Forecasting with foundation models¶

Foundation models (FMs) have triggered a fundamental paradigm shift in time series forecasting, moving the field away from modelling for each dataset and towards generalised representation learning. Driven by the same architectural breakthroughs that power Large Language Models (LLMs), FMs bring zero-shot and in-context learning capabilities to temporal data.

In the context of forecasting, a foundation model is a massively scaled neural network (typically Transformer-based) that has been pre-trained on highly diverse, cross-domain datasets spanning finance, weather, web traffic, retail and more.

Models such as Amazon Chronos, Google TimesFM 2.5, Salesforce Moirai-2, Soda-INRIA TabICL, Prior Labs' TabPFN-TS, and The Forecasting Company T0 treat forecasting as a foundation-model problem. Many frame it as sequence modelling, processing temporal data either as quantized discrete tokens (as in Chronos, which applies scalar quantization) or as continuous patch embeddings (as in TimesFM and Moirai, which group consecutive time steps into fixed-length patches before encoding them); others (TabICL, TabPFN-TS) recast it as tabular in-context learning. Having internalised the structural priors of millions of series during pre-training, they can infer trends, seasonality, and complex dynamics in unseen data without any task-specific weight updates.

Foundation Models vs. Machine Learning Models¶

Foundation models and traditional machine learning models approach forecasting in fundamentally different ways. Understanding these distinctions is crucial for knowing when and how to deploy each method.

Zero-Shot Prediction

Machine learning models require a training phase. You must fit the model on your historical target data so the algorithm can learn the optimal weights and parameters for your specific time series. Foundation models, however, are capable of zero-shot inference. Because their highly generalized weights are already frozen from the massive pre-training phase, they can generate accurate forecasts on your data immediately, leveraging their pre-existing latent representations rather than learning your dataset from scratch.

The Role of the fit Method

Machine learning models must be trained: calling .fit() optimizes the model's internal parameters by minimizing a loss function on your historical data. Foundation models, by contrast, arrive pre-trained: their weights are fixed and are never updated. Calling .fit() on a foundation model is not a training step; it simply stores the historical context (observations, frequency, and any scaling factors) needed at inference time. In some implementations, calling .fit() is entirely optional before prediction.

Context Window vs. Engineered Lags

Machine learning models rely on explicitly engineered features; they require creating a tabular dataset where past values are used as columns to predict the target. Foundation models rely on a context window. You pass a raw, sequential chunk of recent historical data (e.g., the last 512 observations) directly into the model at inference time. The attention mechanism inside the model automatically decides which past data points are most relevant.

In summary, foundation models represent a fundamental paradigm shift, replacing the traditional train → predict pipeline with a pre-train → (context + predict) approach. As major research institutions with access to millions of diverse time series carry out the computationally intensive pre-training phase, end users are completely freed from model training.

However, there is no such thing as a free lunch in machine learning. Skipping the training phase results in a heavier burden during the inference phase. Because their weights are frozen, these models cannot adapt to your data through training. Instead, they adapt implicitly at inference time by processing the historical context through their attention mechanism. Each prediction therefore requires ingesting and attending over a large sequence of raw observations in real time. Consequently, the main drawback of zero-shot forecasting is that the inference process is significantly slower, more computationally expensive and requires your data pipeline to continuously provide large amounts of historical context at runtime.

-	ML Model	Foundation Model
fit	Trains model, updates weights	Stores context & metadata
predict	Uses learned weights	Processes context via attention
Data required at train time	Full history	Not required
Data required at predict time	Last lags observations	Full context window
Computational cost	At train time	At inference time

Impact of the context length¶

Because foundation forecasting models are highly generalized, they lack intrinsic knowledge of your specific dataset. To compensate, they rely on a context window, a specific period of recent historical data, to adapt to your unique scenario at inference time. This context acts as the model's short-term memory, allowing it to calculate the current trajectory of your data and identify whether the series is trending upward, accelerating, or flattening out.

The length of this context window is critical for capturing seasonality and recurring events. To accurately predict a pattern, such as a weekly sales spike or a yearly cycle, the model must actually observe that pattern within the provided history. For instance, if your data has a 365-day seasonality, providing 400 days of context allows the model to recognize and project the cycle, whereas a 30-day window would cause the model to miss the pattern entirely, resulting in a flat or inaccurate forecast.

However, increasing the context length to improve accuracy introduces a significant computational trade-off. Because most foundation models are built on Transformer architectures, the computational complexity of their attention mechanism often scales quadratically ($O(N^2)$) with the length of the input sequence. Consequently, doubling the context window can quadruple the required memory and processing power. This quadratic growth means that pushing context lengths to their theoretical maximum often yields diminishing accuracy gains at rapidly increasing computational cost.

Ultimately, effectively utilizing foundation models requires carefully evaluating this trade-off. The best practice is to analyze the context size and select the shortest possible window that still achieves high predictive performance. Striking this balance ensures accurate, pattern-aware forecasts while preventing the unnecessary waste of computational resources.

Comparative charts of prediction error and elapsed time based on context length.

✏️ Note

For more details about foundation models, visit Forecasting: Principles and Practice, the Pythonic Way.

Foundation Models in skforecast¶

Skforecast's integration is built on two layers. First, FoundationModel acts as a unified wrapper that adapts each model's native API (Chronos-2, TimesFM 2.5, Moirai-2, TabICL, TabPFN-TS, TFC T0) behind a familiar scikit-learn interface (fit, predict, get_params). Second, ForecasterFoundation wraps that estimator to unlock the full skforecast ecosystem. It exposes the same interface as any other skforecast forecaster, meaning users can use backtesting, prediction intervals, and multi-series support with the exact same code.

skforecast ecosystem

ForecasterFoundation (forecasting)

FoundationModel (skforecast Wrapper)

.fit() (Store Context)

.predict() (Zero-Shot Run)

Internal Model Adapters

Chronos

TimesFM

Moirai

TabICL

TabPFN

TFC-T0

Supported Foundation Models¶

	Chronos	TimesFM	Moirai	TabICL	TabPFN-TS	T0
Provider	Amazon	Google	Salesforce	Soda-Inria	Prior Labs	The Forecasting Company
GitHub	chronos-forecasting	timesfm	uni2ts	tabicl	tabpfn-time-series	tfc-t0
Documentation	Chronos models	TimesFM models	Moirai-R models	TabICL Docs	Prior Labs Docs	t0-alpha model card
Available model IDs	amazon/chronos-2 autogluon/chronos-2-small autogluon/chronos-2-synth	google/timesfm-2.5-200m-pytorch	Salesforce/moirai-2.0-R-small	soda-inria/tabicl	priorlabs/tabpfn-ts	theforecastingcompany/t0-alpha
Backend	PyTorch	PyTorch	PyTorch	PyTorch	PyTorch	PyTorch
Forecasting type	Zero-shot	Zero-shot	Zero-shot	Zero-shot	Zero-shot	Zero-shot
Default context_length	8192	512	2048	4096	32768	8192
Max context_length	8192	16384	2048	4096	No hard limit (practical memory ceiling ~65536)	No hard limit, set via context_length
max_horizon	No hard limit, set via steps at predict time	512	No hard limit, set via steps at predict time	No hard limit, set via steps at predict time	No hard limit, set via steps at predict time	No hard limit, set via steps at predict time
Point forecast	Median (0.5 quantile)	Mean (dedicated output array)	Median (0.5 quantile)	Mean (default, configurable to median)	Median (default, configurable to mean/mode)	Median (0.5 quantile)
Covariate support (exog)	Yes	No	No	Yes	Yes	Yes
cross_learning parameter	Yes (multi-series mode only)	No	No	No	No	No
Install command	pip install chronos-forecasting	pip install git+https://github.com/google-research/timesfm.git	pip install uni2ts	pip install tabicl[forecast]	pip install tabpfn-time-series	pip install tfc-t0

💡 Tip

All models run on the CPU. However, a CUDA GPU is recommended for faster inference, especially with long context windows. The MPS backend is also detected automatically by PyTorch and can benefit Apple Silicon users.

It is important to note that context length significantly impacts inference speed. Larger contexts provide the models with more information, but they increase processing time. Although these models boast massive context capacities, shorter contexts often achieve similar results much faster for most use cases.

Input Data Formats¶

ForecasterFoundation accepts several data formats for both the target series and exogenous variables.

Target Series (series)

The series parameter in the .fit() method supports both single-series and multi-series (global model) configurations.

Mode	Allowed Data Type	Description
Single-Series	pd.Series	A single time series with a named index.
Multi-Series (Wide)	pd.DataFrame	Each column represents a separate time series.
Multi-Series (Long)	pd.DataFrame	MultiIndex (Level 0: series ID, Level 1: DatetimeIndex).
Multi-Series (Dict)	dict[str, pd.Series]	Keys are series identifiers, values are pandas Series.

💡 Tip

While Long-format DataFrames are supported, they are converted to dictionaries internally. For best performance, pass a dict[str, pd.Series] directly.

Exogenous Variables (exog)

Exogenous variables must be aligned with the target series index. Currently, Chronos, TabICL, TabPFN-TS, and TFC-T0 support covariates (see the Supported Foundation Models table). TimesFM and Moirai do not accept exogenous variables.

Mode	Allowed Data Type	Description
Single-Series	pd.Series or pd.DataFrame	Aligned to the target series index.
Multi-Series (Dict)	dict[str, pd.Series \| pd.DataFrame \| None]	One entry per series.
Multi-Series (Broadcast)	pd.Series or pd.DataFrame	Automatically applied to all series.
Multi-Series (Long)	pd.DataFrame	MultiIndex (Level 0: series ID, Level 1: DatetimeIndex).

Libraries and data¶

In [1]:

# Libraries
# ==============================================================================
import os
import pandas as pd
import torch
import time
import matplotlib.pyplot as plt
from skforecast.datasets import fetch_dataset
from skforecast.foundation import FoundationModel, ForecasterFoundation
from skforecast.model_selection import (
    TimeSeriesFold,
    backtesting_foundation
)
from skforecast.plot import set_dark_theme

color = '\033[1m\033[38;5;208m' 
print(f"{color}torch version: {torch.__version__}")
print(f"  Cuda available : {torch.cuda.is_available()}")
print(f"  MPS available  : {torch.backends.mps.is_available()}")

# Libraries # ============================================================================== import os import pandas as pd import torch import time import matplotlib.pyplot as plt from skforecast.datasets import fetch_dataset from skforecast.foundation import FoundationModel, ForecasterFoundation from skforecast.model_selection import ( TimeSeriesFold, backtesting_foundation ) from skforecast.plot import set_dark_theme color = '\033[1m\033[38;5;208m' print(f"{color}torch version: {torch.__version__}") print(f" Cuda available : {torch.cuda.is_available()}") print(f" MPS available : {torch.backends.mps.is_available()}")

torch version: 2.12.1+cpu
  Cuda available : False
  MPS available  : False

In [2]:

# Data download
# ==============================================================================
data = fetch_dataset(name='vic_electricity')

# Aggregating in 1H intervals
# ==============================================================================
# The Date column is eliminated so that it does not generate an error when aggregating.
data = data.drop(columns="Date")
data = (
    data
    .resample(rule="h", closed="left", label="right")
    .agg({
        "Demand": "mean",
        "Temperature": "mean",
        "Holiday": "mean",
    })
)
data.head(3)

# Data download # ============================================================================== data = fetch_dataset(name='vic_electricity') # Aggregating in 1H intervals # ============================================================================== # The Date column is eliminated so that it does not generate an error when aggregating. data = data.drop(columns="Date") data = ( data .resample(rule="h", closed="left", label="right") .agg({ "Demand": "mean", "Temperature": "mean", "Holiday": "mean", }) ) data.head(3)

╭──────────────────────────── vic_electricity ─────────────────────────────╮
│ Description:                                                             │
│ Half-hourly electricity demand for Victoria, Australia                   │
│                                                                          │
│ Source:                                                                  │
│ O'Hara-Wild M, Hyndman R, Wang E, Godahewa R (2022).tsibbledata: Diverse │
│ Datasets for 'tsibble'. https://tsibbledata.tidyverts.org/,              │
│ https://github.com/tidyverts/tsibbledata/.                               │
│ https://tsibbledata.tidyverts.org/reference/vic_elec.html                │
│                                                                          │
│ URL:                                                                     │
│ https://raw.githubusercontent.com/skforecast/skforecast-                 │
│ datasets/main/data/vic_electricity.csv                                   │
│                                                                          │
│ Shape: 52608 rows x 4 columns                                            │
╰──────────────────────────────────────────────────────────────────────────╯

Out[2]:

	Demand	Temperature	Holiday
Time
2011-12-31 14:00:00	4323.095350	21.225	1.0
2011-12-31 15:00:00	3963.264688	20.625	1.0
2011-12-31 16:00:00	3950.913495	20.325	1.0

In [3]:

# Split data into train-test
# ==============================================================================
data = data.loc['2012-01-01 00:00:00':'2014-12-30 23:00:00', :].copy()
end_train = '2014-11-30 23:59:00'
data_train = data.loc[: end_train, :].copy()
data_test  = data.loc[end_train:, :].copy()

print(f"Train dates: {data_train.index.min()} --- {data_train.index.max()}  (n={len(data_train)})")
print(f"Test dates : {data_test.index.min()} --- {data_test.index.max()}  (n={len(data_test)})")

# Split data into train-test # ============================================================================== data = data.loc['2012-01-01 00:00:00':'2014-12-30 23:00:00', :].copy() end_train = '2014-11-30 23:59:00' data_train = data.loc[: end_train, :].copy() data_test = data.loc[end_train:, :].copy() print(f"Train dates: {data_train.index.min()} --- {data_train.index.max()} (n={len(data_train)})") print(f"Test dates : {data_test.index.min()} --- {data_test.index.max()} (n={len(data_test)})")

Train dates: 2012-01-01 00:00:00 --- 2014-11-30 23:00:00  (n=25560)
Test dates : 2014-12-01 00:00:00 --- 2014-12-30 23:00:00  (n=720)

Chronos¶

A ForecasterFoundation is created using Amazon's Chronos-2-small model.

In [4]:

# Create ForecasterFoundation
# ==============================================================================
estimator = FoundationModel(model_id="autogluon/chronos-2-small", context_length=500)
forecaster = ForecasterFoundation(estimator=estimator)

# Create ForecasterFoundation # ============================================================================== estimator = FoundationModel(model_id="autogluon/chronos-2-small", context_length=500) forecaster = ForecasterFoundation(estimator=estimator)

Each adapter accepts additional keyword arguments that control model-specific behavior (e.g., context_length, device_map, torch_dtype). These can be passed directly through the FoundationModel constructor.

For the full list of available parameters, see the API reference: ChronosAdapter, TimesFMAdapter, MoiraiAdapter, TabICLAdapter.

💡 Tip

While .fit() is used here to store the historical context and metadata, it is not strictly required. Foundation models can generate forecasts by passing the context directly to .predict() via the context parameter. However, calling .fit() first simplifies subsequent calls to .predict(), .predict_interval(), and .predict_quantiles().

In [5]:

# Train ForecasterFoundation
# ==============================================================================
forecaster.fit(
    series = data_train["Demand"], 
    exog   = data_train[["Temperature", "Holiday"]]
)
forecaster

# Train ForecasterFoundation # ============================================================================== forecaster.fit( series = data_train["Demand"], exog = data_train[["Temperature", "Holiday"]] ) forecaster

Out[5]:

ForecasterFoundation

General Information

• Model ID: autogluon/chronos-2-small
• Context length: 500
• Window size: 500
• Series names: Demand
• Exogenous included: True
• Creation date: 2026-06-18 12:13:00
• Last fit date: 2026-06-18 12:13:00
• Skforecast version: 0.23.0
• Python version: 3.12.13
• Forecaster id: None

Exogenous Variables

Temperature, Holiday

Training Information

• Context range: 'Demand': ['2012-01-01 00:00:00', '2014-11-30 23:00:00']
• Training index type: DatetimeIndex
• Training index frequency:

Model Parameters

• cross_learning: False
• context_length: 500
• device_map: auto
• torch_dtype: None
• predict_kwargs: None

📖 API Reference    📝 User Guide

Three methods can be used to predict the next $n$ steps ahead: predict(), predict_interval(), and predict_quantiles(). All these methods allow for passing context and context_exog to override the historical context used by the underlying model to generate predictions.

In [6]:

# Predictions: point forecast
# ==============================================================================
steps = 24
predictions = forecaster.predict(
                  steps = steps,
                  exog  = data_test[["Temperature", "Holiday"]]
              )

predictions.head(3)

# Predictions: point forecast # ============================================================================== steps = 24 predictions = forecaster.predict( steps = steps, exog = data_test[["Temperature", "Holiday"]] ) predictions.head(3)

Out[6]:

	level	pred
2014-12-01 00:00:00	Demand	5527.679199
2014-12-01 01:00:00	Demand	5511.500977
2014-12-01 02:00:00	Demand	5457.792480

In [7]:

# Predictions: intervals
# ==============================================================================
predictions_intervals = forecaster.predict_interval(
                            steps    = steps,
                            exog     = data_test[["Temperature", "Holiday"]],
                            interval = [0.1, 0.9],  # 80% prediction interval
                        )

predictions_intervals.head(3)

# Predictions: intervals # ============================================================================== predictions_intervals = forecaster.predict_interval( steps = steps, exog = data_test[["Temperature", "Holiday"]], interval = [0.1, 0.9], # 80% prediction interval ) predictions_intervals.head(3)

Out[7]:

	level	pred	lower_bound	upper_bound
2014-12-01 00:00:00	Demand	5527.679199	5372.815918	5689.794434
2014-12-01 01:00:00	Demand	5511.500977	5318.045898	5733.492188
2014-12-01 02:00:00	Demand	5457.792480	5241.040527	5717.425781

Backtesting¶

Backtesting with foundation models works differently than with traditional machine learning forecasters. Since the model's weights are frozen and never updated, the concept of refitting does not apply. The refit and fixed_train_size arguments in TimeSeriesFold are ignored internally.

Instead, what changes across folds is the context window. As backtesting progresses, the amount of historical data available grows. At each fold, the model receives the most recent observations up to the fold boundary. This process has two phases: first, the context expands as more historical data becomes available with each fold; once the available history exceeds the model's context_length, the context stops growing and instead slides forward, always using the last context_length observations before the fold boundary.

Backtesting with expanding context window.

To learn more about backtesting, visit the backtesting user guide.

In [8]:

# Backtesting
# ==============================================================================
cv = TimeSeriesFold(
         steps              = 24,
         initial_train_size = len(data.loc[:end_train]),
         refit              = False
     )

metrics_chronos, backtest_predictions = backtesting_foundation(
    forecaster        = forecaster,
    series            = data['Demand'],
    exog              = data[["Temperature", "Holiday"]],
    cv                = cv,
    metric            = 'mean_absolute_error',
    suppress_warnings = True
)

print("Backtest metrics")
display(metrics_chronos)
print("")
print("Backtest predictions")
backtest_predictions.head(4)

# Backtesting # ============================================================================== cv = TimeSeriesFold( steps = 24, initial_train_size = len(data.loc[:end_train]), refit = False ) metrics_chronos, backtest_predictions = backtesting_foundation( forecaster = forecaster, series = data['Demand'], exog = data[["Temperature", "Holiday"]], cv = cv, metric = 'mean_absolute_error', suppress_warnings = True ) print("Backtest metrics") display(metrics_chronos) print("") print("Backtest predictions") backtest_predictions.head(4)

  0%|          | 0/30 [00:00<?, ?it/s]

Backtest metrics

	mean_absolute_error
0	171.266968

Backtest predictions

Out[8]:

	level	fold	pred
2014-12-01 00:00:00	Demand	0	5527.679199
2014-12-01 01:00:00	Demand	0	5511.500977
2014-12-01 02:00:00	Demand	0	5457.792480
2014-12-01 03:00:00	Demand	0	5402.819824

In [9]:

# Plot predictions
# ==============================================================================
set_dark_theme()
fig, ax = plt.subplots(figsize=(7, 3))
data_test['Demand'].plot(ax=ax, label='test')
backtest_predictions['pred'].plot(ax=ax, label='predictions')
ax.legend();

# Plot predictions # ============================================================================== set_dark_theme() fig, ax = plt.subplots(figsize=(7, 3)) data_test['Demand'].plot(ax=ax, label='test') backtest_predictions['pred'].plot(ax=ax, label='predictions') ax.legend();

Multiple series (global model)¶

The class ForecasterFoundation allows modeling and forecasting multiple series with a single model.

In [10]:

# Data
# ==============================================================================
data_multiseries = fetch_dataset(name="items_sales")
display(data_multiseries.head(3))

# Data # ============================================================================== data_multiseries = fetch_dataset(name="items_sales") display(data_multiseries.head(3))

╭─────────────────────── items_sales ───────────────────────╮
│ Description:                                              │
│ Simulated time series for the sales of 3 different items. │
│                                                           │
│ Source:                                                   │
│ Simulated data.                                           │
│                                                           │
│ URL:                                                      │
│ https://raw.githubusercontent.com/skforecast/skforecast-  │
│ datasets/main/data/simulated_items_sales.csv              │
│                                                           │
│ Shape: 1097 rows x 3 columns                              │
╰───────────────────────────────────────────────────────────╯

	item_1	item_2	item_3
date
2012-01-01	8.253175	21.047727	19.429739
2012-01-02	22.777826	26.578125	28.009863
2012-01-03	27.549099	31.751042	32.078922

In [11]:

# Split data into train-test
# ==============================================================================
end_train = '2014-07-15 23:59:00'
data_multiseries_train = data_multiseries.loc[:end_train, :].copy()
data_multiseries_test  = data_multiseries.loc[end_train:, :].copy()

# Split data into train-test # ============================================================================== end_train = '2014-07-15 23:59:00' data_multiseries_train = data_multiseries.loc[:end_train, :].copy() data_multiseries_test = data_multiseries.loc[end_train:, :].copy()

In [12]:

# Plot time series
# ==============================================================================
set_dark_theme()
fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(7, 5), sharex=True)

for i, col in enumerate(data_multiseries.columns):
    data_multiseries_train[col].plot(ax=axes[i], label='train')
    data_multiseries_test[col].plot(ax=axes[i], label='test')
    axes[i].set_title(col)
    axes[i].set_ylabel('sales')
    axes[i].set_xlabel('')
    axes[i].legend(loc='upper left')

fig.tight_layout()
plt.show();

# Plot time series # ============================================================================== set_dark_theme() fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(7, 5), sharex=True) for i, col in enumerate(data_multiseries.columns): data_multiseries_train[col].plot(ax=axes[i], label='train') data_multiseries_test[col].plot(ax=axes[i], label='test') axes[i].set_title(col) axes[i].set_ylabel('sales') axes[i].set_xlabel('') axes[i].legend(loc='upper left') fig.tight_layout() plt.show();

In this example, instead of calling fit(), the context is passed directly to the predict() method.

In [13]:

# Create and train ForecasterFoundation
# ==============================================================================
estimator = FoundationModel(model_id = "autogluon/chronos-2-small", context_length=500)
forecaster = ForecasterFoundation(estimator = estimator)

# fit() is optional; context is passed directly to predict()
# forecaster.fit(series=data_multiseries_train)

forecaster

# Create and train ForecasterFoundation # ============================================================================== estimator = FoundationModel(model_id = "autogluon/chronos-2-small", context_length=500) forecaster = ForecasterFoundation(estimator = estimator) # fit() is optional; context is passed directly to predict() # forecaster.fit(series=data_multiseries_train) forecaster

Out[13]:

ForecasterFoundation

General Information

• Model ID: autogluon/chronos-2-small
• Context length: 500
• Window size: 500
• Series names: None
• Exogenous included: False
• Creation date: 2026-06-18 12:13:03
• Last fit date: None
• Skforecast version: 0.23.0
• Python version: 3.12.13
• Forecaster id: None

Exogenous Variables

None

Training Information

• Context range: Not fitted
• Training index type: Not fitted
• Training index frequency: Not fitted

Model Parameters

• cross_learning: False
• context_length: 500
• device_map: auto
• torch_dtype: None
• predict_kwargs: None

📖 API Reference    📝 User Guide

In [14]:

# Predictions for all series (levels)
# ==============================================================================
steps = len(data_multiseries_test)
predictions_items = forecaster.predict(
                        steps   = steps, 
                        levels  = None,  # All levels are predicted
                        context = data_multiseries_train
                    )

predictions_items.head()

# Predictions for all series (levels) # ============================================================================== steps = len(data_multiseries_test) predictions_items = forecaster.predict( steps = steps, levels = None, # All levels are predicted context = data_multiseries_train ) predictions_items.head()

╭────────────────────────────────── InputTypeWarning ──────────────────────────────────╮
│ Passing a DataFrame (either wide or long format) as `series` requires additional     │
│ internal transformations, which can increase computational time. It is recommended   │
│ to use a dictionary of pandas Series instead. For more details, see:                 │
│ https://skforecast.org/latest/user_guides/independent-multi-time-series-forecasting. │
│ html#input-data                                                                      │
│                                                                                      │
│ Category : skforecast.exceptions.InputTypeWarning                                    │
│ Location :                                                                           │
│ /opt/homebrew/Caskroom/miniconda/base/envs/skforecast_py12/lib/python3.12/site-packa │
│ ges/skforecast/utils/utils.py:3072                                                   │
│ Suppress : warnings.simplefilter('ignore', category=InputTypeWarning)                │
╰──────────────────────────────────────────────────────────────────────────────────────╯

Out[14]:

	level	pred
2014-07-16	item_1	25.523060
2014-07-16	item_2	10.456669
2014-07-16	item_3	11.862239
2014-07-17	item_1	25.296780
2014-07-17	item_2	10.701235

In [15]:

# Plot predictions
# ==============================================================================
set_dark_theme()
fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(7, 5), sharex=True)

for i, col in enumerate(data_multiseries.columns):
    
    data_multiseries_train[col].plot(ax=axes[i], label='train')
    data_multiseries_test[col].plot(ax=axes[i], label='test')
    predictions_items.query(f"level == '{col}'")['pred'].plot(
        ax=axes[i], label='predictions', color='white'
    )

    axes[i].set_title(col)
    axes[i].set_ylabel('sales')
    axes[i].set_xlabel('')
    axes[i].legend(loc='upper left')

fig.tight_layout()
plt.show();

# Plot predictions # ============================================================================== set_dark_theme() fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(7, 5), sharex=True) for i, col in enumerate(data_multiseries.columns): data_multiseries_train[col].plot(ax=axes[i], label='train') data_multiseries_test[col].plot(ax=axes[i], label='test') predictions_items.query(f"level == '{col}'")['pred'].plot( ax=axes[i], label='predictions', color='white' ) axes[i].set_title(col) axes[i].set_ylabel('sales') axes[i].set_xlabel('') axes[i].legend(loc='upper left') fig.tight_layout() plt.show();

In [16]:

# Interval predictions for item_1 and item_2
# ==============================================================================
predictions_intervals = forecaster.predict_interval(
                            steps    = 24,
                            levels   = ['item_1', 'item_2'],
                            context  = data_multiseries_train,
                            interval = [0.1, 0.9],  # 80% prediction interval
                        )

predictions_intervals.head()

# Interval predictions for item_1 and item_2 # ============================================================================== predictions_intervals = forecaster.predict_interval( steps = 24, levels = ['item_1', 'item_2'], context = data_multiseries_train, interval = [0.1, 0.9], # 80% prediction interval ) predictions_intervals.head()

╭────────────────────────────────── InputTypeWarning ──────────────────────────────────╮
│ Passing a DataFrame (either wide or long format) as `series` requires additional     │
│ internal transformations, which can increase computational time. It is recommended   │
│ to use a dictionary of pandas Series instead. For more details, see:                 │
│ https://skforecast.org/latest/user_guides/independent-multi-time-series-forecasting. │
│ html#input-data                                                                      │
│                                                                                      │
│ Category : skforecast.exceptions.InputTypeWarning                                    │
│ Location :                                                                           │
│ /opt/homebrew/Caskroom/miniconda/base/envs/skforecast_py12/lib/python3.12/site-packa │
│ ges/skforecast/utils/utils.py:3072                                                   │
│ Suppress : warnings.simplefilter('ignore', category=InputTypeWarning)                │
╰──────────────────────────────────────────────────────────────────────────────────────╯

Out[16]:

	level	pred	lower_bound	upper_bound
2014-07-16	item_1	25.464172	24.582005	26.430851
2014-07-16	item_2	10.649371	8.679635	13.302808
2014-07-17	item_1	25.270245	24.255964	26.327969
2014-07-17	item_2	10.834243	8.717452	13.826941
2014-07-18	item_1	25.175859	24.079084	26.286255

Other foundation models¶

The examples above use the Amazon Chronos model, but the same code structure applies to any other foundation model supported by skforecast. The following subsections demonstrate that the pipeline is identical regardless of the underlying model; only the model_id changes. To use a different model, simply pass it when instantiating the FoundationModel wrapper.

TimesFM 2.5¶

A ForecasterFoundation is created using Google's TimesFM-2.5-200m model.

In [17]:

# Create ForecasterFoundation
# ==============================================================================
estimator = FoundationModel(model_id="google/timesfm-2.5-200m-pytorch", context_length=500)
forecaster = ForecasterFoundation(estimator = estimator)

# Create ForecasterFoundation # ============================================================================== estimator = FoundationModel(model_id="google/timesfm-2.5-200m-pytorch", context_length=500) forecaster = ForecasterFoundation(estimator = estimator)

In [18]:

# Train ForecasterFoundation
# ==============================================================================
forecaster.fit(series=data_train["Demand"])
forecaster

# Train ForecasterFoundation # ============================================================================== forecaster.fit(series=data_train["Demand"]) forecaster

Out[18]:

ForecasterFoundation

General Information

• Model ID: google/timesfm-2.5-200m-pytorch
• Context length: 500
• Window size: 500
• Series names: Demand
• Exogenous included: False
• Creation date: 2026-06-18 12:13:05
• Last fit date: 2026-06-18 12:13:05
• Skforecast version: 0.23.0
• Python version: 3.12.13
• Forecaster id: None

Exogenous Variables

None

Training Information

• Context range: 'Demand': ['2012-01-01 00:00:00', '2014-11-30 23:00:00']
• Training index type: DatetimeIndex
• Training index frequency:

Model Parameters

• context_length: 500
• max_horizon: 512
• forecast_config_kwargs: None

📖 API Reference    📝 User Guide

In [19]:

# Predictions: point forecast
# ==============================================================================
steps = 24
predictions = forecaster.predict(steps=steps)
predictions.head(3)

# Predictions: point forecast # ============================================================================== steps = 24 predictions = forecaster.predict(steps=steps) predictions.head(3)

Out[19]:

	level	pred
2014-12-01 00:00:00	Demand	5658.414551
2014-12-01 01:00:00	Demand	5671.861328
2014-12-01 02:00:00	Demand	5747.937500

In [20]:

# Predictions: intervals
# ==============================================================================
predictions_intervals = forecaster.predict_interval(
    steps    = steps,
    interval = [0.1, 0.9],  # 80% prediction interval
)
predictions_intervals.head(3)

# Predictions: intervals # ============================================================================== predictions_intervals = forecaster.predict_interval( steps = steps, interval = [0.1, 0.9], # 80% prediction interval ) predictions_intervals.head(3)

Out[20]:

	level	pred	lower_bound	upper_bound
2014-12-01 00:00:00	Demand	5658.414551	5541.003906	5790.344727
2014-12-01 01:00:00	Demand	5671.861328	5470.189453	5899.113281
2014-12-01 02:00:00	Demand	5747.937500	5450.533203	6064.878418

In [21]:

# Backtesting
# ==============================================================================
cv = TimeSeriesFold(
         steps              = 24,
         initial_train_size = len(data.loc[:end_train]),
         refit              = False
     )

metrics_timesfm, backtest_predictions = backtesting_foundation(
    forecaster        = forecaster,
    series            = data['Demand'],
    cv                = cv,
    metric            = 'mean_absolute_error',
    suppress_warnings = True
)

print("Backtest metrics")
display(metrics_timesfm)
print("")
print("Backtest predictions")
backtest_predictions.head(4)

# Backtesting # ============================================================================== cv = TimeSeriesFold( steps = 24, initial_train_size = len(data.loc[:end_train]), refit = False ) metrics_timesfm, backtest_predictions = backtesting_foundation( forecaster = forecaster, series = data['Demand'], cv = cv, metric = 'mean_absolute_error', suppress_warnings = True ) print("Backtest metrics") display(metrics_timesfm) print("") print("Backtest predictions") backtest_predictions.head(4)

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Backtest metrics

	mean_absolute_error
0	160.357016

Backtest predictions

Out[21]:

	level	fold	pred
2014-07-16 00:00:00	Demand	0	6189.843262
2014-07-16 01:00:00	Demand	0	5988.113281
2014-07-16 02:00:00	Demand	0	5830.691406
2014-07-16 03:00:00	Demand	0	5696.287598

Moirai¶

A ForecasterFoundation is created using Salesforce's Moirai-2.0-R-small model.

In [22]:

# Create ForecasterFoundation
# ==============================================================================
estimator = FoundationModel(model_id="Salesforce/moirai-2.0-R-small", context_length=500)
forecaster = ForecasterFoundation(estimator=estimator)

# Create ForecasterFoundation # ============================================================================== estimator = FoundationModel(model_id="Salesforce/moirai-2.0-R-small", context_length=500) forecaster = ForecasterFoundation(estimator=estimator)

In [23]:

# Train ForecasterFoundation
# ==============================================================================
forecaster.fit(series=data_train["Demand"])
forecaster

# Train ForecasterFoundation # ============================================================================== forecaster.fit(series=data_train["Demand"]) forecaster

Out[23]:

ForecasterFoundation

General Information

• Model ID: Salesforce/moirai-2.0-R-small
• Context length: 500
• Window size: 500
• Series names: Demand
• Exogenous included: False
• Creation date: 2026-06-18 12:13:21
• Last fit date: 2026-06-18 12:13:21
• Skforecast version: 0.23.0
• Python version: 3.12.13
• Forecaster id: None

Exogenous Variables

None

Training Information

• Context range: 'Demand': ['2012-01-01 00:00:00', '2014-11-30 23:00:00']
• Training index type: DatetimeIndex
• Training index frequency:

Model Parameters

• context_length: 500
• device: auto

📖 API Reference    📝 User Guide

In [24]:

# Predictions: point forecast
# ==============================================================================
steps = 24
predictions = forecaster.predict(steps=steps)
predictions.head(3)

# Predictions: point forecast # ============================================================================== steps = 24 predictions = forecaster.predict(steps=steps) predictions.head(3)

/var/folders/wt/8tvn563d5v55nspfbydgqb9r0000gp/T/ipykernel_80689/2957951684.py:4: UserWarning: MPS device is not supported by Moirai because the uni2ts library uses float64 operations internally. Falling back to CPU.
  predictions = forecaster.predict(steps=steps)

Out[24]:

	level	pred
2014-12-01 00:00:00	Demand	5731.725098
2014-12-01 01:00:00	Demand	5870.827148
2014-12-01 02:00:00	Demand	5959.208008

In [25]:

# Predictions: intervals
# ==============================================================================
predictions_intervals = forecaster.predict_interval(
    steps    = steps,
    interval = [0.1, 0.9],  # 80% prediction interval
)
predictions_intervals.head(3)

# Predictions: intervals # ============================================================================== predictions_intervals = forecaster.predict_interval( steps = steps, interval = [0.1, 0.9], # 80% prediction interval ) predictions_intervals.head(3)

Out[25]:

	level	pred	lower_bound	upper_bound
2014-12-01 00:00:00	Demand	5731.725098	5517.738281	5940.647461
2014-12-01 01:00:00	Demand	5870.827148	5548.743164	6176.802246
2014-12-01 02:00:00	Demand	5959.208008	5599.377441	6323.206055

In [26]:

# Backtesting
# ==============================================================================
cv = TimeSeriesFold(
         steps              = 24,
         initial_train_size = len(data.loc[:end_train]),
         refit              = False
     )

metrics_moirai, backtest_predictions = backtesting_foundation(
    forecaster        = forecaster,
    series            = data['Demand'],
    cv                = cv,
    metric            = 'mean_absolute_error',
    suppress_warnings = True
)

print("Backtest metrics")
display(metrics_moirai)
print("")
print("Backtest predictions")
backtest_predictions.head(4)

# Backtesting # ============================================================================== cv = TimeSeriesFold( steps = 24, initial_train_size = len(data.loc[:end_train]), refit = False ) metrics_moirai, backtest_predictions = backtesting_foundation( forecaster = forecaster, series = data['Demand'], cv = cv, metric = 'mean_absolute_error', suppress_warnings = True ) print("Backtest metrics") display(metrics_moirai) print("") print("Backtest predictions") backtest_predictions.head(4)

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Backtest metrics

	mean_absolute_error
0	161.691111

Backtest predictions

Out[26]:

	level	fold	pred
2014-07-16 00:00:00	Demand	0	6222.097656
2014-07-16 01:00:00	Demand	0	6114.366211
2014-07-16 02:00:00	Demand	0	5969.839844
2014-07-16 03:00:00	Demand	0	5920.479492

TabICL¶

A ForecasterFoundation is created using Soda-Inria's TabICL model.

In [27]:

# Create ForecasterFoundation
# ==============================================================================
estimator = FoundationModel(model_id="soda-inria/tabicl", context_length=500)
forecaster = ForecasterFoundation(estimator=estimator)

# Create ForecasterFoundation # ============================================================================== estimator = FoundationModel(model_id="soda-inria/tabicl", context_length=500) forecaster = ForecasterFoundation(estimator=estimator)

In [28]:

# Train ForecasterFoundation
# ==============================================================================
forecaster.fit(
    series = data_train["Demand"], 
    exog   = data_train[["Temperature", "Holiday"]]
)
forecaster

# Train ForecasterFoundation # ============================================================================== forecaster.fit( series = data_train["Demand"], exog = data_train[["Temperature", "Holiday"]] ) forecaster

Out[28]:

ForecasterFoundation

General Information

• Model ID: soda-inria/tabicl
• Context length: 500
• Window size: 500
• Series names: Demand
• Exogenous included: True
• Creation date: 2026-06-18 12:13:23
• Last fit date: 2026-06-18 12:13:23
• Skforecast version: 0.23.0
• Python version: 3.12.13
• Forecaster id: None

Exogenous Variables

Temperature, Holiday

Training Information

• Context range: 'Demand': ['2012-01-01 00:00:00', '2014-11-30 23:00:00']
• Training index type: DatetimeIndex
• Training index frequency:

Model Parameters

• context_length: 500
• point_estimate: mean
• tabicl_config: None
• temporal_features: None

📖 API Reference    📝 User Guide

In [29]:

# Predictions: point forecast
# ==============================================================================
steps = 24
predictions = forecaster.predict(
                  steps = steps,
                  exog  = data_test[["Temperature", "Holiday"]]
              )

predictions.head(3)

# Predictions: point forecast # ============================================================================== steps = 24 predictions = forecaster.predict( steps = steps, exog = data_test[["Temperature", "Holiday"]] ) predictions.head(3)

Predicting time series: 100%|██████████| 1/1 [00:01<00:00,  1.64s/it]

Out[29]:

	level	pred
2014-12-01 00:00:00	Demand	5590.919922
2014-12-01 01:00:00	Demand	5662.487305
2014-12-01 02:00:00	Demand	5661.673828

In [30]:

# Predictions: intervals
# ==============================================================================
predictions_intervals = forecaster.predict_interval(
                            steps    = steps,
                            exog     = data_test[["Temperature", "Holiday"]],
                            interval = [0.1, 0.9],  # 80% prediction interval
                        )

predictions_intervals.head(3)

# Predictions: intervals # ============================================================================== predictions_intervals = forecaster.predict_interval( steps = steps, exog = data_test[["Temperature", "Holiday"]], interval = [0.1, 0.9], # 80% prediction interval ) predictions_intervals.head(3)

Predicting time series: 100%|██████████| 1/1 [00:01<00:00,  1.62s/it]

Out[30]:

	level	pred	lower_bound	upper_bound
2014-12-01 00:00:00	Demand	5617.177246	5159.889648	5952.953125
2014-12-01 01:00:00	Demand	5678.133301	5215.844727	6059.711426
2014-12-01 02:00:00	Demand	5677.455566	5131.913086	6149.851074

In [31]:

# Backtesting
# ==============================================================================
cv = TimeSeriesFold(
         steps              = 24,
         initial_train_size = len(data.loc[:end_train]),
         refit              = False
     )

metrics_tabicl, backtest_predictions = backtesting_foundation(
    forecaster        = forecaster,
    series            = data['Demand'],
    exog              = data[["Temperature", "Holiday"]],
    cv                = cv,
    metric            = 'mean_absolute_error',
    suppress_warnings = True
)

print("Backtest metrics")
display(metrics_tabicl)
print("")
print("Backtest predictions")
backtest_predictions.head(4)

# Backtesting # ============================================================================== cv = TimeSeriesFold( steps = 24, initial_train_size = len(data.loc[:end_train]), refit = False ) metrics_tabicl, backtest_predictions = backtesting_foundation( forecaster = forecaster, series = data['Demand'], exog = data[["Temperature", "Holiday"]], cv = cv, metric = 'mean_absolute_error', suppress_warnings = True ) print("Backtest metrics") display(metrics_tabicl) print("") print("Backtest predictions") backtest_predictions.head(4)

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Backtest metrics

	mean_absolute_error
0	170.101612

Backtest predictions

Out[31]:

	level	fold	pred
2014-07-16 00:00:00	Demand	0	6371.091309
2014-07-16 01:00:00	Demand	0	6311.228516
2014-07-16 02:00:00	Demand	0	6289.091309
2014-07-16 03:00:00	Demand	0	6268.157715

TabPFN-TS¶

A ForecasterFoundation is created using Prior Labs' TabPFN-TS model. TabPFN-TS frames forecasting as tabular regression: the series is featurized (running index, calendar features, automatically detected seasonal features) and a TabPFN regressor predicts the forecast horizon zero-shot.

TabPFN-TS requires a Free Prior Labs API key to run inference. You can obtain one by signing up at https://priorlabs.ai. By default inference runs locally (mode='local', CUDA > MPS > CPU); pass mode='client' to use the Prior Labs cloud API instead (no GPU needed, requires an API key).

In [32]:

# Check if Prior Labs API key is set
# ==============================================================================
print(os.getenv("TABPFN_TOKEN") is not None)

# Check if Prior Labs API key is set # ============================================================================== print(os.getenv("TABPFN_TOKEN") is not None)

True

In [33]:

# Create ForecasterFoundation
# ==============================================================================
estimator = FoundationModel(
    model_id="priorlabs/tabpfn-ts", context_length=500, mode='local'
)
forecaster = ForecasterFoundation(estimator=estimator)

# Create ForecasterFoundation # ============================================================================== estimator = FoundationModel( model_id="priorlabs/tabpfn-ts", context_length=500, mode='local' ) forecaster = ForecasterFoundation(estimator=estimator)

In [34]:

# Train ForecasterFoundation
# ==============================================================================
forecaster.fit(
    series = data_train["Demand"], 
    exog   = data_train[["Temperature", "Holiday"]]
)
forecaster

# Train ForecasterFoundation # ============================================================================== forecaster.fit( series = data_train["Demand"], exog = data_train[["Temperature", "Holiday"]] ) forecaster

Out[34]:

ForecasterFoundation

General Information

• Model ID: priorlabs/tabpfn-ts
• Context length: 500
• Window size: 500
• Series names: Demand
• Exogenous included: True
• Creation date: 2026-06-18 12:17:35
• Last fit date: 2026-06-18 12:17:35
• Skforecast version: 0.23.0
• Python version: 3.12.13
• Forecaster id: None

Exogenous Variables

Temperature, Holiday

Training Information

• Context range: 'Demand': ['2012-01-01 00:00:00', '2014-11-30 23:00:00']
• Training index type: DatetimeIndex
• Training index frequency:

Model Parameters

• context_length: 500
• mode: local
• point_estimate: median
• tabpfn_model_config: None
• temporal_features: None

📖 API Reference    📝 User Guide

In [35]:

# Predictions: point forecast
# ==============================================================================
steps = 24
predictions = forecaster.predict(
                  steps = steps,
                  exog  = data_test[["Temperature", "Holiday"]]
              )

predictions.head(3)

# Predictions: point forecast # ============================================================================== steps = 24 predictions = forecaster.predict( steps = steps, exog = data_test[["Temperature", "Holiday"]] ) predictions.head(3)

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Out[35]:

	level	pred
2014-12-01 00:00:00	Demand	5528.235352
2014-12-01 01:00:00	Demand	5535.009277
2014-12-01 02:00:00	Demand	5486.875977

In [36]:

# Predictions: intervals
# ==============================================================================
predictions_intervals = forecaster.predict_interval(
                            steps    = steps,
                            exog     = data_test[["Temperature", "Holiday"]],
                            interval = [0.1, 0.9],  # 80% prediction interval
                        )

predictions_intervals.head(3)

# Predictions: intervals # ============================================================================== predictions_intervals = forecaster.predict_interval( steps = steps, exog = data_test[["Temperature", "Holiday"]], interval = [0.1, 0.9], # 80% prediction interval ) predictions_intervals.head(3)

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Out[36]:

	level	pred	lower_bound	upper_bound
2014-12-01 00:00:00	Demand	5528.235352	5016.570312	5739.664551
2014-12-01 01:00:00	Demand	5535.009277	5065.455566	5804.239258
2014-12-01 02:00:00	Demand	5486.875977	4944.363770	5816.429688

In [37]:

# Backtesting
# ==============================================================================
cv = TimeSeriesFold(
         steps              = 24,
         initial_train_size = len(data.loc[:end_train]),
         refit              = False
     )

metrics_tabpfn, backtest_predictions = backtesting_foundation(
    forecaster        = forecaster,
    series            = data['Demand'],
    exog              = data[["Temperature", "Holiday"]],
    cv                = cv,
    metric            = 'mean_absolute_error',
    suppress_warnings = True
)

print("Backtest metrics")
display(metrics_tabpfn)
print("")
print("Backtest predictions")
backtest_predictions.head(4)

# Backtesting # ============================================================================== cv = TimeSeriesFold( steps = 24, initial_train_size = len(data.loc[:end_train]), refit = False ) metrics_tabpfn, backtest_predictions = backtesting_foundation( forecaster = forecaster, series = data['Demand'], exog = data[["Temperature", "Holiday"]], cv = cv, metric = 'mean_absolute_error', suppress_warnings = True ) print("Backtest metrics") display(metrics_tabpfn) print("") print("Backtest predictions") backtest_predictions.head(4)

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Backtest metrics

	mean_absolute_error
0	159.3229

Backtest predictions

Out[37]:

	level	fold	pred
2014-07-16 00:00:00	Demand	0	6210.371094
2014-07-16 01:00:00	Demand	0	6114.570312
2014-07-16 02:00:00	Demand	0	6066.964355
2014-07-16 03:00:00	Demand	0	6033.796875

The Forecasting Company T0¶

A ForecasterFoundation is created using The Forecasting Company's T0 model. T0 is a zero-shot time series transformer that supports future-known covariates, exogenous variables whose values are available over both the context window and the forecast horizon.

Skforecast exogenous variables map directly onto this channel: their past and future values are combined into the single covariate stream the model expects. Covariates must be numeric, so encode any categorical features as numbers beforehand. The point forecast is the median (0.5 quantile), and arbitrary quantiles in the (0, 1) range are available for prediction intervals.

In [38]:

# Create ForecasterFoundation
# ==============================================================================
estimator = FoundationModel(model_id="theforecastingcompany/t0-alpha", context_length=500)
forecaster = ForecasterFoundation(estimator=estimator)

# Create ForecasterFoundation # ============================================================================== estimator = FoundationModel(model_id="theforecastingcompany/t0-alpha", context_length=500) forecaster = ForecasterFoundation(estimator=estimator)

In [39]:

# Train ForecasterFoundation
# ==============================================================================
forecaster.fit(
    series = data_train["Demand"], 
    exog   = data_train[["Temperature", "Holiday"]]
)
forecaster

# Train ForecasterFoundation # ============================================================================== forecaster.fit( series = data_train["Demand"], exog = data_train[["Temperature", "Holiday"]] ) forecaster

Out[39]:

ForecasterFoundation

General Information

• Model ID: theforecastingcompany/t0-alpha
• Context length: 500
• Window size: 500
• Series names: Demand
• Exogenous included: True
• Creation date: 2026-06-18 12:26:28
• Last fit date: 2026-06-18 12:26:28
• Skforecast version: 0.23.0
• Python version: 3.12.13
• Forecaster id: None

Exogenous Variables

Temperature, Holiday

Training Information

• Context range: 'Demand': ['2012-01-01 00:00:00', '2014-11-30 23:00:00']
• Training index type: DatetimeIndex
• Training index frequency:

Model Parameters

• context_length: 500
• device_map: auto
• torch_dtype: None

📖 API Reference    📝 User Guide

In [40]:

# Predictions: point forecast
# ==============================================================================
steps = 24
predictions = forecaster.predict(
                  steps = steps,
                  exog  = data_test[["Temperature", "Holiday"]]
              )

predictions.head(3)

# Predictions: point forecast # ============================================================================== steps = 24 predictions = forecaster.predict( steps = steps, exog = data_test[["Temperature", "Holiday"]] ) predictions.head(3)

Out[40]:

	level	pred
2014-12-01 00:00:00	Demand	5663.061523
2014-12-01 01:00:00	Demand	5740.972656
2014-12-01 02:00:00	Demand	5797.895020

In [41]:

# Predictions: intervals
# ==============================================================================
predictions_intervals = forecaster.predict_interval(
                            steps    = steps,
                            exog     = data_test[["Temperature", "Holiday"]],
                            interval = [0.1, 0.9],  # 80% prediction interval
                        )

predictions_intervals.head(3)

# Predictions: intervals # ============================================================================== predictions_intervals = forecaster.predict_interval( steps = steps, exog = data_test[["Temperature", "Holiday"]], interval = [0.1, 0.9], # 80% prediction interval ) predictions_intervals.head(3)

Out[41]:

	level	pred	lower_bound	upper_bound
2014-12-01 00:00:00	Demand	5663.061523	5529.620605	5805.176758
2014-12-01 01:00:00	Demand	5740.972656	5525.629883	5947.431152
2014-12-01 02:00:00	Demand	5797.895020	5502.964355	6049.715820

In [42]:

# Backtesting
# ==============================================================================
cv = TimeSeriesFold(
         steps              = 24,
         initial_train_size = len(data.loc[:end_train]),
         refit              = False
     )

metrics_t0, backtest_predictions = backtesting_foundation(
    forecaster        = forecaster,
    series            = data['Demand'],
    exog              = data[["Temperature", "Holiday"]],
    cv                = cv,
    metric            = 'mean_absolute_error',
    suppress_warnings = True
)

print("Backtest metrics")
display(metrics_t0)
print("")
print("Backtest predictions")
backtest_predictions.head(4)

# Backtesting # ============================================================================== cv = TimeSeriesFold( steps = 24, initial_train_size = len(data.loc[:end_train]), refit = False ) metrics_t0, backtest_predictions = backtesting_foundation( forecaster = forecaster, series = data['Demand'], exog = data[["Temperature", "Holiday"]], cv = cv, metric = 'mean_absolute_error', suppress_warnings = True ) print("Backtest metrics") display(metrics_t0) print("") print("Backtest predictions") backtest_predictions.head(4)

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Backtest metrics

	mean_absolute_error
0	127.08197

Backtest predictions

Out[42]:

	level	fold	pred
2014-07-16 00:00:00	Demand	0	6226.978027
2014-07-16 01:00:00	Demand	0	6120.694336
2014-07-16 02:00:00	Demand	0	6029.494141
2014-07-16 03:00:00	Demand	0	5974.883789

Model comparison¶

The following table summarizes the backtesting results (Mean Absolute Error) for the five foundation models on the same dataset.

In [43]:

# Comparison of backtesting metrics
# ==============================================================================
comparison = pd.DataFrame({
    "Model": [
        "Chronos-2 (small)*",
        "TimesFM-2.5 (200m)",
        "Moirai-2.0-R (small)",
        "TabICL*",
        "TabPFN-TS*",
        "TFC T0*"
    ],
    "mean_absolute_error": [
        metrics_chronos["mean_absolute_error"].iloc[0],
        metrics_timesfm["mean_absolute_error"].iloc[0],
        metrics_moirai["mean_absolute_error"].iloc[0],
        metrics_tabicl["mean_absolute_error"].iloc[0],
        metrics_tabpfn["mean_absolute_error"].iloc[0],
        metrics_t0["mean_absolute_error"].iloc[0]
    ],
}).sort_values(by="mean_absolute_error")

comparison.style.highlight_min(
    subset="mean_absolute_error", color="green"
).format(precision=4)

# Comparison of backtesting metrics # ============================================================================== comparison = pd.DataFrame({ "Model": [ "Chronos-2 (small)*", "TimesFM-2.5 (200m)", "Moirai-2.0-R (small)", "TabICL*", "TabPFN-TS*", "TFC T0*" ], "mean_absolute_error": [ metrics_chronos["mean_absolute_error"].iloc[0], metrics_timesfm["mean_absolute_error"].iloc[0], metrics_moirai["mean_absolute_error"].iloc[0], metrics_tabicl["mean_absolute_error"].iloc[0], metrics_tabpfn["mean_absolute_error"].iloc[0], metrics_t0["mean_absolute_error"].iloc[0] ], }).sort_values(by="mean_absolute_error") comparison.style.highlight_min( subset="mean_absolute_error", color="green" ).format(precision=4)

Out[43]:

	Model	mean_absolute_error
5	TFC T0*	127.0820
4	TabPFN-TS*	159.3229
1	TimesFM-2.5 (200m)	160.3570
2	Moirai-2.0-R (small)	161.6911
3	TabICL*	170.1016
0	Chronos-2 (small)*	171.2670

* Chronos-2 (small), TabICL, TabPFN-TS and TFC T0 allow the inclusion of exogenous features.

⚠ Warning: Data Leakage

These examples use a widely available public dataset for illustrative purposes. It is highly probable that the foundation models were exposed to these data points during their pre-training phase. As a result, the predictions may be more optimistic than what would be achieved in a real-world production environment with private or novel data.

Selection of context length¶

As described in the Impact of the context length section, the context length has a direct effect on both the model's predictive accuracy and the computation time required to generate forecasts. Furthermore, because the context must be sent to the model every time a prediction is made, it also increases the amount of data transferred when the model is deployed in production. It is therefore important to identify the optimal context length that strikes a good balance between predictive accuracy and inference time.

The following code shows how to evaluate the impact of the context length on the predictive accuracy and inference time of a foundation model. The example uses the Amazon Chronos-2-small model, but the same approach can be applied to any other foundation model supported by skforecast.

In [ ]:

# Influence of the context length in the forecasting accuracy and speed
# ==============================================================================
model_id = 'autogluon/chronos-2-small'
context_lengths = [100, 500, 1000, 5000]

model_ids_allow_exog = {
    'autogluon/chronos-2-small', 'soda-inria/tabicl', 'priorlabs/tabpfn-ts', 'theforecastingcompany/t0-alpha'
}
if model_id in model_ids_allow_exog:
    exog = data[["Temperature", "Holiday"]]
else:
    exog = None

cv = TimeSeriesFold(
         steps              = 24,
         initial_train_size = len(data.loc[:end_train]),
         refit              = False
     )

results_metrics = []
results_elapsed_time = []
for context_length in context_lengths:

    estimator = FoundationModel(model_id=model_id, context_length=context_length)
    forecaster = ForecasterFoundation(estimator=estimator)

    start = time.perf_counter()
    metrics, backtest_predictions = backtesting_foundation(
        forecaster        = forecaster,
        series            = data['Demand'],
        exog              = exog,
        cv                = cv,
        metric            = 'mean_absolute_error',
        suppress_warnings = True,
        show_progress     = False
    )
    elapsed_time = time.perf_counter() - start

    results_metrics.append(metrics.at[0, 'mean_absolute_error'])
    results_elapsed_time.append(elapsed_time)

results = pd.DataFrame(
    {
        'metric': results_metrics,
        'elapsed_time': results_elapsed_time
    },
    index=context_lengths
)
results

# Influence of the context length in the forecasting accuracy and speed # ============================================================================== model_id = 'autogluon/chronos-2-small' context_lengths = [100, 500, 1000, 5000] model_ids_allow_exog = { 'autogluon/chronos-2-small', 'soda-inria/tabicl', 'priorlabs/tabpfn-ts', 'theforecastingcompany/t0-alpha' } if model_id in model_ids_allow_exog: exog = data[["Temperature", "Holiday"]] else: exog = None cv = TimeSeriesFold( steps = 24, initial_train_size = len(data.loc[:end_train]), refit = False ) results_metrics = [] results_elapsed_time = [] for context_length in context_lengths: estimator = FoundationModel(model_id=model_id, context_length=context_length) forecaster = ForecasterFoundation(estimator=estimator) start = time.perf_counter() metrics, backtest_predictions = backtesting_foundation( forecaster = forecaster, series = data['Demand'], exog = exog, cv = cv, metric = 'mean_absolute_error', suppress_warnings = True, show_progress = False ) elapsed_time = time.perf_counter() - start results_metrics.append(metrics.at[0, 'mean_absolute_error']) results_elapsed_time.append(elapsed_time) results = pd.DataFrame( { 'metric': results_metrics, 'elapsed_time': results_elapsed_time }, index=context_lengths ) results

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Out[ ]:

	metric	elapsed_time
100	214.318950	2.500289
500	171.266983	2.885307
1000	155.492158	3.365345
5000	158.398215	7.331956

In [14]:

# Plot results
# ==============================================================================
fig, ax = plt.subplots(figsize=(7, 3))
results['metric'].plot(ax = ax)
ax.set_title("Prediction error vs context length")
ax.set_xlabel("context length")
ax.set_ylabel("mean absolute error")

fig, ax = plt.subplots(figsize=(7, 3))
results['elapsed_time'].plot(ax = ax)
ax.set_title("Elapsed time vs context length")
ax.set_xlabel("context length")
ax.set_ylabel("Elapsed time");

# Plot results # ============================================================================== fig, ax = plt.subplots(figsize=(7, 3)) results['metric'].plot(ax = ax) ax.set_title("Prediction error vs context length") ax.set_xlabel("context length") ax.set_ylabel("mean absolute error") fig, ax = plt.subplots(figsize=(7, 3)) results['elapsed_time'].plot(ax = ax) ax.set_title("Elapsed time vs context length") ax.set_xlabel("context length") ax.set_ylabel("Elapsed time");