Time series forecasting: classical statistics and deep learning

Updated October 21, 2026

Time series forecasting uses either classical statistical models that decompose trends and seasonality or deep learning models that learn patterns from data. Prophet automates forecasts with an additive model, while DeepAR, N-BEATS, and GraphCast address probabilistic, interpretable, and weather-specific tasks. A decoder-only foundation model offers zero-shot forecasting across many datasets.

Classical statistical models

Classical forecasting often relies on explicit decomposition of a series into trend, seasonality, and holiday effects. The Prophet procedure, developed by Meta's Core Data Science team, implements this as an additive model and is available in R and Python. It is designed to produce completely automated forecasts that can be tuned by hand with interpretable parameters, as described in the Prophet project documentation.

Prophet works best when the series has strong seasonal effects and several seasons of historical data. It handles missing data and dramatic changes in the trend better than many alternatives, and it typically manages outliers without requiring manual cleanup. The procedure fits models in Stan, so forecasts are produced in seconds even on messy data.

Deep learning architectures

DeepAR, introduced in the paper DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks, trains an autoregressive recurrent network on many related time series. This approach produces probabilistic forecasts, meaning it estimates the future probability distribution rather than a single value. The paper reports accuracy improvements of around 15% compared to widely used classical methods on several real-world datasets.

N-BEATS, described in the N-BEATS paper, is a deep neural architecture based on backward and forward residual links. It contains no time-series-specific components in its basic configuration, yet it outperformed a statistical benchmark by 11% and the prior M4 competition winner by 3% on test datasets. It is also interpretable and fast to train.

GraphCast, presented in the GraphCast paper, is a machine learning method that learns directly from reanalysis data. It predicts hundreds of weather variables globally over 10 days in under one minute, and it outperformed the most accurate operational deterministic systems on 90% of 1380 verification targets.

A more recent development is the time-series foundation model described in the decoder-only foundation model paper. This model is pretrained on a large corpus of time series using a patched-decoder attention architecture. Its zero-shot performance on public datasets comes close to the accuracy of dedicated supervised models trained for each dataset, working across different history lengths, prediction lengths, and temporal granularities.

Choosing a forecasting approach

The choice between classical statistical models and deep learning depends on the nature of the data and the requirements of the application. Classical methods like Prophet are well suited to datasets with clear seasonality and a need for interpretable forecasts that can be adjusted by analysts. They work without large volumes of training data and handle common data quality issues.

Deep learning models shine when many related series are available, as DeepAR demonstrates, or when the goal is to capture complex nonlinear patterns. N-BEATS offers interpretability through its residual design, while GraphCast specifically addresses weather forecasting with a global scope. Foundation models such as the decoder-only approach provide a zero-shot capability that can be applied to new domains without retraining.

Each method has trade-offs. Classical models are fast and transparent, while deep learning models often achieve higher accuracy at the cost of more computation and tuning. The table below summarizes key characteristics from the referenced papers.

Practical considerations

When evaluating a forecasting method, one should first examine the series for seasonal patterns and the amount of historical data available. If the series is small and seasonality is strong, a classical additive model is a reasonable starting point. If many related series exist or the pattern is highly nonlinear, a deep learning approach may be more effective.

Probabilistic forecasts, as produced by DeepAR, are valuable for inventory and risk decisions because they convey uncertainty. Interpretable architectures like N-BEATS help stakeholders understand which components of the model contribute to the prediction. For weather, GraphCast demonstrates that machine learning can outperform traditional numerical models in both accuracy and speed.

Finally, the rise of foundation models indicates that pretraining on diverse time series can yield a general-purpose forecaster. Such a model can be used directly on a new dataset without additional training, as shown by the decoder-only architecture. The choice ultimately depends on the data, the required output type, and the operational constraints.

Frequently asked questions

What is the difference between classical and deep learning forecasting?

Classical models like Prophet use explicit decomposition of trend and seasonality, while deep learning models learn patterns from data automatically. Deep learning often requires more data but can capture complex nonlinear relationships.

When should Prophet be used?

Prophet is most effective for series with strong seasonal effects and several seasons of historical data. It also handles missing data and outliers well, and its forecasts can be tuned by hand.

What does probabilistic forecasting mean?

Probabilistic forecasting estimates the probability distribution of future values instead of a single point estimate. DeepAR produces such forecasts, which are useful for decision making under uncertainty.

What is zero-shot forecasting?

Zero-shot forecasting means a model can make predictions on a new dataset without additional training. The decoder-only foundation model demonstrates this by achieving accuracy close to supervised models on public datasets.