IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Applications of time series models
An analyst fits an ARIMA model to monthly claim counts and finds the sample autocorrelation function of the raw series decays very slowly from a value near 1. What is the most appropriate next step?
Difference the series once and re-examine its ACF and PACF. A very slowly decaying sample ACF indicates non-stationarity from a unit root, and differencing is the standard remedy before identifying the ARMA orders in the Box-Jenkins approach.
- AFit a pure MA model to the raw series
- BTake the first difference and examine the ACF and PACF of the differenced seriesCorrect
- CTake logarithms only and assume stationarity
- DTake the square of the series
- Fit an AR(1) with coefficient greater than 1
Explanation
A slowly decaying sample ACF near 1 suggests a unit root, i.e. non-stationarity. Differencing the series once and re-examining the ACF and PACF is the standard Box-Jenkins step before identifying p and q.
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
- A stationary AR(1) process X_t = 0.5 X_{t-1} + e_t has e_t white noise with variance 9. What is the variance of X_t?
- 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?
- Consider the AR(2) process X_t = 1.2 X_{t-1} - 0.2 X_{t-2} + e_t. Which statement is correct?
- An actuary fits an MA(1) model X_t = e_t + theta e_{t-1}. For the model to be invertible, which condition on theta is required?
- For a stationary AR(1) process X_t = 0.8 X_{t-1} + e_t with white-noise variance 3.6, what is the variance of X_t?
- A random walk with drift is defined by X_t = X_{t-1} + 2 + e_t, where e_t is white noise with variance 9. Which statement is correct?