peterindia.netForecasting Algorithms
From a seasonal naive baseline to ARIMA, gradient boosting and pretrained foundation models: how each algorithm works, where it shines, what to watch for and how to judge a forecast.
Forecast the last value, the value from the same season last cycle, or the last value plus the average historical change.
Smooths a series, or splits it into trend, seasonal and remainder components (classical and STL decomposition) that can each be forecast.
Weights recent observations more heavily. Holt adds a trend, Holt-Winters adds seasonality, and ETS frames the family as state-space models with prediction intervals.
Models a series from its own past values (autoregression) and past errors (moving average) after differencing to remove trend. SARIMA adds seasonal terms.
Uses Fourier terms to represent long or multiple seasonal cycles, with ARIMA errors on top. TBATS is a related automatic approach for complex seasonality.
Forecasts several related series together, with each one explained by the past of all the others.
An additive model of trend, seasonality and holiday effects fitted with a Bayesian-style procedure, designed for business series with strong calendar effects.
Turns forecasting into tabular regression using lagged values, rolling statistics, calendar features and external drivers as inputs.
A feed-forward network that predicts the next value from lagged inputs, optionally with seasonal lags.
Recurrent networks that keep a hidden state across time steps and learn long-range dependencies from sequences.
An autoregressive recurrent network trained across many related series that outputs a probability distribution for each step.
A deep stack of fully connected blocks that forecast and subtract their contribution, with optional trend and seasonality blocks for interpretability.
An attention-based model that combines static, known-future and observed inputs and reports which variables and time steps mattered.
Efficient attention models for long input and output windows. PatchTST splits each series into patches and treats them as tokens.
A pretrained model family that tokenises values and forecasts with a language-model architecture, giving zero-shot predictions on new series.
A decoder-only foundation model pretrained on a large corpus of time series for zero-shot forecasting.
A universal forecasting transformer trained on a large archive of time series and designed to handle any frequency and number of variables.
An open decoder-only foundation model for probabilistic univariate forecasting that uses lagged values as covariates.
A starting point, not a rule. Always compare against a baseline.
| Short, regular series with trend and seasonality | Exponential smoothing (ETS) or ARIMA |
|---|---|
| Daily business data with holidays and promotions | Prophet, or gradient boosting with calendar features |
| Many related series (retail, telecom) | Gradient boosting, DeepAR or N-BEATS |
| Multiple seasonal cycles (hourly demand) | Dynamic harmonic regression or TBATS |
| Rich covariates and long horizons | Temporal Fusion Transformer or PatchTST |
| No history or a new series | Foundation models such as Chronos or TimesFM |
| Any project, at the start | A seasonal naive baseline, then compare |
Evaluate on data the model has not seen, ordered in time.
| MAE | Mean absolute error. Easy to read, in the same units as the data. |
|---|---|
| RMSE | Root mean squared error. Penalises large misses more heavily. |
| MAPE / sMAPE | Percentage errors. Intuitive, but unstable when actual values are near zero. |
| MASE | Scales error against a naive forecast so results compare across series. |
| Pinball / CRPS | Score probabilistic forecasts and prediction intervals, not just point values. |
Use rolling-origin cross-validation so each test set lies after its training data. See accuracy measures and time series cross-validation in Forecasting: Principles and Practice, and forecast combinations for averaging models.
Open-source toolkits that implement most of the algorithms above.
Models, libraries, databases and visualisation tools for time-series work.
Quick answers.
There is no single best algorithm. Exponential smoothing and ARIMA are strong on short, regular series, gradient boosting is strong across many related series with covariates, and deep or foundation models can help at scale or with little history. Start with a seasonal naive baseline and compare.
Only when you have enough data and a reason, such as many related series, rich covariates or long horizons. On small datasets, classical models are often as accurate and far easier to maintain.
Hold out the most recent data, or use rolling-origin cross-validation so the model is always tested on the future. Report errors such as MAE or MASE, and use pinball loss or CRPS if you produce prediction intervals.
They are large models pretrained on many time series that can forecast a new series without training, called zero-shot forecasting. They are promising baselines, but you should validate them on your own data.
This page explains how each algorithm works, when to use it and how to judge it. The models page collects tutorials and resources for each model.
It depends on how predictable the series is. Forecast accuracy usually falls as the horizon grows, so always report error by horizon and show prediction intervals.
Core explanations follow Forecasting: Principles and Practice (3rd ed.) by Rob J. Hyndman and George Athanasopoulos, plus the original papers and documentation linked on each card. Statements about relative accuracy are general guidance; results vary by dataset.