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Forecasting time series with missing values
Missing values in time series forecasting¶
In many real use cases of forecasting, although historical data are available, it is common for the time series to be incomplete. The presence of missing values in the data is a major problem since most forecasting algorithms require the time series to be complete in order to train a model.
A commonly employed strategy to overcome this problem is to impute missing values before training the model, for example, using a moving average. However, the quality of the imputations may not be good, impairing the training of the model. One way to improve the imputation strategy is to combine it with weighted time series forecasting. The latter consists of reducing the weight of the imputed observations and thus their influence during model training.
This document shows two examples of how skforecast makes it easy to apply this strategy.
Libraries¶
# Libraries
# ==============================================================================
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
plt.style.use('fivethirtyeight')
dark_style = {
'figure.facecolor': '#212946',
'axes.facecolor': '#212946',
'savefig.facecolor':'#212946',
'axes.grid': True,
'axes.grid.which': 'both',
'axes.spines.left': False,
'axes.spines.right': False,
'axes.spines.top': False,
'axes.spines.bottom': False,
'grid.color': '#2A3459',
'grid.linewidth': '1',
'text.color': '0.9',
'axes.labelcolor': '0.9',
'xtick.color': '0.9',
'ytick.color': '0.9',
'font.size': 12,
'lines.linewidth': 1.5
}
plt.rcParams.update(dark_style)
from sklearn.linear_model import Ridge
from lightgbm import LGBMRegressor
from sklearn.metrics import mean_absolute_error
from skforecast.ForecasterAutoreg import ForecasterAutoreg
from skforecast.model_selection import backtesting_forecaster
Note
In this document, a forecaster of typeForecasterAutoreg is used. The same strategy can be applied with any forecaster from skforecast.
Data¶
# Data download
# ==============================================================================
url = (
'https://raw.githubusercontent.com/JoaquinAmatRodrigo/'
'Estadistica-machine-learning-python/master/data/usuarios_diarios_bicimad.csv'
)
data = pd.read_csv(url, sep=',')
# Data preprocessing
# ==============================================================================
data['fecha'] = pd.to_datetime(data['fecha'], format='%Y-%m-%d')
data = data[['fecha', 'Usos bicis total día']]
data.columns = ['date', 'users']
data = data.set_index('date')
data = data.asfreq('D')
data = data.sort_index()
data.head(3)
# Generating gaps with missing values
# ==============================================================================
gaps = [
['2020-09-01', '2020-10-10'],
['2020-11-08', '2020-12-15'],
]
for gap in gaps:
data.loc[gap[0]:gap[1]] = np.nan
# Split data into train-test
# ==============================================================================
data = data.loc['2020-06-01': '2021-06-01']
end_train = '2021-03-01'
data_train = data.loc[: end_train, :]
data_test = data.loc[end_train:, :]
print(f"Dates train : {data_train.index.min()} --- {data_train.index.max()} (n={len(data_train)})")
print(f"Dates test : {data_test.index.min()} --- {data_test.index.max()} (n={len(data_test)})")
# Time series plot
# ==============================================================================
fig, ax = plt.subplots(figsize=(12, 4))
data_train.users.plot(ax=ax, label='train', linewidth=1)
data_test.users.plot(ax=ax, label='test', linewidth=1)
for gap in gaps:
ax.plot(
[pd.to_datetime(gap[0]), pd.to_datetime(gap[1])],
[data.users[pd.to_datetime(gap[0]) - pd.Timedelta(days=1)],
data.users[pd.to_datetime(gap[1]) + pd.Timedelta(days=1)]],
color = 'red',
linestyle = '--',
label = 'gap'
)
ax.set_title('Number of users BiciMAD')
handles, labels = plt.gca().get_legend_handles_labels()
by_label = dict(zip(labels, handles))
ax.legend(by_label.values(), by_label.keys(), loc='lower right');
Impute missing values¶
# Value imputation using linear interpolation
# ======================================================================================
data['users_imputed'] = data['users'].interpolate(method='linear')
data_train = data.loc[: end_train, :]
data_test = data.loc[end_train:, :]
Using imputed values in model training¶
# Create recursive multi-step forecaster (ForecasterAutoreg)
# ==============================================================================
forecaster = ForecasterAutoreg(
regressor = LGBMRegressor(random_state=123),
lags = 14
)
# Backtesting: predict next 7 days at a time.
# ==============================================================================
metric, predictions = backtesting_forecaster(
forecaster = forecaster,
y = data.users_imputed,
initial_train_size = len(data.loc[:end_train]),
fixed_train_size = False,
steps = 7,
metric = 'mean_absolute_error',
refit = True,
verbose = False
)
print(f"Backtesting metric (mean_absolute_error): {metric:.2f}")
predictions.head(4)
Give weight of zero to imputed values¶
To minimize the influence on the model of imputed values, a custom function is defined to create weights following the rules:
Weight of 0 if the index date has been imputed or is within 14 days ahead of an imputed day.
Weight of 1 otherwise.
If an observation has a weight of 0, it has no influence at all during model training.
Note
Imputed values should neither participate in the training process as a target nor as a predictor (lag). Therefore, values within a window size as large as the lags used should also be excluded.# Custom function to create weights
# ==============================================================================
def custom_weights(index):
"""
Return 0 if index is in any gap.
"""
gaps = [
['2020-09-01', '2020-10-10'],
['2020-11-08', '2020-12-15'],
]
missing_dates = [pd.date_range(
start = pd.to_datetime(gap[0]) + pd.Timedelta('14d'),
end = pd.to_datetime(gap[1]) + pd.Timedelta('14d'),
freq = 'D'
) for gap in gaps]
missing_dates = pd.DatetimeIndex(np.concatenate(missing_dates))
weights = np.where(index.isin(missing_dates), 0, 1)
return weights
Again, a ForecasterAutoreg is trained but this time including the custom_weights function.
# Create recursive multi-step forecaster (ForecasterAutoreg)
# ==============================================================================
forecaster = ForecasterAutoreg(
regressor = LGBMRegressor(random_state=123),
lags = 14,
weight_func = custom_weights
)
# Backtesting: predict next 7 days at a time.
# ==============================================================================
metric, predictions = backtesting_forecaster(
forecaster = forecaster,
y = data.users_imputed,
initial_train_size = len(data.loc[:end_train]),
fixed_train_size = False,
steps = 7,
metric = 'mean_absolute_error',
refit = True,
verbose = False
)
print(f"Backtesting metric (mean_absolute_error): {metric:.2f}")
predictions.head(4)
Giving a weight of 0 to the imputed values (excluding it from the model training) improves the forecasting performance.
Información de sesión¶
import session_info
session_info.show(html=False)
¿How to cite this document?
Exclude covid impact in time series forecasting by Joaquín Amat Rodrigo and Javier Escobar Ortiz, available under a CC BY-NC-SA 4.0 at https://www.cienciadedatos.net/documentos/py45-weighted-time-series-forecasting.html 
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This work by Joaquín Amat Rodrigo and Javier Escobar Ortiz is licensed under a Attribution-NonCommercial-ShareAlike 4.0 International.