unlike separate univariate AR(1) models.

  1. AEach series is regressed only on its own past value, so the two equations are independent
  2. BEach series is regressed on the lagged values of both series, allowing feedback between themCorrect
  3. CEach series is regressed on the current value of the other series only
  4. DIt requires the two series to be uncorrelated at all lags
  5. It can only be fitted if both series are white noise

Explanation

A VAR(1) writes the vector of series at time t as a function of the vector at time t-1 plus a vector of errors. Every equation therefore contains lagged values of all series, which allows feedback. Option 0 describes two separate AR(1) models, which ignores cross-dependence.

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