Actuarial›Exam SRM›Time Series Models
Exam SRM topic · 5–10% of exam

Time Series Models

Introduction to time series analysis including autoregressive, moving average, and ARIMA models.

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Per-objective worked-example outlines

For each learning objective on Time Series Models, here is the approach an exam item would test — the setup, the ordering of your reasoning, and the formula or identity you need to bring to the page. Approaches, not full solutions, by design. Verify against the current soa.org syllabus before your sitting.

Identify stationarity and apply differencing to achieve stationarity

Setup

A time series plot and autocorrelation function are shown and you must judge whether the series is stationary and, if not, how to make it so.

Approach

Look at the time plot for trend, seasonality, and changing variance. Check the ACF for slow decay (suggesting non-stationarity). Apply first differencing to remove a linear trend or seasonal differencing for a seasonal pattern. Re-check the ACF — for a stationary series, autocorrelations should drop off quickly.

Key identity

ARIMA(p, d, q): differencing order d makes the series stationary.

Fit and interpret autoregressive, moving average, and ARIMA models

Setup

You are given an ACF and PACF plot, and must propose an ARIMA(p, d, q) model.

Approach

AR(p) has PACF cutting off at lag p with ACF tailing off; MA(q) has ACF cutting off at lag q with PACF tailing off; ARMA has both tailing off. Combine with the differencing order d from stationarity. Estimate parameters by maximum likelihood; check residuals for white noise behavior.

Key identity

AR(p): PACF cuts off at p. MA(q): ACF cuts off at q. ARMA: both tail off.

Assess time series model fit using residual diagnostics

Setup

A fitted ARIMA model produces a residual series and you must judge whether the fit is adequate.

Approach

Residuals should look like white noise: ACF inside the confidence bands, no patterns in the residual plot, no remaining seasonality. Use the Ljung-Box test for joint autocorrelation across many lags. Compare candidate models on AIC/BIC. Refit with a more complex model if patterns persist.

Key identity

Ljung-Box statistic: Q = n(n + 2) Σ ρ̂_k^2 / (n - k), df = h - p - q.

Common exam traps on Time Series Models

Recurring patterns where candidates lose points on Time Series Models-style items. Each entry pairs the trap with the fix.

Trap

Treating a series with trend as stationary because it is "smooth".

Fix

Stationarity requires constant mean and variance; trend violates this even if the series looks smooth.

Trap

Confusing the cutoff behavior in ACF and PACF for AR vs MA.

Fix

AR cuts off in PACF; MA cuts off in ACF. The opposite plot tails off in each case.

Trap

Over-differencing a series.

Fix

Differencing too much introduces unit roots in the MA part and reduces interpretability; stop when the series looks stationary.

Trap

Comparing AIC across models with different differencing orders.

Fix

AIC requires identical observations; differencing changes the effective sample size.

Where to find Time Series Models in popular manuals

Pointers to where each major vendor covers this topic, so you can grab the right chapter without combing the full manual. We do not reproduce vendor content — just the location. Chapter and lesson numbers shift between editions; use these as a guide, not as a citation.

ACTEX

Time series chapter at the end of the SRM manual

Coaching Actuaries

Learn modules on Time Series Models; Adapt category "Time Series"

The Infinite Actuary

Time series video block on ARIMA and diagnostics

6-day Time Series Models micro plan

A focused 6-day sub-schedule for Time Series Models specifically, at roughly 1.5–2.5 hours per day. Drop it inside your full Exam SRM plan as a single coverage module.

Day 1

Read the stationarity and differencing chapter; practice identifying trend and seasonality on plots.

Day 2

Drill 10 problems on ACF/PACF interpretation for AR, MA, and ARMA processes.

Day 3

Practice fitting ARIMA orders — 8 problems including seasonal differencing.

Day 4

Residual diagnostics — 6 problems including Ljung-Box and AIC comparisons.

Day 5

Mixed 12-problem timed drill on time series.

Day 6

Re-do flagged problems and write a one-page ARIMA cheat sheet.

How exclam.ai helps you master Time Series Models

Flashcards from your manual

Upload your ACTEX Exam SRM digital edition, scanned ASM pages, TIA handouts, or your own notes. exclam.ai extracts the Time Series Models sections and generates flashcards automatically, tuned to the exam traps above.

Worked-example drilling

Each per-objective approach above maps to a quiz template. exclam.ai re-surfaces missed items until you can recall both the setup and the key identity from cold.

FSRS spaced repetition

Because Time Series Models is 5–10% of your exam, losing it during review costs you. FSRS brings it back at the optimal moment.

Time Series Models in the Exam SRM context

SOA Exam SRM has 5 topic areas. Time Series Models is weighted at approximately 5–10% of the exam, here is where it sits relative to the other topics.

Topic areaWeight
Basics of Statistical Learning7–13%
Linear Models40–50%
Decision Trees20–25%
Principal Components and Cluster Analysis5–10%
→ Time Series Models5–10%

Other Exam SRM topics

Basics of Statistical Learning

7–13%

Supervised and unsupervised learning, model assessment, bias-variance tradeoff, and resampling methods including cross-validation.

Study this topic

Linear Models

40–50%

Ordinary least squares regression, generalized linear models, variable selection, and regularization techniques.

Study this topic

Decision Trees

20–25%

Classification and regression trees, pruning, and ensemble methods including bagging, random forests, and boosting.

Study this topic

Principal Components and Cluster Analysis

5–10%

Dimension reduction via principal components analysis and unsupervised clustering via k-means and hierarchical clustering.

Study this topic

Start practicing Time Series Models today

Upload your ACTEX Exam SRM digital edition, scanned ASM pages, TIA handouts, or your own notes. exclam.ai generates a fully guided study plan with adaptive flashcards and quizzes for this topic.

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