Interactive Tools

§ 01 — Time series foundations

01 The Random Walk Stock prices as a random walk with drift: annual drift and volatility, fat-tailed shocks, a forecast cone that widens with √t, and the noise behind every apparent trend. → 02 Stationarity Visualizer Why constant mean, variance, and autocovariance matter — trending, seasonal, and white-noise processes compared through ensemble versus time means. →

§ 02 — Exponential smoothing

03 Simple Exponential Smoothing How α trades stability for responsiveness — and why α near 1 is a confession that your model is missing trend or season. → 04 Holt's Linear Trend Level and trend decomposed, each with its own smoothing parameter — flat forecasts become sloped ones. → 05 Holt–Winters Seasonal The full triple: α, β*, and γ working together to capture level, trend, and seasonality at once. →

§ 03 — ARIMA

06 AR(1) & MA(1) Building Blocks Past values versus past errors: stationarity conditions, autocorrelation signatures, and how each block forecasts. → 07 SARIMA Explorer Dial in (p, d, q)(P, D, Q)ₖ on the airline-passengers data and watch trend and seasonality get captured — forecasts with confidence intervals included. →

§ 04 — Machine learning

08 Bias–Variance Tradeoff Repeated sampling makes bias and variance visible: fit polynomials to noisy draws and watch underfitting and overfitting emerge on a live tradeoff curve. → 09 Cross-Validation K-Fold, Stratified, and Leave-One-Out, animated fold by fold — see exactly where validation scores come from. → 10 Learning Curves Training and validation error as data grows — diagnose high bias versus high variance, and learn when more data actually helps. → 11 Gradient Descent & SGD Watch optimization crawl a contour loss surface in real time. Compare smooth Batch GD with noisy SGD, and push the learning rate until it diverges. → 12 Decision Trees for Time Series Trees partitioning lag space, rendered as both structure and decision boundaries — and why they struggle with trend once forecasts go recursive. → 13 Bagging Many trees, bootstrap resamples, one averaged forecast on the airline-passengers data — watch test error fall as trees are added, see which months each tree trained on, and why trees can't extrapolate a trend. → 14 Boosting Small trees added one round at a time on the airline-passengers data — watch each tree fit the residuals, see training and test error part ways, and find the round where early stopping should quit. → 15 Histogram vs GOSS Splitting How LightGBM finds splits fast — histograms test fewer thresholds, GOSS looks at fewer rows. Dial the bins, top_rate, and other_rate, and see when GOSS wins and when it doesn’t. →

§ 05 — Leakage & dependence — where honest backtests live or die

16 Time Series Cross-Validation Purged K-Fold with embargo, Walk-Forward windows, and Combinatorial Purged CV with backtest-path reconstruction — the machinery that keeps evaluations honest. → 17 Time Series Bootstrapping Moving Block, Circular Block, Stationary, and parametric AR(1) bootstraps — resampling dependent data without destroying its structure. →

§ 06 — Deep learning

18 Deep Neural Networks, Live Configure layers, neurons, activations, and lags, then train in your browser with TensorFlow.js — live loss curves, feature importance, and a linear-regression benchmark to keep the hype honest. → 19 RNN vs DNN Train both side by side and discover the key lesson: preprocessing (log + differencing) turns RNN performance from poor to excellent on non-stationary data. →

§ 07 — From around the web

↗ Neural Network Visualization A curated external find: architectures, activations, and how networks learn. Opens on Notion. ↗