Time Series and Forecasting
A time series is a sequence of measurements in time order, and a forecast is a statement about values you have not seen yet. Start from trend, seasonality and noise, learn autocorrelation and stationarity, and build the classical models: exponential smoothing, ARIMA and SARIMA, state-space models and the Kalman filter. Then evaluate forecasts honestly with backtesting, forecast with gradient boosting, recurrent, convolutional and transformer networks and pretrained foundation models, give every forecast calibrated uncertainty, and detect anomalies.
For students, engineers and researchers who want to forecast real data and know why a method works. You need expectation, variance and covariance, the normal distribution and least squares (probability-and-statistics track), matrix multiplication and eigenvalues (linear-algebra track), and Python with NumPy and pandas. The machine-learning lessons also use gradient boosting (ml-fundamentals) and neural networks (deep-learning). Each lesson links the exact prerequisites.
Quick recap
The key takeaways of all lessons on one page
All interactive figures
Every figure of the track on one page
Videos and books
The best free courses
Glossary
Every technical term of the track with a short definition
Concept map
How the lessons of this track connect to each other and to other tracks.
Keeps every lesson page and figure of this track in this browser, so you can read it without internet.
Time series data
What makes time-ordered data special, trend, seasonality and noise, decomposition, stationarity and autocorrelation.
-
01
Time series data: trend, seasonality, noise and decompositionWhat makes time-ordered data special, how to look at it, and how to split a series into trend-cycle, seasonal and remainder parts with moving averages, classical decomposition and STL.
60 min
4 figures
Beginner -
02
Stationarity, autocorrelation, ACF and PACFWhite noise, random walks and AR(1); weak stationarity; the sample ACF with its band and the Ljung–Box test; the PACF; differencing, unit-root tests and spurious regression.
80 min
5 figures
Intermediate
First forecasts and honest evaluation
Simple benchmark forecasts, backtesting with a rolling origin, error metrics and leakage, then exponential smoothing up to Holt-Winters.
-
03
Benchmark forecasts and honest evaluation: backtesting, metrics and leakageThe four benchmark forecasts every method must beat, residual checks, rolling-origin backtests with expanding or sliding windows and a gap, point-forecast metrics from MAE to MASE, which forecast each metric rewards, and how leakage makes bad models look good.
75 min
4 figures
Beginner -
04
Exponential smoothing: from simple smoothing to Holt-Winters and ETSSimple exponential smoothing in three equivalent forms, choosing the smoothing parameter, Holt's linear and damped trend, additive and multiplicative Holt-Winters, and the ETS state-space models that add a likelihood and prediction intervals.
75 min
4 figures
Intermediate
ARIMA and state-space models
Autoregressive and moving-average models, differencing and seasonal ARIMA with prediction intervals, and the Kalman filter for state-space models.
-
05
Autoregressive and moving-average models (AR, MA, ARMA)A series that remembers its own past (AR) or past shocks (MA). Stationarity from roots and eigenvalues, the AR(2) triangle and quasi-cycles, Yule–Walker, invertibility, ACF/PACF patterns, AIC, and an AR(2) for the sunspot cycle.
90 min
5 figures
Intermediate -
06
ARIMA and SARIMA: differencing, forecasting and prediction intervalsDifference a series until it is stationary, model the rest as ARMA, and forecast step by step. Why intervals widen with the horizon (the ψ-weights), what the constant and d do to the long-run forecast, seasonal ARIMA and the airline model on CO₂, the Box–Jenkins workflow and regression with ARIMA errors.
90 min
5 figures
Intermediate -
07
State-space models and the Kalman filterA hidden state moves by a linear rule and we see it through noise. The Kalman filter tracks it exactly with a predict step and an update step, gives forecasts with intervals and the likelihood, and its steady state is simple exponential smoothing.
110 min
5 figures
Advanced
Machine learning and deep learning for forecasting
Forecasting as supervised learning with lag features and gradient boosting, then recurrent, convolutional and transformer networks and pretrained foundation models.
-
08
Forecasting with machine learning: lag features, gradient boosting and multi-step strategiesTurn a series into a table of lag, rolling and calendar features without leakage. Why trees cannot extrapolate a trend and how to fix it, recursive versus direct multi-step forecasts, global models for many series, and gradient boosting with honest time-based validation.
90 min
5 figures
Intermediate -
09
Deep learning for forecasting: RNNs, temporal CNNs, transformers and foundation modelsHow neural networks forecast a series from a window of its past. Recurrent networks and DeepAR, causal dilated convolutions and their receptive field, linear and MLP models such as DLinear and N-BEATS, transformers with patches, and pretrained foundation models used zero-shot, with honest evaluation.
120 min
5 figures
Advanced
Uncertainty and anomalies
Quantile and distribution forecasts, the pinball loss and CRPS, conformal prediction intervals, and anomaly and change-point detection.
-
10
Probabilistic forecasting: quantiles, CRPS and conformal intervalsA forecast should say how uncertain it is. Quantile forecasts from the pinball loss, calibration and sharpness, the PIT histogram, the CRPS, split conformal intervals with a coverage guarantee, and adaptive conformal inference for series that change.
110 min
5 figures
Advanced -
11
Anomaly and change-point detection in time seriesFind values, shapes and lasting changes that do not fit the normal behaviour of a series. Expected value plus residual plus a robust threshold, the false-alarm budget, CUSUM for change points, the matrix profile for unusual shapes, and honest evaluation without point adjustment.
90 min
5 figures
Intermediate