Bounded Forecasts

Learn how to generate forecasts with upper and lower bounds to match your business constraints.

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.

Tutorial

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'
)

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)

	ds	y	unique_id
84	1984-01-01	100.58	eggs
85	1985-01-01	76.84	eggs
86	1986-01-01	81.10	eggs
87	1987-01-01	69.60	eggs
88	1988-01-01	64.55	eggs
89	1989-01-01	80.36	eggs
90	1990-01-01	79.79	eggs
91	1991-01-01	74.79	eggs
92	1992-01-01	64.86	eggs
93	1993-01-01	62.27	eggs

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)

Figure 1: Annual Egg Prices Trend from 1900s to 1990s

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
)

Figure 2: Bounded Forecasts with TimeGPT Using Log Transformation

The forecast and the prediction intervals look reasonable.

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
)

Figure 3: Unbounded Forecast with Possible Negative Intervals

For example, in 1995:

timegpt_fcst_without_transform

	unique_id	ds	TimeGPT	TimeGPT-lo-99.5	TimeGPT-lo-90	TimeGPT-lo-80	TimeGPT-hi-80	TimeGPT-hi-90	TimeGPT-hi-99.5
0	eggs	1994-01-01	66.859756	43.103240	46.131448	49.319034	84.400479	87.588065	90.616273
1	eggs	1995-01-01	64.993477	-20.924112	-4.750041	12.275298	117.711656	134.736995	150.911066
2	eggs	1996-01-01	66.695808	6.499170	8.291150	10.177444	123.214173	125.100467	126.892446
3	eggs	1997-01-01	66.103325	17.304282	24.966939	33.032894	99.173756	107.239711	114.902368
4	eggs	1998-01-01	67.906517	4.995371	12.349648	20.090992	115.722042	123.463386	130.817663
5	eggs	1999-01-01	66.147575	29.162207	31.804460	34.585779	97.709372	100.490691	103.132943
6	eggs	2000-01-01	66.062637	14.671932	19.305822	24.183601	107.941673	112.819453	117.453343
7	eggs	2001-01-01	68.045769	3.915282	13.188964	22.950736	113.140802	122.902573	132.176256
8	eggs	2002-01-01	66.718903	-42.212631	-30.583703	-18.342726	151.780531	164.021508	175.650436
9	eggs	2003-01-01	67.344078	-86.239911	-44.959745	-1.506939	136.195095	179.647901	220.928067

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.

References

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