STAT 320 · Year 3 · Semester 2 · 3 credits · Mathematics & Statistics

Time Series & Forecasting

From stochastic trends to predictive intervals: mastering time series, state-space dynamics, and mortality forecasting for actuarial practice.

Full practice exam · 30 Q · 120 min

Season 1 · 8 episodes

Signal and Solvency

When a hundred-and-eighty-million-dollar reserve deficit threatens Northern Solvency Mutual with regulatory takeover, newly appointed lead actuary Maya Lin must replace fifty years of naive trend lines with modern time series science before the state commissioner pulls the carrier's license.

Protagonist · Maya Lin, ACAS and newly promoted Lead Quantitative Actuary at Northern Solvency Mutual

Setting · Northern Solvency Mutual headquarters in Chicago, under active supervisory examination by the Illinois Department of Insurance

Stakes · Failure to quantify true loss trends, interest rate volatility, and longevity shifts will trigger mandatory capital conservation, rating downgrades, and the forced runoff of an eighty-year-old policyholder-owned institution.

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Episodes

Season finale: At the emergency supervisory board hearing, Maya deploys an end-to-end time series pipeline—from SARIMA loss indications and Kalman state-space updates to GARCH volatility bounds, ESG market projections, and Lee-Carter mortality paths—defending reserve adequacy, restoring capital surplus, and establishing a new enterprise forecasting benchmark.

From the lecturer: Welcome to STAT 320. Time series forecasting is the mathematical bridge connecting historical claim frequency, inflation trajectories, asset returns, and demographic shifts to sound actuarial decisions. To master this material, treat every film as an interactive seminar: keep pencil, grid paper, and an open R or Python terminal beside you. When we establish the lag-operator polynomials, set up Yule-Walker linear systems, or execute the Kalman filter measurement update, pause the playback and advance the algebra on paper before comparing your result with the screen. This course is mathematically rigorous and maps directly to the Time Series syllabus of CAS Exam MAS-II, while establishing the dynamic modeling competencies required for ASOP No. 27 (Economic Assumptions) and ASOP No. 43 (Loss Reserving). Focus deeply on the operational reality that in-sample fit is cheap, but honest out-of-sample forecast validation under rolling origins is what protects solvency. Let us build models that respect temporal uncertainty.

Cold open

At six forty-five in the morning, Maya finds a confidential red folder on her desk. The chief actuary has resigned, and the state insurance commissioner has issued a forty-eight-hour show-cause notice: the commercial liability loss trend has blown past historical averages for six straight quarters, yet the legacy models still assume zero autocorrelation around a flat three percent mean.

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Transcript

Distinguish between strict and weak (covariance) stationarity in actuarial loss and economic time series.
Derive the theoretical autocovariance and autocorrelation functions (ACF) for linear stochastic processes.
Compute and interpret the partial autocorrelation function (PACF) using the Yule-Walker equations.
Identify candidate autoregressive and moving average orders from empirical sample ACF and PACF diagnostic plots.