Missing Values

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Missing Values in Time Series

TimeGPT requires time series data without missing values. While you may have multiple series starting and ending on different dates, each one must maintain a continuous data sequence.

This tutorial shows you how to handle missing values for use with TimeGPT. For reference, this tutorial is based on the skforecast tutorial: Forecasting Time Series with Missing Values.

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Tutorial

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Step 1: Load Data

Load the daily bike rental counts dataset using pandas. Note that the original column names are in Spanish; you will rename them to match ds and y.

import pandas as pd

df = pd.read_csv('https://raw.githubusercontent.com/JoaquinAmatRodrigo/Estadistica-machine-learning-python/master/data/usuarios_diarios_bicimad.csv')
df = df[['fecha', 'Usos bicis total día']]
df.rename(columns={'fecha': 'ds', 'Usos bicis total día': 'y'}, inplace=True)
df.head()

Next, convert your dates to timestamps and assign a unique identifier (unique_id) to handle multiple series if needed:

df['ds'] = pd.to_datetime(df['ds'])
df['unique_id'] = 'id1'
df = df[['unique_id', 'ds', 'y']]

Reserve the last 93 days for testing:

train_df = df[:-93]
test_df = df[-93:]

To simulate missing data, remove specific date ranges from the training dataset:

mask = ~((train_df['ds'] >= '2020-09-01') & (train_df['ds'] <= '2020-10-10')) & \
       ~((train_df['ds'] >= '2020-11-08') & (train_df['ds'] <= '2020-12-15'))
train_df_gaps = train_df[mask]

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Step 2: Initialize TimeGPT

Initialize a NixtlaClient object with your Nixtla API key:

from nixtla import NixtlaClient

nixtla_client = NixtlaClient(api_key='my_api_key_provided_by_nixtla')

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Step 3: Visualize Data

Plot your dataset and examine the gaps introduced above:

nixtla_client.plot(train_df_gaps)

Note that there are two gaps in the data: from September 1, 2020, to October 10, 2020, and from November 8, 2020, to December 15, 2020. To better visualize these gaps, you can use the max_insample_length argument of the plot method or you can simply zoom in on the plot.

nixtla_client.plot(train_df_gaps, max_insample_length=800)

Additionally, notice a period from March 16, 2020, to April 21, 2020, where the data shows zero rentals. These are not missing values, but actual zeros corresponding to the COVID-19 lockdown in the city.

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Step 4: Fill Missing Values

You can use fill_gaps from utilsforecast to insert the missing dates:

Before using TimeGPT, we need to ensure that:

1. All timestamps from the start date to the end date are present in the data.
2. The target column contains no missing values.

To address the first issue, we will use the fill_gaps function from utilsforecast, a Python package from Nixtla that provides essential utilities for time series forecasting, such as functions for data preprocessing, plotting, and evaluation.

The fill_gaps function will fill in the missing dates in the data. To do this, it requires the following arguments:

• df: The DataFrame containing the time series data.
• freq (str or int): The frequency of the data.

from utilsforecast.preprocessing import fill_gaps

print('Number of rows before filling gaps:', len(train_df_gaps))
train_df_complete = fill_gaps(train_df_gaps, freq='D')
print('Number of rows after filling gaps:', len(train_df_complete))

Number of rows before filling gaps: 2851
Number of rows after filling gaps: 2929

NOTE: In this tutorial, the data contains only one time series. However, TimeGPT supports passing multiple series to the model. In this case, none of the time series can have missing values from their individual earliest timestamp until their individual latest timestamp. If these individual time series have missing values, the user must decide how to fill these gaps for the individual time series. The fill_gaps function provides a couple of additional arguments to assist with this (refer to the documentation for complete details), namely start and end.

Now we need to decide how to fill the missing values in the target column. In this tutorial, we will use interpolation, but it is important to consider the specific context of your data when selecting a filling strategy. For example, if you are dealing with daily retail data, a missing value most likely indicates that there were no sales on that day, and you can fill it with zero. Conversely, if you are working with hourly temperature data, a missing value probably means that the sensor was not functioning, and you might prefer to use interpolation to fill the missing values.

In this case, we will handle the newly inserted missing values by interpolation.

train_df_complete['y'] = train_df_complete['y'].interpolate(
  method='linear', limit_direction='both'
)
train_df_complete.isna().sum()

unique_id    0
ds           0
y            0
dtype: int64

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Step 5: Forecast with TimeGPT

Typically, a horizon > 2 times the typical seasonality is considered long. In this case, the data has a seasonality of 7 days and a horizon of 93 days. Since the forecast horizon is long compared to the frequency of the data (daily), we will use timegpt-1-long-horizon model.

fcst = nixtla_client.forecast(
    train_df_complete,
    h=len(test_df),
    model='timegpt-1-long-horizon'
)

Visualize the forecasts against the actual test data:

nixtla_client.plot(test_df, fcst)

Evaluate performance using utilsforecast. We will use Mean Absolute Error (MAE) as the evaluation metric, but you can choose others like MSE, RMSE, etc.:

from utilsforecast.evaluation import evaluate
from utilsforecast.losses import mae

fcst['ds'] = pd.to_datetime(fcst['ds'])
result = test_df.merge(fcst, on=['ds', 'unique_id'], how='left')

evaluate(result, metrics=[mae])

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Step 6: Conclusion

• Always ensure that your data is free of missing dates and values before forecasting with TimeGPT.
• Select a gap-filling strategy based on your domain knowledge (linear interpolation, constant filling, etc.).

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References

• Exclude COVID Impact in Time Series Forecasting
• Forecasting Time Series with Missing Values