Bounded Forecasts

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Why Generate Bounded Forecasts?

In forecasting, we often want to make sure the predictions stay within a certain range. For example, for predicting the sales of a product, we may require all forecasts to be positive. Thus, the forecasts may need to be bounded.

This tutorial shows how to generate bounded forecasts with TimeGPT by transforming data prior to forecasting.

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Tutorial

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Step 1: Import Packages

First, we install and import the required packages.

import pandas as pd
import numpy as np

from nixtla import NixtlaClient

Next, initialize your Nixtla client with the API key:

nixtla_client = NixtlaClient(
    # defaults to os.environ.get("NIXTLA_API_KEY")
    api_key='my_api_key_provided_by_nixtla'
)

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Step 2: Load Data

We use the annual egg prices dataset from Forecasting, Principles and Practices. We expect egg prices to be strictly positive, so we want to bound our forecasts to be positive.

NOTE: If you do not have pyreadr, you can install it with pip:

pip install pyreadr

import pyreadr
from pathlib import Path

url = 'https://github.com/robjhyndman/fpp3package/raw/master/data/prices.rda'
dst_path = str(Path.cwd().joinpath('prices.rda'))
result = pyreadr.read_r(pyreadr.download_file(url, dst_path), dst_path)

df = result['prices'][['year', 'eggs']]
df = df.dropna().reset_index(drop=True)
df = df.rename(columns={'year': 'ds', 'eggs': 'y'})
df['ds'] = pd.to_datetime(df['ds'], format='%Y')
df['unique_id'] = 'eggs'

df.tail(10)

We can have a look at how the prices have evolved in the 20th century, demonstrating that the price is trending down.

nixtla_client.plot(df)

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Step 3: Generate Bounded Forecasts with TimeGPT

First, we transform the target data. In this case, we will log-transform the data prior to forecasting, such that we can only forecast positive prices.

df_transformed = df.copy()
df_transformed['y'] = np.log(df_transformed['y'])

We will create forecasts for the next 10 years, and we include an 80, 90 and 99.5 percentile of our forecast distribution.

timegpt_fcst_with_transform = nixtla_client.forecast(
    df=df_transformed,
    h=10,
    freq='Y',
    level=[80, 90, 99.5]
)

After having created the forecasts, we need to inverse the transformation that we applied earlier. With a log-transformation, this simply means we need to exponentiate the forecasts:

cols_to_transform = [
    col for col in timegpt_fcst_with_transform if col not in ['unique_id', 'ds']
]

for col in cols_to_transform:
    timegpt_fcst_with_transform[col] = np.exp(timegpt_fcst_with_transform[col])

Now, we can plot the forecasts. We include a number of prediction intervals, indicating the 80, 90 and 99.5 percentile of our forecast distribution.

nixtla_client.plot(
    df,
    timegpt_fcst_with_transform,
    level=[80, 90, 99.5],
    max_insample_length=20
)

The forecast and the prediction intervals look reasonable.

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Step 4: Compare with Unbounded Forecast

Let’s compare these forecasts to the situation where we don’t apply a transformation. In this case, it may be possible to forecast a negative price.

timegpt_fcst_without_transform = nixtla_client.forecast(
    df=df,
    h=10,
    freq='Y',
    level=[80, 90, 99.5]
)

Indeed, we now observe prediction intervals that become negative:

nixtla_client.plot(
    df,
    timegpt_fcst_without_transform,
    level=[80, 90, 99.5],
    max_insample_length=20
)

For example, in 1995:

timegpt_fcst_without_transform

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Conclusion

Log-transformations are a simple and effective way to enforce non-negative predictions. This tutorial demonstrated how TimeGPT accommodates bounded forecasts to enhance forecast realism and reliability.

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References

• Hyndman, Rob J., and George Athanasopoulos (2021). Forecasting: Principles and Practice (3rd Ed)