Quantitative Predictive Analysis [/kˈwɑntɪˌteɪtɪv prɪˈdɪktɪv æˈnælɪsɪs/] n - These pages collect the tools used, abused, and retired on quantitative trading desks. Not a textbook; a field guide to what truly gets used when the object is to forecast returns, estimate risk, and trade size without losing the firm.

The mathematics below is not exotic for its own sake. It is the minimum viable machinery by which a desk turns prices, volumes, and fundamental data into decisions. Some of it is elegant; much of it is a discipline of damage control. The unifying theme is prediction under uncertainty: making a bet, sizing it, and knowing when the model has ceased to work.

Foundations

Begin here, if you want the bedrock.

• Linear Factor Models in Trading [/ˈlinear ˈfaktor ˈmodels ˈin ˈtradɪŋ/] n - how returns decompose into priced exposures, and why a factor portfolio is rarely the same as a good portfolio.
• Time Series Decomposition and Forecasting [/ˈtime ˈseries ˈdekomposiʃən ˈand ˈforekastɪŋ/] n - trend, seasonality, cycle, and the humility required to separate signal from smoothing.
• ARIMA and Conditional Mean Models [/ˈarima ˈand ˈkonditional ˈmean ˈmodels/] n - Box-Jenkins in practice, and why the best forecast is oft a modest one.
• Cointegration and Pairs Trading [/ˈkointegraʃən ˈand ˈpairs ˈtradɪŋ/] n - the original statistical arbitrage, and the reason most pairs cease to be pairs.
• Stochastic Calculus in Finance [/ˈstokhastik ˈkalkulus ˈin ˈfinanse/] n - Ito’s lemma, SDEs, and the boundary between pricing and prediction.

Time series methods

These tools fill the gaps in the foundations: stationarity, memory structure, seasonality, and latent states.

• Stationarity and Unit Root Tests [/ˈstationariti ˈand ˈunit ˈroot ˈtests/] n - ADF, KPSS, and why a wandering level wrecks inference.
• Autocorrelation Function and Partial Autocorrelation [/ˈautokorrelaʃən ˈfunkʃən ˈand ˈpartial ˈautokorrelaʃən/] n - reading ACF and PACF to identify AR and MA orders.
• Seasonal ARIMA and Exponential Smoothing [/ˈseasonal ˈarima ˈand ˈexponential ˈsmoothɪŋ/] n - SARIMA, Holt-Winters, and modeling calendar-driven patterns.
• State Space Models and the Kalman Filter [/ˈstate ˈspase ˈmodels ˈand ˈthe ˈkalman ˈfilter/] n - filtering latent states from noisy observations.

Pricing, volatility, and risk

Here mathematics meets capital allocation.

• The Black-Scholes Framework [/ˈthe ˈblakk-skholes ˈframework/] n - the benchmark every trader learns, then learns to distrust.
• The Greeks in Practice [/ˈthe ˈgreeks ˈin ˈpraktise/] n - delta, gamma, vega, theta, and the higher-order sensitivities that run an option book.
• Volatility Modeling with GARCH [/ˈvolatiliti ˈmodelɪŋ ˈwith ˈgarkh/] n - forecasting variance when yesterday’s variance is the dominant regressor.
• EWMA and RiskMetrics [/ˈewma ˈand ˈriskmetriks/] n - one-parameter variance and covariance updates for fast environments.
• Bayesian Updating for Beliefs [/ˈbayesian ˈupdatɪŋ ˈfor ˈbeliefs/] n - turning priors and evidence into posterior weights, above all when the dataset is small.
• Value at Risk and Expected Shortfall [/ˈvalue ˈat ˈrisk ˈand ˈexpektɪd ˈshortfall/] n - regulatory comfort numbers that become useful only when you understand what they hide.

Factors, portfolios, and covariance

Having decomposed returns, you must assemble them again into a portfolio.

• Modern Portfolio Optimization [/ˈmodern ˈportfolio ˈoptimizaʃən/] n - from Markowitz to robust and shrinkage methods, and why constraints beat elegant solutions.
• Risk Parity and Equal Risk Contribution [/ˈrisk ˈpariti ˈand ˈequal ˈrisk ˈkontribuʃən/] n - sizing by risk rather than by dollars.
• Factor Zoo and Multi-Factor Models [/ˈfaktor ˈzoo ˈand ˈmulti-faktor ˈmodels/] n - navigating hundreds of published factors without getting data-mined.
• Principal Components and Eigenportfolios [/ˈprinsipal ˈkomponents ˈand ˈeigenportfolios/] n - PCA, eigenvalues, and finding the market factor in a covariance matrix.
• Random Matrix Theory [/ˈrandom ˈmatrix ˈtheori/] n - using Marchenko-Pastur to separate signal from noise in large covariance matrices.
• Copulas and Tail Dependence [/ˈkopulas ˈand ˈtail ˈdependense/] n - modeling dependence beyond Pearson correlation, above all in the tails.

Models and execution

Once you hold a signal, you must still trade it.

• Machine Learning Alpha Models [/ˈmakhine ˈlearnɪŋ ˈalfa ˈmodels/] n - where gradient boosting and neural nets help, and where they become very expensive toys.
• Feature Engineering for Predictive Signals [/ˈfeature ˈengineerɪŋ ˈfor ˈprediktive ˈsignals/] n - the art of building inputs that mean the same thing in 2008 and 2024.
• Information Coefficient and Signal Decay [/ˈinformaʃən ˈkoeffisient ˈand ˈsignal ˈdekai/] n - measuring predictive power and how swiftly it vanishes.
• Market Microstructure and Execution [/ˈmarket ˈmikrostrukture ˈand ˈexekuʃən/] n - bid-ask, order flow, and why your backtest price was never available.
• Market Impact and Optimal Execution [/ˈmarket ˈimpakt ˈand ˈoptimal ˈexekuʃən/] n - the hidden tax that turns a profitable signal into a flat P&L.
• Transaction Costs and Slippage Models [/ˈtransakʃən ˈkosts ˈand ˈslippage ˈmodels/] n - explicit, implicit, and opportunity costs in backtests and live trading.
• High-Frequency Data and Tick Analytics [/ˈhigh-frequensi ˈdata ˈand ˈtikk ˈanalytiks/] n - trade-and-quote data, classification, and signature plots.
• Monte Carlo Methods in Quantitative Research [/ˈmonte ˈkarlo ˈmethods ˈin ˈquantitative ˈresearkh/] n - sampling your way through path dependence and non-linear portfolios.

Robustness and improvement

Most of the job is not finding alpha. It is keeping alpha once you think you have it.

• Backtesting and Multiple Comparison Bias [/ˈbakktestɪŋ ˈand ˈmultiple ˈkomparison ˈbias/] n - why a Sharpe of 2.0 after five hundred trials is not a Sharpe of 2.0.
• Cross-Validation in Finance [/ˈkross-validaʃən ˈin ˈfinanse/] n - why k-fold fails for time series, and how purged and embargoed methods mend it.
• Regime Switching and Hidden Markov Models [/ˈregime ˈswitkhɪŋ ˈand ˈhidden ˈmarkov ˈmodels/] n - detecting that the market you modeled is not the market you are trading.
• Alpha Decay and Model Lifecycle [/ˈalfa ˈdekai ˈand ˈmodel ˈlifesykle/] n - the half-life of an edge, and the discipline of rebuilding before it disappears.
• Kelly Criterion and Optimal Bet Sizing [/ˈkelli ˈkriterion ˈand ˈoptimal ˈbet ˈsizɪŋ/] n - sizing bets to maximize growth without blowing up.
• Stress Testing and Scenario Design [/ˈstress ˈtestɪŋ ˈand ˈssenario ˈdesign/] n - answering the question that correlation matrices cannot.
• The Quantitative Research Workflow [/ˈthe ˈquantitative ˈresearkh ˈworkflow/] n - how the pieces fit together, from idea to production to decommissioning.

How to Read These Pages

These are evergreen notes, linked one to another as the rest of this site is. Follow a link and it opens beside the current note. The best entry point depends on what you mean to repair: a forecast, a risk number, or a process.

If you are new to the broader site, its original concern is data center power and operations; see About these pages and The Engines of the Hall. This quant section is a separate branch of the same commonplace.