Global Forecasting Walkthrough
API Usage
All individual forecasters (e.g. lasso
/ xgboost
) have the same API. Use **kwargs
to pass custom hyperparameters into the underlying regressor (e.g. sklearn's LinearRegression
regressor in functime's linear_model
forecaster). Forecasters with automated hyperparameter tuning (e.g. auto_lasso
and auto_xgboost
) follow a similar API design. View API reference for details and supported global forecasters.
functime
also has the following benchmark models implemented as pure Polars queries.
Benchmark Forecasters
naive
: random walk forecastersnaive
: seasonal naive forecaster
Quickstart
Want to go straight into code? Run through every forecasting example with the following script:
quickstart.py
import json
from timeit import default_timer
import polars as pl
from functime.cross_validation import train_test_split
from functime.forecasting import auto_linear_model, linear_model, naive, snaive
from functime.metrics import smape
from functime.preprocessing import scale
from functime.seasonality import add_fourier_terms
start_time = default_timer()
# Load data
y = pl.read_parquet(
"https://github.com/functimeorg/functime/raw/main/data/commodities.parquet"
)
entity_col, time_col = y.columns[:2]
X = y.select([entity_col, time_col]).pipe(add_fourier_terms(sp=12, K=6)).collect()
print("🎯 Target variable (y):\n", y)
print("📉 Exogenous variables (X):\n", X)
# Traintest splits
test_size = 3
freq = "1mo"
y_train, y_test = train_test_split(test_size)(y)
X_train, X_test = train_test_split(test_size)(X)
# Paralleized naive forecasts!
y_pred_naive = naive(freq="1mo")(y=y_train, fh=3)
y_pred_snaive = snaive(freq="1mo", sp=12)(y=y_train, fh=3)
# Univariate timeseries fit with automated lags and hyperparameter tuning
auto_forecaster = auto_linear_model(
freq=freq, test_size=test_size, min_lags=12, max_lags=18, n_splits=3, time_budget=3
)
auto_forecaster.fit(y=y_train)
# Predict
y_pred = auto_forecaster.predict(fh=test_size)
# Score
scores = smape(y_true=y_test, y_pred=y_pred)
print("✅ Predictions (univariate):\n", y_pred.sort(entity_col))
print("💯 Scores (univariate):\n", scores.sort("smape"))
print("💯 Scores summary (univariate):\n", scores.select("smape").describe())
# Retrieve best lags and hyperparameters
best_params = auto_forecaster.best_params
print(f"✨ Best parameters (y only):\n{json.dumps(best_params, indent=4)}")
# Multivariate
forecaster = linear_model(**best_params)
forecaster.fit(y=y_train, X=X_train)
# Predict
y_pred = forecaster.predict(fh=test_size, X=X_test)
# Score
scores_with_exog = smape(y_true=y_test, y_pred=y_pred)
print("✅ Predictions (multivariate):\n", y_pred.sort(entity_col))
print("💯 Scores (multivariate):\n", scores_with_exog.sort("smape"))
print(
"💯 Scores summary (multivariate):\n", scores_with_exog.select("smape").describe()
)
# Check uplift from Fourier features
uplift = (
scores_with_exog.join(scores, on=entity_col, suffix="_univar")
.with_columns(
uplift=pl.col("smape_univar")  pl.col("smape"),
has_uplift=pl.col("smape_univar")  pl.col("smape") > 0,
)
.select([entity_col, "uplift", "has_uplift"])
)
# NOTE: Fourier features lead to uplift for ~20% of commodities
# However, at the expense of an overall mean and variance SMAPE
# (likely due to overfitting on seasonal features)
print("💯 Uplift:\n", uplift.sort("uplift", descending=True))
print("💯 Proportion with uplift:", uplift.get_column("has_uplift").mean())
# "Direct" strategy forecasting
best_params["max_horizons"] = test_size # Override max_horizons
best_params["strategy"] = "direct" # Override strategy
# Predict using the "functional" API
y_pred = linear_model(**best_params)(y=y_train, fh=test_size)
# "Ensemble" strategy forecasting
best_params["strategy"] = "ensemble" # Override strategy
# Backtesting
y_preds = linear_model(**best_params).backtest(y=y_train, X=X_train)
print("✅ Backtests:", y_preds)
# Forecast with target transforms and feature transforms
forecaster = linear_model(
freq="1mo",
lags=24,
target_transform=scale(),
feature_transform=add_fourier_terms(sp=12, K=6),
)
y_pred = forecaster(y=y_train, fh=test_size)
elapsed_time = default_timer()  start_time
print(f"⏱️ Elapsed time: {elapsed_time}")
Prepare Data
Load a collection of time series, also known as panel data, into a polars.LazyFrame
(recommended) or polars.DataFrame
and split them into train/test subsets.
import polars as pl
from functime.cross_validation import train_test_split
from functime.metrics import mase
from functime.seasonality import add_calendar_effects
# Load data
y = pl.read_parquet("https://github.com/functimeorg/functime/raw/main/data/commodities.parquet")
entity_col, time_col = y.columns[:2]
X = (
y.select([entity_col, time_col])
.pipe(add_calendar_effects(["month"]))
.collect()
)
# Traintest splits
test_size = 3
freq = "1mo"
y_train, y_test = train_test_split(test_size)(y)
X_train, X_test = train_test_split(test_size)(X)
Supported Data Schemas
X: polars.LazyFrame  polars.DataFrame
and y: polars.LazyFrame  polars.DataFrame
must contain at least three columns.
The first column must represent the entity
/ series_id
dimension.
The second column must represent the time
dimension as an integer, pl.Date
, or pl.Datetime
series.
Remaining columns are considered as features.
Fit / Predict / Score
functime
forecasters expose sklearncompatible .fit
and .predict
methods.
functime.metrics
contains a comprehensive range of scoring functions for both point and probabilistic forecasts.
Supported Forecast Metrics
from functime.forecasting import linear_model
from functime.metrics import mase
# Fit
forecaster = linear_model(lags=24, freq="1mo")
forecaster.fit(y=y_train)
# Predict
y_pred = forecaster.predict(fh=3)
# Score
scores = mase(y_true=y_test, y_pred=y_pred, y_train=y_train)
functime ❤️ currying
Every transformer
and splitter
are curried functions.
from functime.preprocessing import boxcox, impute
# Use df.pipe to chain operations together
X_splits: pl.LazyFrame = (
X.pipe(boxcox(method="mle"))
.pipe(impute(method="linear"))
)
# Call .collect to execute query
X_new = X_splits.collect()
You can also use any forecaster
as a curried function to run fitpredict in a single line of code.
functime is lazy
transformers
and splitters
in cross_validation
, feature_extraction
, and preprocessing
are lazy.
These callables return LazyFrames
, which represents a Lazy computation graph/query against the input DataFrame
/ LazyFrame
.
No computation is run until the collect()
method is called on the LazyFrame
.
X
and y
should be preprocessed lazily for optimal performance.
Lazy evaluation allows polars
to optimize all operations on the input DataFrame
/ LazyFrame
at once.
Lazy preprocessing in functime
allows for more efficient group_by
operations.
With lazy transforms, operations seriesbyseries (e.g. boxcox
, impute
, diff
) are chained in parallel: group_by
is only called once.
By contrast, with eager transforms, operations seriesbyseries is called in sequence: group_byaggregate
is called per transform.
Global Forecasting
Every forecaster
exposes a scikitlearn fit
and predict
API.
The fit
method takes y
and X
(optional).
The predict
method takes the forecast horizon fh: int
, frequency alias freq: str
, and X
(optional).
Supported Frequency Aliases
 1s (1 second)
 1m (1 minute)
 30m (30 minute)
 1h (1 hour)
 1d (1 day)
 1w (1 week)
 1mo (1 calendar month)
 3mo (1 calendar quarter)
 1y (1 calendar year)
 1i (1 index count)
from functime.forecasting import linear_model
from functime.metrics import mase
# Fit
forecaster = linear_model(lags=24, freq="1mo")
forecaster.fit(y=y_train)
# Predict
y_pred = forecaster.predict(fh=3)
# Score
scores = mase(y_true=y_test, y_pred=y_pred, y_train=y_train)
Global vs Local Forecasting
functime
only supports global forecasters.
Global forecasters fit and predict a collection of time series using a single model.
Local forecasters (e.g. ARIMA, ETS, Theta) fit and predict one series per model.
Example collections of time series, which are also known as panel data, include:
 Sales across product in a retail store
 Churn rates across customer segments
 Sensor data across devices in a factory
 Delivery times across trucks in a logistics fleet
Global forecasters, trained on a collection of similar time series, consistently outperform local forecasters.^{1} Most notably, all top 50 competitors in the M5 Forecasting Competition used a global LightGBM forecasting model.^{2}
Save 100x in Cloud spend
Local forecasting is expensive and slow. To productionize forecasts at scale (>1,000 series), local models have no choice but distributed computing. Every fitpredict call per local model per series are executed in parallel across the distributed cluster. Running a distributed cluster, however, is a significant cost and time sink for any data team.
functime
believes that the vast majority of businesses do not need distributed computing to produce highquality forecasts.
Every forecaster
, transformer
, splitter
, and metric
in functime
operates globally across collections of time series.
We rewrote every time series operation in polars
for blazing fast multithreaded parallelism.
If you are working at a reasonablescale company, you most likely don't need Databricks to scale your forecasts. Use functime
.
Benchmark Forecasters
Naive and seasonal naive forecasters are surprisingly hard to beat!
You should always consider using the naive and seasonal naive forecasts as benchmarks.
functime
implements embarressingly parallel versions of the naive (random walk) and seasonal naive forecasters.
These forecasters are expressed as pure Polars queries and executed in lazy streaming mode for speed and memory efficiency.
from functime.forecasting import naive, snaive
y_pred_naive = naive(freq="1mo")(y=y_train, fh=12)
# sp = seasonal periods (length of one seasonal cycle)
y_pred_snaive = snaive(freq="1mo", sp=12)(y=y_train, fh=12)
Exogenous Regressors
Every forecaster in functime
supports exogenous regressors.
from functime.forecasting import linear_model
forecaster = linear_model(lags=24, fit_intercept=False, freq="1mo")
forecaster.fit(y=y_train, X=X_train)
y_pred = forecaster.predict(fh=3, X=X_test)
Naive Forecasting
It is best practice to run naive forecasts (random walk, seasonal naive) as benchmarks. These simple forecasting methods can be remarkably difficult to beat!^{3}
Transformations / Preprocessing
Every forecaster has two optional parameters target_transform
and feature_transform
, which can take a single functime
transformer (e.g. diff(order=1, fill_strategy="backward")
, detrend(method="linear")
) or a list of transformers!
target_transform
applies a transformation ony
before fit and predict. An inverse transformation is then applied after predict to return the final forecast.feature_transform
applies a transformation onX
before fit and predict.
We recommend using target_transform
and feature_transform
to avoid common pitfalls such as inconsistent feature engineering and data leakage.
Check out the API reference for preprocessing and feature_extraction for a list of supported transformations.
Target Transform
from functime.forecasting import linear_model
from functime.preprocessing import diff, scale, boxcox
# Apply first differences
forecaster = linear_model(freq="1mo", lags=12, target_transform=diff(order=1, fill_strategy="backward"))
# Or local standardization
forecaster = linear_model(freq="1mo", lags=12, target_transform=scale())
# Or Boxcox
forecaster = linear_model(freq="1mo", lags=12, target_transform=boxcox())
# Or chain first differences then boxcox!
forecaster = linear_model(
freq="1mo",
lags=12,
target_transform=[
diff(order=1, fill_strategy="backward"),
boxcox()
]
)
Feature Transform
from functime.forecasting import linear_model
from functime.seasonality import add_fourier_terms
from functime.preprocessing import roll
# Include Fourier terms to model complex seasonality
forecaster = linear_model(
freq="1mo",
lags=12,
feature_transform=add_fourier_terms(sp=12, K=3)
)
# Create moving average features on exogenous regressors!
forecaster = linear_model(
freq="1mo",
lags=12,
feature_transform=roll(window_sizes=[6, 12], stats=["mean", "std"], freq="1mo")
)
# Or include both Fourier terms and lags!
forecaster = linear_model(
freq="1mo",
lags=12,
feature_transform=[
add_fourier_terms(sp=12, K=3),
roll(window_sizes=[6, 12], stats=["mean", "std"], freq="1mo")
]
)
Target and Feature Transform
from functime.forecasting import linear_model
forecaster = linear_model(
freq="1mo",
lags=12,
target_transform=scale(),
feature_transform=add_fourier_terms(sp=12, K=3)
)
Forecast Strategies
functime
supports three forecast strategies: recursive
, direct
multistep, and a simple ensemble of both recursive
and direct
.
from functime.forecasting import linear_model
# Recursive (Default)
recursive_forecaster = linear_model(strategy="recursive")
y_pred_rec = recursive_model(y_train, fh)
# Direct
max_horizons = 12 # Number of direct models
direct_forecaster = = linear_model(strategy="direct",max_horizons=max_horizons, freq="1mo")
y_pred_dir = recursive_model(y_train, fh)
# Ensemble
ensemble_forecaster = linear_model(strategy="ensemble", max_horizons=max_horizons, freq="1mo")
y_pred_ens = ensemble_model(y=y_train, fh=3)
max_horizons
is the number of models specific to each forecast horizon.
For example, if max_horizons = 12
, then twelve forecasters are fitted in total: the 1step ahead forecast, the 2steps ahead forecast, the 3steps ahead forecast, ..., and the final 12steps ahead forecast.
Censored Forecasts
Most realworld datasets in ecommerce and logistics contain zeros in the target variable: e.g. periods with no sales. To address this problem, functime
implements the censored_model
forecaster, which trains a binary classifier and two forecasters. The binary classifier predicts the probability that a forecast falls above or below a certain threshold (e.g. zero). The final forecast is a weighted average of the above and below threshold forecasters.
from functime.forecasting import censored_model
# Load the M5 competition Walmart dataset
y_train = pl.read_parquet("data/m5_y_train_sample.parquet")
X_train = pl.read_parquet("data/m5_X_train_sample.parquet")
# Fitpredict given threshold = 0.0
y_pred = censored_model(lags=3, threshold=0.0, freq="1d")(
y=y_train, X=X_train, fh=fh, X_future=X_test
)
Custom Classfier and Regressors
By default, censored_model
uses sklearn's HistGradientBoostingClassifier
and HistGradientBoostingRegressor
.
To use your own classifier and regressor, implement a function that takes X
and y
numpy arrays and returns a fitted sklearncompatible classifier and regressor.
from sklearn.neural_network import MLPRegressor
from sklearn.ensemble import RandomForestClassifier
def regress(X: np.ndarray, y: np.ndarray):
regressor = MLPRegressor()
regressor.fit(X=X, y=y)
return regressor
def classify(X: np.ndarray, y: np.ndarray):
classifier = RandomForestClassifier()
classifier.fit(X=X, y=y))
return classifier
# Censored model with custom classifier and regressor
forecaster = censored_model(
lags=3,
threshold=0.0,
freq="1d",
classify=classify,
regress=regress
)
y_pred = forecaster(y=y_train, X=X_train, fh=fh, X_future=X_test)
Automated Parameter Tuning
Forecasters in auto_forecasting automatically tune the number of lagged regressors and the model's hyperparameters (e.g. alpha
for Lasso
). Crossvalidation, lags tuning, and model parameters tuning are performed simultaneously for maximum efficiency.
Optimal Lag Length
auto_{model}
forecasters automatically select the optimal number of lags via crossvalidation.
These forecasters conduct a search over possible models within min_lags
and max_lags
.
The best model is the model with the lowest average RMSE (root mean squared error) across splits.
from functime.forecasting import auto_linear_model
# Fit then predict
forecaster = auto_linear_model(min_lags=20, max_lags=24, freq="1mo")
forecaster.fit(y=y_train, X=X_train)
y_pred = forecaster.predict(fh=3, X=X_test)
# Fit and predict
y_pred = auto_linear_model(min_lags=20, max_lags=24, freq="1mo")(
y=y_train,
X=X_train,
X_future=X_test,
fh=3
)
Hyperparameter Tuning
auto_{model}
forecasters automatically select the optimal number of lags via crossvalidation.
These forecasters conduct a search over possible models within min_lags
and max_lags
.
The best model is the model with the lowest average RMSE (root mean squared error) across splits.
Sane Hyperparameter Defaults
Sane defaults are used if search_space
or points_to_evaluate
are left as None
.
functime
specify default hyperparameters search spaces according to bestpractices from industry, top Kaggle solutions, and research.
functime
uses FLAML
under the hood to conduct hyperparameter tuning.
from flaml import tune
from functime.forecasting import auto_lightgbm
# Specify search space, initial conditions, and time budget
search_space = {
"reg_alpha": tune.loguniform(1e08, 10.0),
"reg_lambda": tune.loguniform(1e08, 10.0),
"num_leaves": tune.randint(
2, 2**max_depth if max_depth > 0 else 2**DEFAULT_TREE_DEPTH
),
"colsample_bytree": tune.uniform(0.4, 1.0),
"subsample": tune.uniform(0.4, 1.0),
"subsample_freq": tune.randint(1, 7),
"min_child_samples": tune.qlograndint(5, 100, 5),
}
points_to_evaluate = [
{
"num_leaves": 31,
"colsample_bytree": 1.0,
"subsample": 1.0,
"min_child_samples": 20,
}
]
time_budget = 420
# Fit model
forecaster = auto_lightgbm(
freq="1mo',
min_lags=20,
max_lags=24,
time_budget=time_budget,
search_space=search_space,
points_to_evaluate=points_to_evaluate
)
forecaster.fit(y=y_train)
# Get best lags and model hyperparameters
best_params = forecaster.best_params
Backtesting
Every forecaster
and auto_forecaster
has a backtest
method.
functime
supports both expanding_window_split
and sliding_window_split
for backtesting and crossvalidation.
from functime.forecasting import linear_model
forecaster = linear_model(lags=24, fit_intercept=False, freq="1mo")
y_preds, y_resids = forecaster.backtest(
y=y_train,
X=X_train,
test_size=6,
step_size=1,
n_splits=3,
window_size=1, # Only applicable if `strategy` equals "sliding"
strategy="expanding",
# Raises ValueError if drop_short=False and there are
# entities with insufficient length for crossvalidation
drop_short=True
)
Probabilistic Forecasts
functime
supports two methods for generating prediction intervals.
Quantile Regression
Supported by LightGBM
, XGBoost
, and Catboost
forecasters and their automated equivalents.
from functime.forecasting import auto_lightgbm
# Forecasts at 10th and 90th percentile
y_pred_10 = auto_lightgbm(alpha=0.1, freq="1d")(y=y_train, fh=28)
y_pred_90 = auto_lightgbm(alpha=0.9, freq="1d")(y=y_train, fh=28)
Conformal Prediction
functime
currently supports batch prediction intervals (EnbPI) from the paper Conformal prediction interval for dynamic timeseries
from functime.conformal import conformalize
from functime.forecasting import linear_model
forecaster = linear_model(lags=24, fit_intercept=False, freq="1mo")
y_preds, y_resids = forecaster.backtest(y=y_train, X=X_train)
# Forecasts at 10th and 90th percentile
# Requires forecast (y_pred), backtest values (y_preds),
# and residuals from backtest (y_resid)
y_pred_quantiles = conformalize(
y_pred=y_pred,
y_preds=y_preds,
y_resids=y_resids,
alphas=[0.1, 0.9]
)

MonteroManso, P., & Hyndman, R. J. (2021). Principles and algorithms for forecasting groups of time series: Locality and globality. International Journal of Forecasting, 37(4), 16321653. ↩

Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2022). M5 accuracy competition: Results, findings, and conclusions. International Journal of Forecasting. ↩

https://otexts.com/fpp3/simplemethods.html ↩