Probabilistic Forecasting

Prerequisites This tutorial assumes basic familiarity with StatsForecast. For a minimal example visit the Quick Start

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Introduction

Important Although the terms are often confused, prediction intervals are not the same as confidence intervals.

Warning In practice, most prediction intervals are too narrow since models do not account for all sources of uncertainty. A discussion about this can be found here.

1. Install libraries
2. Load and explore the data
3. Train models
4. Plot prediction intervals

Tip You can use Colab to run this Notebook interactively

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Install libraries

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Load and explore the data

import pandas as pd

train = pd.read_csv('https://auto-arima-results.s3.amazonaws.com/M4-Hourly.csv')
test = pd.read_csv('https://auto-arima-results.s3.amazonaws.com/M4-Hourly-test.csv').rename(columns={'y': 'y_test'})

train.head()

test.head()

n_series = 8 
uids = train['unique_id'].unique()[:n_series] # select first n_series of the dataset
train = train.query('unique_id in @uids')
test = test.query('unique_id in @uids')

• df: A pandas dataframe with columns [unique_id, ds, y].
• forecasts_df: A pandas dataframe with columns [unique_id, ds] and models.
• plot_random: bool = True. Plots the time series randomly.
• models: List[str]. A list with the models we want to plot.
• level: List[float]. A list with the prediction intervals we want to plot.
• engine: str = plotly. It can also be matplotlib. plotly generates interactive plots, while matplotlib generates static plots.

from statsforecast import StatsForecast

StatsForecast.plot(train, test, plot_random=False)

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Train models

• HistoricAverage
• Naive
• RandomWalkWithDrift
• SeasonalNaive

from statsforecast.models import (
    AutoETS, 
    HistoricAverage, 
    Naive, 
    RandomWalkWithDrift, 
    SeasonalNaive
)

# Create a list of models and instantiation parameters 
models = [
    AutoETS(season_length=24),
    HistoricAverage(), 
    Naive(), 
    RandomWalkWithDrift(), 
    SeasonalNaive(season_length=24)
]

• df: The dataframe with the training data.
• models: The list of models defined in the previous step.
• freq: A string indicating the frequency of the data. See pandas’ available frequencies.
• n_jobs: An integer that indicates the number of jobs used in parallel processing. Use -1 to select all cores.

sf = StatsForecast( 
    models=models, 
    freq=1,
    n_jobs=-1
)

• h: An integer that represent the forecasting horizon. In this case, we’ll forecast the next 48 hours.
• level: A list of floats with the confidence levels of the prediction intervals. For example, level=[95] means that the range of values should include the actual future value with probability 95%.

levels = [80, 90, 95, 99] # confidence levels of the prediction intervals 

forecasts = sf.forecast(df=train, h=48, level=levels)
forecasts.head()

test = test.merge(forecasts, how='left', on=['unique_id', 'ds'])

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Plot prediction intervals

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AutoETS

sf.plot(train, test, plot_random=False, models=['AutoETS'], level=levels)

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Historic Average

sf.plot(train, test, plot_random=False, models=['HistoricAverage'], level=levels)

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Naive

sf.plot(train, test, plot_random=False, models=['Naive'], level=levels)

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Random Walk with Drift

sf.plot(train, test, plot_random=False, models=['RWD'], level=levels)

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Seasonal Naive

sf.plot(train, test, plot_random=False, models=['SeasonalNaive'], level=levels)

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References