In this tutorial, we explore in detail the cross-validation function in neuralforecast.

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1. Libraries

Make sure to install neuralforecast to follow along. 
!pip install neuralforecast

import logging
import matplotlib.pyplot as plt
import pandas as pd
from utilsforecast.plotting import plot_series

from neuralforecast import NeuralForecast
from neuralforecast.models import NHITS

logging.getLogger("pytorch_lightning").setLevel(logging.ERROR)

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2. Read the data

For this tutorial, we use part of the hourly M4 dataset. It is stored in a parquet file for efficiency. You can use ordinary pandas operations to read your data in other formats likes .csv. The input to NeuralForecast is always a data frame in long format with three columns: unique_id, ds and y:
  • The unique_id (string, int or category) represents an identifier for the series.
  • The ds (datestamp or int) column should be either an integer indexing time or a datestampe ideally like YYYY-MM-DD for a date or YYYY-MM-DD HH:MM:SS for a timestamp.
  • The y (numeric) represents the measurement we wish to forecast.
Depending on your internet connection, this step should take around 10 seconds. 
Y_df = pd.read_parquet('https://datasets-nixtla.s3.amazonaws.com/m4-hourly.parquet')
Y_df.head()
unique_iddsy
0H11605.0
1H12586.0
2H13586.0
3H14559.0
4H15511.0
For simplicity, we use only a single series to explore in detail the cross-validation functionality. Also, let’s use the first 700 time steps, such that we work with round numbers, making it easier to visualize and understand cross-validation. 
Y_df = Y_df.query("unique_id == 'H1'")[:700]
Y_df.head()
unique_iddsy
0H11605.0
1H12586.0
2H13586.0
3H14559.0
4H15511.0
plot_series(Y_df)

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3. Using cross-validation

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3.1 Using n_windows

To use the cross_validation method, we can either: - Set the sizes of a validation and test set - Set a number of cross-validation windows Let’s see how it works in a minimal example. Here, we use the NHITS model and set the horizon to 100, and give an input size of 200. First, let’s use n_windows = 4. We also set step_size equal to the horizon. This parameter controls the distance between each cross-validation window. By setting it equal to the horizon, we perform chained cross-validation where the windows do not overlap. 
h = 100
nf = NeuralForecast(models=[NHITS(h=h, input_size=2*h, max_steps=500, enable_progress_bar=False, logger=False)], freq=1);
cv_df = nf.cross_validation(Y_df, n_windows=4, step_size=h, verbose=0)
cv_df.head()

Seed set to 1
unique_iddscutoffNHITSy
0H1301300490.048950485.0
1H1302300537.713867525.0
2H1303300612.900635585.0
3H1304300689.346313670.0
4H1305300760.153992747.0
cutoffs = cv_df['cutoff'].unique()

plt.figure(figsize=(15,5))
plt.plot(Y_df['ds'], Y_df['y'])
plt.plot(cv_df['ds'], cv_df['NHITS'], label='NHITS', ls='--')

for cutoff in cutoffs:
    plt.axvline(x=cutoff, color='black', ls=':')

plt.xlabel('Time steps')
plt.ylabel('Target [H1]')
plt.legend()
plt.tight_layout()
In the figure above, we see that we have 4 cutoff points, which correspond to our four cross-validation windows. Of course, notice that the windows are set from the end of the dataset. That way, the model trains on past data to predict future data.
Important note We start counting at 0, so counting from 0 to 99 results in a sequence of 100 data points.
Thus, the model is initially trained using time steps 0 to 299. Then, to make predictions, it takes time steps 100 to 299 (input size of 200) and it makes predictions for time steps 300 to 399 (horizon of 100). Then, the actual values from 200 to 399 (because our model has an input_size of 200) are used to generate predictions over the next window, from 400 to 499. This process is repeated until we run out of windows.

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3.2 Using a validation and test set

Instead of setting a number of windows, we can define a validation and test set. In that case, we must set n_windows=None 
cv_df_val_test = nf.cross_validation(Y_df, val_size=200, test_size=200, step_size=h, n_windows=None)

cutoffs = cv_df_val_test['cutoff'].unique()
plt.figure(figsize=(15,5))

# Plot the original data and NHITS predictions
plt.plot(Y_df['ds'], Y_df['y'])
plt.plot(cv_df_val_test['ds'], cv_df_val_test['NHITS'], label='NHITS', ls='--')

# Add highlighted areas for validation and test sets
plt.axvspan(Y_df['ds'].iloc[300], Y_df['ds'].iloc[499], alpha=0.2, color='yellow', label='Validation Set')
plt.axvspan(Y_df['ds'].iloc[500], Y_df['ds'].iloc[699], alpha=0.2, color='red', label='Test Set')

# Add vertical lines for cutoffs
for cutoff in cutoffs:
    plt.axvline(x=cutoff, color='black', ls=':')

# Set labels and legend
plt.xlabel('Time steps')
plt.ylabel('Target [H1]')
plt.legend()

plt.tight_layout()
plt.show()
Here, we predict only the test set, which corresponds to the last 200 time steps. Since the model has a forecast horizon of 100, and step_size is also set to 100, there are only two cross-validation windows in the test set (200/100 = 2). Thus, we only see two cutoff points.

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3.3 Cross-validation with refit

In the previous sections, we trained the model only once and predicted over many cross-validation windows. However, in real life, we often retrain our model with new observed data before making the next set of predictions. We can simulate that process using refit=True. That way, the model is retrained at every step in the cross-validation process. In other words, the training set is gradually expanded with new observed values and the model is retrained before making the next set of predictions. 
cv_df_refit = nf.cross_validation(Y_df, n_windows=4, step_size=h, refit=True)

cutoffs = cv_df_refit['cutoff'].unique()

plt.figure(figsize=(15,5))
plt.plot(Y_df['ds'], Y_df['y'])
plt.plot(cv_df_refit['ds'], cv_df_refit['NHITS'], label='NHITS', ls='--')

for cutoff in cutoffs:
    plt.axvline(x=cutoff, color='black', ls=':')

plt.xlabel('Time steps')
plt.ylabel('Target [H1]')
plt.legend()
plt.tight_layout()
Notice that when we run cross-validation with refit=True, there were 4 training loops that were completed. This is expected because the model is now retrained with new data for each fold in the cross-validation: - fold 1: train on the first 300 steps, predict the next 100 - fold 2: train on the first 400 steps, predict the next 100 - fold 3: train on the first 500 steps, predict the next 100 - fold 4: train on the first 600 steps, predict the next 100

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3.4 Overlapping windows in cross-validation

In the case where step_size is smaller than the horizon, we get overlapping windows. This means that we make predictions more than once for some time steps. This is useful to test the model over more forecast windows, and it provides a more robust evaluation, as the model is tested across different segments of the series. However, it comes with a higher computation cost, as we are making predictions more than once for some of the time steps. 
cv_df_refit_overlap = nf.cross_validation(Y_df, n_windows=2, step_size=50, refit=True)

cutoffs = cv_df_refit_overlap['cutoff'].unique()

fold1 = cv_df_refit_overlap.query("cutoff==550")
fold2 = cv_df_refit_overlap.query("cutoff==600")

plt.figure(figsize=(15,5))
plt.plot(Y_df['ds'], Y_df['y'])
plt.plot(fold1['ds'], fold1['NHITS'], label='NHITS (fold 1)', ls='--', color='blue')
plt.plot(fold2['ds'], fold2['NHITS'], label='NHITS (fold 2)', ls='-.', color='red')

for cutoff in cutoffs:
    plt.axvline(x=cutoff, color='black', ls=':')

plt.xlabel('Time steps')
plt.ylabel('Target [H1]')
plt.xlim(500, 700)
plt.legend()
plt.tight_layout()
In the figure above, we see that our two folds overlap between time steps 601 and 650, since the step size is 50. This happens because: - fold 1: model is trained using time steps 0 to 550 and predicts 551 to 650 (h=100) - fold 2: model is trained using time steps 0 to 600 (step_size=50) and predicts 601 to 700 Be aware that when evaluating a model trained with overlapping cross-validation windows, some time steps have more than one prediction. This may bias your evaluation metric, as the repeated time steps are taken into account in the metric multiple times.