Free SOA Exam SRM (Statistics for Risk Modeling) Time Series Models Practice Questions
Time series modeling on SOA Exam SRM covers ARIMA processes, stationarity testing, autocorrelation analysis, forecasting methods, and model identification and selection criteria (AIC, BIC).
Sample Questions
Question 1
Easy
For a forecast to be useful, the prediction interval should:
Solution
A is correct.
Prediction intervals widen as the forecast horizon increases because uncertainty about future values grows over time. For stationary models (like AR), the interval width converges to a finite limit; for non-stationary models (like random walks), the width grows without bound.
Prediction intervals widen as the forecast horizon increases because uncertainty about future values grows over time. For stationary models (like AR), the interval width converges to a finite limit; for non-stationary models (like random walks), the width grows without bound.
Question 2
Medium
Differencing a time series means computing:
Solution
C is correct.
First differencing computes , the change between consecutive observations. This is commonly used to remove trends and achieve stationarity.
First differencing computes , the change between consecutive observations. This is commonly used to remove trends and achieve stationarity.
Question 3
Hard
An AR(1) process has and . Compute the unconditional variance and the autocovariance at lag 5, . What is ?
Solution
C is correct.
Step 1 — Unconditional variance:
Step 2 —
Step 3 — Autocovariance at lag 5:
Step 1 — Unconditional variance:
Step 2 —
Step 3 — Autocovariance at lag 5: