Time-Series Finance

Stochastic processes handed you the rulebook for how prices wander, but a rulebook is only theory until you point it at real data. Time-series finance is the forensics — fit the rules to an actual return series, forecast both the next move and the next storm, and refuse to be fooled by a backtest that looks too good to be true.

Here’s the pipeline you’ll build, from raw prices to a validated, risk-aware model:

• Stationarity & unit roots — why a stock’s price flunks (it carries a unit root, shocks never decay) while its return sails through, and how the augmented Dickey–Fuller test, logs, and differencing turn an un-modelable series into a modelable one.
• Autocorrelation, ACF & PACF — the fingerprint readers that say whether today’s return predicts tomorrow’s, judged against the white-noise band ($\pm 2/\sqrt{n}$) and confirmed with the Ljung–Box test.
• AR, MA & ARIMA(p,d,q) — the workhorse mean models (own past values, past shocks, and their combination), with order chosen honestly via AIC/BIC and validated on the residuals.
• Volatility clustering & ARCH/GARCH — modeling risk itself: the ARCH insight, the three-parameter GARCH(1,1), and the persistence $\alpha + \beta$ that sets how slowly a volatility shock fades.
• EWMA & RiskMetrics — the one-parameter cousin behind J.P. Morgan’s Value-at-Risk numbers, and why a fixed $\lambda = 0.94$ beat a fitted GARCH for firm-wide, auditable daily risk.
• Backtesting traps — the three deadliest ways to fool yourself (look-ahead bias, overfitting, data-snooping) and the discipline that defends against them: parsimony, out-of-sample holdouts, and walk-forward analysis.

This is the expert rung where the abstract machinery of randomness-through-time becomes a working pipeline you can run on tonight’s closing prices — and a graded final exam runs the whole thing back at you, one locked question at a time.