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How to choose among classical forecasting methods
Use the structure of the series and the forecast horizon to narrow the candidates, then let time-ordered validation decide. A method that fits the historical data closely can still forecast poorly, especially when a trend changes or seasonal patterns shift.
- Level: Is the series roughly stable around a changing or fixed average?
- Trend: Does it rise or fall, and is that movement likely to persist over the horizon?
- Seasonality: Does a pattern recur at a known interval, such as yearly for monthly data?
- Intermittency: Are there many zero or no-demand periods between nonzero observations?
- Inputs and operations: Are future predictor values actually available? How much interpretability, fitting effort, and maintenance can the forecast support?
Compare candidates using out-of-sample errors and, when uncertainty matters, interval quality. A temporal holdout or rolling-origin evaluation preserves the order of observations; randomly shuffling a time series can leak future information into training. The sktime forecasting tutorial demonstrates temporal splitting and forecasting horizons. The documentation does not establish a universal winner across datasets.
The 11 methods at a glance
| Method | Best starting point | Main caution |
|---|---|---|
| Naive (last value) | Stable level; essential baseline | Does not model trend or seasonality |
| Seasonal naive | Recurring seasonal pattern | Requires a defensible seasonal period |
| Drift / linear trend | Trend extrapolation baseline | Assumes the estimated trend remains informative |
| Moving average | Local level smoothing | A smoothing rule alone is not a complete forecasting model |
| Simple exponential smoothing (SES) | Changing level without trend or seasonality | Does not represent trend or seasonal structure |
| Holt linear trend | Level plus continuing trend | Trend may become implausible farther out |
| Damped-trend Holt | Trend that should taper with horizon | Still depends on a fitted trend being useful |
| Holt-Winters / seasonal exponential smoothing | Level, trend, and recurring seasonality | Choose additive or multiplicative seasonality carefully |
| Theta | Trend and smoothed level in a compact method | Validate against simpler alternatives |
| ARIMA / seasonal ARIMA | Serial dependence, differencing, and optional seasonality | Automatic order selection is not an accuracy guarantee |
| STL-based forecasting | Seasonal series with a forecastable remainder | Decomposition does not make future seasonal patterns certain |
Simple baselines and trend methods
1. Naive (last-value) forecast
The naive forecast repeats the most recent observed value at every step of the forecast horizon. It is a useful reference: a more elaborate model should demonstrate that it improves on this baseline in time-ordered validation. In sktime, the documented configuration is NaiveForecaster(strategy="last") (sktime tutorial).
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2. Seasonal naive
Seasonal naive repeats the value from the same position in the latest observed cycle. For monthly data with hypothesized annual seasonality, the sktime example uses seasonal period sp=12. That is an example, not a universal setting: choose the period from the data’s calendar and domain, and provide enough history to represent the cycle (sktime tutorial).
3. Drift / linear trend extrapolation
Drift extends an average historical change into the future; a fitted linear trend similarly projects a straight-line pattern. These are simple ways to test whether a trend adds value beyond the naive forecast. Their long-range forecasts rely on the estimated trend remaining informative, so they can mislead when growth saturates, reverses, or is interrupted. sktime lists trend-based forecasters in its forecasting API.
4. Moving average
A moving average smooths a chosen window of recent observations, often to estimate a local level or reduce short-term noise. The window length is a modeling choice: a short window reacts quickly but is noisy, while a longer one smooths more but can lag when the level changes. A smoothing filter is not automatically a forecast procedure; to forecast, specify how its estimated level is extended forward and validate that rule. The cited current library pages do not highlight a dedicated moving-average forecaster among the classes described here.
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Exponential smoothing, ETS, and Theta
5. Simple exponential smoothing (SES)
SES updates a level by weighting the latest observation against the previous level, with more recent values receiving greater influence. It suits a series whose level changes but has no material trend or seasonality. In ETS terminology, the simplest form has additive error, no trend, and no seasonality; the statsmodels ETS documentation explains this component framework.
6. Holt linear trend
Holt’s method extends level smoothing with a trend component. Consider it when a changing level and roughly continuing trend are plausible. The sktime API documents exponential smoothing with a configurable trend option (sktime forecasting API).
7. Damped-trend Holt
A damped trend reduces the trend contribution as the forecast horizon grows, rather than extending it indefinitely at full strength. This can be a more cautious candidate when the recent direction may persist for a while but should not compound unchanged forever. sktime documents a damped trend option in its exponential-smoothing configuration (sktime forecasting API).
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8. Holt-Winters / seasonal exponential smoothing
Seasonal exponential smoothing adds a repeating seasonal component, commonly alongside level and trend. Use additive seasonality when seasonal swings are roughly constant in size; use multiplicative seasonality when their size tends to scale with the series level and the data support that form. ETS names the error, trend, and seasonal components; not every combination is stable or suitable. The statsmodels ETS notebook describes the model family and cautions that some combinations can be unstable.
9. Theta method
The Theta method combines a linear time trend with simple exponential smoothing, providing a compact way to represent both trend and smoothed level. Statsmodels describes the method in its time-series documentation, which names the method’s original 2000 reference. Treat it as a candidate to validate, not as a default winner.
Autoregressive and decomposition methods
10. ARIMA and seasonal ARIMA
ARIMA models serial dependence and uses differencing when needed to address changing levels or trends. Seasonal ARIMA adds seasonal structure when a recurring cycle is appropriate. The sktime tutorial demonstrates ARIMA with a seasonal order and AutoARIMA; the API also lists SARIMAX capability (sktime tutorial; sktime API). Automatic order selection can save manual search, but it does not guarantee the best future accuracy. Check residual behavior and compare forecasts on later observations.
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11. STL-based forecasting
STL separates a series into seasonal and remainder components. In the statsmodels STL forecasting approach, a model forecasts the seasonally adjusted remainder, then the seasonal component is projected from its final cycle and recombined with the remainder forecast. This is useful when seasonality is prominent but the remainder can be modeled more simply. See statsmodels time-series documentation for STLForecast. If demand is intermittent—many zero periods between nonzero values—Croston is a different specialized candidate rather than a synonym for STL; sktime lists it for intermittent time series (sktime API).
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.A practical Python workflow
The following pattern uses sktime’s forecasting interface. Install the package in your environment and check the API for the version you use; library signatures can change. Keep the final observations as a temporal test set, fit only on earlier observations, and specify a horizon that matches the real decision task.
- Set up the series and horizon. Use a correctly indexed pandas Series with a frequency appropriate to the data. Choose a forecast horizon in the same time units as the index.
- Make a temporal split. Reserve the latest observations for testing. Do not shuffle the dates.
- Fit a baseline first. Compare the naive and, where justified, seasonal-naive forecasts before increasing complexity.
- Fit relevant candidates. Add ETS, ARIMA, trend, or decomposition methods only when their assumptions fit the series and forecast horizon.
- Score forecasts on the held-out period. Use metrics that match the cost of errors and inspect performance across more than one origin when data allow.
The sktime tutorial demonstrates temporal train/test splitting, a forecasting horizon, naive and seasonal-naive models, ExponentialSmoothing, AutoETS, ARIMA, and AutoARIMA (tutorial and runnable examples). Use the current API reference for exact class configuration (sktime API).
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When forecasts need external predictors
Some forecasting methods accept exogenous series as X. For many such forecasters, prediction-time X must cover the entire forecast horizon. A future value that is not known when the forecast is issued cannot be supplied as though it were certain; use a genuinely known calendar variable or separately forecast the predictor, and account for that uncertainty. The sktime tutorial describes this input pattern (sktime tutorial).
How to interpret forecast intervals
Statsmodels documents forecast results that include forecast variance and, for many methods, prediction intervals (statsmodels time-series documentation). Treat these as uncertainty estimates conditional on model assumptions and inputs, not guarantees that actual values will stay inside the interval. Poorly specified models or unexpected structural changes can make intervals misleading.
Further reading
For a fuller treatment of ETS, statsmodels points to Hyndman and Athanasopoulos, Forecasting: Principles and Practice, third edition (2019). The reference is listed in the statsmodels ETS notebook.
Quick Recap
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