IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Applications of time series models
The sample ACF of a stationary series shows a sharp cut-off after lag 2 and the sample PACF decays gradually. Which model is most suitable?
An MA(2) model is most suitable. A moving average process of order q has an autocorrelation function that cuts off after lag q, while its partial autocorrelation function decays gradually, matching the pattern described.
- AAR(2)
- BMA(2)Correct
- CARMA(1,1)
- DAR(1)
- White noise
Explanation
An MA(q) process has an ACF that is zero beyond lag q and a PACF that tails off. A cut-off in the ACF after lag 2 with a decaying PACF indicates MA(2). AR(2) would show the reverse pattern.
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.
More Applications of time series models questions
- An MA(1) model is X_t = mu + e_t + 0.5 e_{t-1}, with mu = 20. At time n the last observation is X_n = 23 and the estimated residual is e_n =…
- Let X_t = 5 + 0.4t + e_t, where e_t are independent N(0, 4) variables. Which statement is correct?
- The sample partial autocorrelation function of a stationary series of 400 observations shows significant spikes at lags 1 and 2 and is negli…
- A time series Y_t is described as ARIMA(1,1,0). Which statement correctly describes the process?
- An analyst fits an ARIMA model to monthly claim counts and finds the sample autocorrelation function of the raw series decays very slowly fr…
- For an AR(2) process X_t = 0.5 X_{t-1} + 0.2 X_{t-2} + e_t, the lag-1 autocorrelation rho_1 is obtained from the Yule-Walker equations. What…