Quantitative Methods
A practical methods library for applied quantitative research and investment practice
This library explains the statistical, econometric, portfolio, data-design, machine-learning, and foundation-model methods used across SlackQuant research and investment systems. Each article connects intuition and formal definitions with reproducible implementation, common failure modes, and examples of how the method matters in research and investment practice.
Current articles
Core Methods
Out-of-Sample Forecast Evaluation
Can a forecasting procedure predict outcomes that were unavailable when each forecast was made? It covers information sets, repeated forecast origins, pseudo-out-of-sample versus genuine real-time evaluation, leakage boundaries, and a small example that separates development fit from held-out performance.
Rolling vs Expanding Windows
How much historical data should a repeated forecasting procedure carry forward? It separates rolling forecast origins from rolling estimation windows, explains the adaptation-versus-estimation trade-off, and shows how the two window designs respond differently after a structural break.
Look-Ahead Bias and Data Leakage
When can a historical test accidentally see the future? It distinguishes look-ahead bias from broader data leakage, maps common contamination paths, and shows how a centered feature can appear stronger simply because it crosses the forecast-origin information boundary.
Diebold–Mariano Test
Does a lower realized forecast loss represent a statistically distinguishable advantage? It builds the test from paired loss differentials, explains long-run variance and the HLN small-sample adjustment, and shows why a lower RMSE need not imply statistically distinguishable predictive accuracy.
Model Confidence Set
When does the evidence justify a single winning model, and when should uncertainty remain set-valued? It explains sequential equal-performance testing, elimination rules, and bootstrap uncertainty, then shows how five ranked models can narrow to a two-model confidence set rather than a forced single winner.
Block Bootstrap
How should uncertainty be resampled when observations are serially dependent? It explains moving-block bootstrap intuition and block-length sensitivity, then shows how IID resampling can erase serial dependence that matters for uncertainty estimates.
Multivariate Probabilistic Forecast Evaluation
How should a joint predictive distribution be evaluated beyond point accuracy? It combines proper scoring rules, marginal calibration, dependence diagnostics, portfolio-tail calibration, and dependence-aware inference while explaining why no single score can establish overall model quality.
Investment Methods
Portfolio Backtesting and Rebalancing
Which weights earn each period’s returns, how do those weights drift, and when does a rebalance affect the portfolio? It explains gross wealth accounting, pre-trade weight drift, buy-and-hold versus periodic rebalancing, explicit turnover conventions, and the information timing needed to avoid hidden rebalancing or look-ahead.
Drawdown, Underwater Duration, and Recovery
How deep is a portfolio below its running peak, how long has it been underwater, and has recovery actually occurred? It separates peak-normalized drawdown from alternative conventions, distinguishes current underwater age from completed peak-to-recovery duration, and treats unrecovered terminal episodes as censored rather than complete.
Turnover, Transaction Costs, and Net Performance
How much rebalancing does a strategy require after portfolio weights drift, and how do declared transaction-cost assumptions change net wealth? It distinguishes full-L1 from one-way turnover, matches each cost quote to its traded-notional denominator, and applies modeled costs multiplicatively to the portfolio wealth path.
Momentum and Trend Signals
How should past-return momentum be defined and timed before it becomes a portfolio decision? It separates time-series/absolute from cross-sectional momentum, makes lookback and optional skip-month conventions explicit, and audits signal-to-holding-period timing and parameter sensitivity.
Strategy Similarity and Decision Diversification
Do multiple strategies really make different decisions, or merely carry different labels? It separates return correlation from holdings/exposure similarity and evaluates what, when, and how-much disagreement without forcing them into a universal scalar score.
Rolling Holding-Period Analysis
What do 5-, 10-, 15-, and 20-year outcomes look like across different starting dates? It distinguishes endpoint from path outcomes and explains why heavily overlapping rolling windows are descriptive historical observations rather than IID probability trials.
Benchmark-Relative Portfolio Evaluation
How should a portfolio be evaluated in active space? It defines active return, tracking error, information ratio, relative wealth, and benchmark-relative drawdown while separating absolute Sharpe from benchmark-relative metrics and clarifying benchmark choice.
Cross-Sectional Ranking, Top-K Selection, and Hold Buffers
How should heterogeneous model outputs become stable portfolio membership? It separates ordinal rank from normalized rank strength, defines Top-K entry and incumbent hold buffers, and makes the turnover/path-dependence trade-off explicit.
Dynamic Currency Hedging and FX Overlay Accounting
How should a currency overlay be timed, accounted for, and separated from the underlying portfolio? It distinguishes raw versus admissible FX observations, defines base-currency wealth and hedge ratios, and keeps hedge P&L, costs, Official decisions, and Preview states on explicit clocks.
EWMA-t Scenario Simulation
How can the current multi-asset covariance environment be converted into heavy-tailed joint future paths? It combines exponentially weighted covariance estimation with covariance-targeted multivariate Student-t innovations, explicit degrees-of-freedom and decay conventions, and Monte Carlo stability checks.
Scenario-Based Portfolio Stress Testing
How should a joint scenario cloud be mapped into portfolio loss and path-risk diagnostics? It revalues baseline and candidate portfolios on the same future paths, separates portfolio-weight effects from scenario-generation effects, and distinguishes scenario-conditioned what-if analysis from optimization and realized-loss claims.
Machine Learning Methods
Regularized Linear Models: Ridge, Lasso, and Elastic Net
How can a linear predictor remain stable when features are numerous, noisy, or correlated? It compares Ridge, Lasso, and Elastic Net, makes scaling and penalty conventions explicit, and treats preprocessing and penalty selection as part of the leakage-controlled forecasting procedure.
Time-Series Model Selection and Hyperparameter Tuning
How should hyperparameters be selected when the tuning procedure itself must respect historical information sets? It covers chronological folds, nested evaluation, target maturity, gap design, fold-local preprocessing, and the important conditions under which ordinary K-fold is not automatically invalid.
Reinforcement Learning for Adaptive Portfolio Risk Control
How can reinforcement learning be used as a bounded risk-control layer without turning the controller into the alpha engine? It covers state/action/reward design, offline coverage, chronological evaluation, policy freezing, fail-closed deployment, and Core-versus-Adaptive attribution.
Forecast Combination and Model Averaging
When should several models be combined instead of forcing a single winner? It separates equal and estimated combinations, forecast-scale compatibility, rank aggregation, weight-estimation risk, and model-combination weights from downstream portfolio allocations.
Pretrained Time-Series Foundation Models
How should pretrained forecasting models be evaluated without confusing zero-shot inference with information-free prediction? It separates downstream inference timing from pretrained knowledge, distinguishes model architectures, audits future covariates and pretraining overlap, and separates retrospective technology counterfactuals from historical real-time OOS claims.
Research Design & Technical Methods
Information Timing, Data Vintages, and Real-Time Macro Data
Which macro observations were truly admissible at each forecast or portfolio decision? It separates reference periods, source release dates, database vintages, actual availability, revisions, and forecast cutoffs, with a fail-closed rule when exact point-in-time evidence is unavailable.
Point-in-Time Dynamic Universe Construction
How should an investable opportunity set evolve without backfilling future constituents into the past? It separates listing availability, liquidity/history eligibility, exposure representative selection, model readiness, and prospective candidate-pool governance.
Stress Archetypes and Representative Scenario Geometry
How can a large adverse scenario tail be converted into interpretable stress families without overstating probability claims? It defines mutually exclusive archetypes, a residual Other category, volatility-normalized geometry, feasible medoid-style representatives, and simulation-stability and external-relevance checks.
Library principles
The library is application-driven rather than encyclopedic. Methods are added when they materially support SlackQuant research, investment systems, or applied quantitative practice.
Each computed illustration is accompanied by the data and code needed to reproduce it. Synthetic examples are clearly labeled as illustrations rather than presented as empirical evidence.
Future additions
Future additions are added when they materially support active SlackQuant research, investment systems, or applied quantitative practice.