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Grid search SARIMAX and ARIMA models

SARIMAX (Seasonal Auto-Regressive Integrated Moving Average with eXogenous factors) is a generalization of the ARIMA model that allows incorporating seasonality and exogenous variables. This model have a total of 6 hyperparameters that must specified when training the model:

  • p: Trend autoregression order.

  • d: Trend difference order.

  • q: Trend moving average order.

  • P: Seasonal autoregressive order.

  • D: Seasonal difference order.

  • Q: Seasonal moving average order.

  • m: The number of time steps for a single seasonal period.

One way to find the best values is by using grid search. The grid_search_sarimax function of the skforecast.model_selection_statsmodels module is a wrapper that automates this process using the SARIMAX implementation available in the statsmodels library.

Libraries

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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from skforecast.model_selection_statsmodels import grid_search_sarimax

Data

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# Download data
# ==============================================================================
url = ('https://raw.githubusercontent.com/JoaquinAmatRodrigo/skforecast/master/data/h2o.csv')
data = pd.read_csv(url, sep=',', header=0, names=['y', 'datetime'])

# Data preprocessing
# ==============================================================================
data['datetime'] = pd.to_datetime(data['datetime'], format='%Y/%m/%d')
data = data.set_index('datetime')
data = data.asfreq('MS')
data = data['y']
data = data.sort_index()

# Split train-test
# ==============================================================================
steps = 24
data_train = data.loc[: '2001-01-01']
data_val = data.loc['2001-01-01' : '2006-01-01']
data_test  = data.loc['2006-01-01':]

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param_grid = {'order': [(12, 0, 0), (12, 2, 0), (12, 1, 0), (12, 1, 1), (14, 1, 4)],
             'seasonal_order': [(0, 0, 0, 0)],
             'trend': [None, 'n', 'c']}

results_grid = grid_search_sarimax(
                y = data.loc[:'2006-01-01'],
                param_grid = param_grid,
                initial_train_size = len(data_train),
                steps = 7,
                metric = 'mean_absolute_error',
                refit = False,
                verbose = False,
                fit_kwargs = {'maxiter': 200, 'disp': 0}
             )

print(results_grid.to_markdown(tablefmt="github", index=False))

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root       INFO  Number of models compared: 15
100%|█████████████████████████████████████████████████████| 15/15 [01:08<00:00,  4.60s/it]

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results_grid
params metric order seasonal_order trend
{'order': (12, 1, 1), 'seasonal_order': (0, 0, 0, 0), 'trend': None} 0.0504759 (12, 1, 1) (0, 0, 0, 0)
{'order': (12, 1, 1), 'seasonal_order': (0, 0, 0, 0), 'trend': 'n'} 0.0504759 (12, 1, 1) (0, 0, 0, 0) n
{'order': (14, 1, 4), 'seasonal_order': (0, 0, 0, 0), 'trend': None} 0.0505509 (14, 1, 4) (0, 0, 0, 0)
{'order': (14, 1, 4), 'seasonal_order': (0, 0, 0, 0), 'trend': 'n'} 0.0505509 (14, 1, 4) (0, 0, 0, 0) n
{'order': (12, 1, 1), 'seasonal_order': (0, 0, 0, 0), 'trend': 'c'} 0.0518921 (12, 1, 1) (0, 0, 0, 0) c
{'order': (12, 1, 0), 'seasonal_order': (0, 0, 0, 0), 'trend': None} 0.0528397 (12, 1, 0) (0, 0, 0, 0)
{'order': (12, 1, 0), 'seasonal_order': (0, 0, 0, 0), 'trend': 'n'} 0.0528397 (12, 1, 0) (0, 0, 0, 0) n
{'order': (12, 1, 0), 'seasonal_order': (0, 0, 0, 0), 'trend': 'c'} 0.0534996 (12, 1, 0) (0, 0, 0, 0) c
{'order': (14, 1, 4), 'seasonal_order': (0, 0, 0, 0), 'trend': 'c'} 0.0537079 (14, 1, 4) (0, 0, 0, 0) c
{'order': (12, 2, 0), 'seasonal_order': (0, 0, 0, 0), 'trend': None} 0.054425 (12, 2, 0) (0, 0, 0, 0)
{'order': (12, 2, 0), 'seasonal_order': (0, 0, 0, 0), 'trend': 'n'} 0.054425 (12, 2, 0) (0, 0, 0, 0) n
{'order': (12, 2, 0), 'seasonal_order': (0, 0, 0, 0), 'trend': 'c'} 0.0544985 (12, 2, 0) (0, 0, 0, 0) c
{'order': (12, 0, 0), 'seasonal_order': (0, 0, 0, 0), 'trend': None} 0.0636531 (12, 0, 0) (0, 0, 0, 0)
{'order': (12, 0, 0), 'seasonal_order': (0, 0, 0, 0), 'trend': 'n'} 0.0636531 (12, 0, 0) (0, 0, 0, 0) n
{'order': (12, 0, 0), 'seasonal_order': (0, 0, 0, 0), 'trend': 'c'} 0.0640216 (12, 0, 0) (0, 0, 0, 0) c