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 has a total of 6 hyperparameters that must be 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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# Libraries
# ==============================================================================
import pandas as pd
import matplotlib.pyplot as plt
from skforecast.model_selection_statsmodels import grid_search_sarimax
# Libraries
# ==============================================================================
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':]

# Plot
# ==============================================================================
fig, ax=plt.subplots(figsize=(9, 4))
data_train.plot(ax=ax, label='train')
data_val.plot(ax=ax, label='validation')
data_test.plot(ax=ax, label='test')
ax.legend();
# 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':]

# Plot
# ==============================================================================
fig, ax=plt.subplots(figsize=(9, 4))
data_train.plot(ax=ax, label='train')
data_val.plot(ax=ax, label='validation')
data_test.plot(ax=ax, label='test')
ax.legend();

Grid Search¶

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import warnings
warnings.filterwarnings('ignore')
import warnings
warnings.filterwarnings('ignore')

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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),
                   fixed_train_size = False,
                   steps = 7,
                   metric = 'mean_absolute_error',
                   refit = False,
                   verbose = False,
                   fit_kwargs = {'maxiter': 200, 'disp': 0}
               )

results_grid
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),
                   fixed_train_size = False,
                   steps = 7,
                   metric = 'mean_absolute_error',
                   refit = False,
                   verbose = False,
                   fit_kwargs = {'maxiter': 200, 'disp': 0}
               )

results_grid

root       INFO  Number of models compared: 15
100%|█████████████████████████████████████████████████████| 15/15 [00:29<00:00,  1.97s/it]

Out[5]:

	params	metric	order	seasonal_order	trend
12	{'order': (14, 1, 4), 'seasonal_order': (0, 0,...	0.050256	(14, 1, 4)	(0, 0, 0, 0)	None
13	{'order': (14, 1, 4), 'seasonal_order': (0, 0,...	0.050256	(14, 1, 4)	(0, 0, 0, 0)	n
9	{'order': (12, 1, 1), 'seasonal_order': (0, 0,...	0.050467	(12, 1, 1)	(0, 0, 0, 0)	None
10	{'order': (12, 1, 1), 'seasonal_order': (0, 0,...	0.050467	(12, 1, 1)	(0, 0, 0, 0)	n
14	{'order': (14, 1, 4), 'seasonal_order': (0, 0,...	0.051899	(14, 1, 4)	(0, 0, 0, 0)	c
11	{'order': (12, 1, 1), 'seasonal_order': (0, 0,...	0.051981	(12, 1, 1)	(0, 0, 0, 0)	c
6	{'order': (12, 1, 0), 'seasonal_order': (0, 0,...	0.052858	(12, 1, 0)	(0, 0, 0, 0)	None
7	{'order': (12, 1, 0), 'seasonal_order': (0, 0,...	0.052858	(12, 1, 0)	(0, 0, 0, 0)	n
8	{'order': (12, 1, 0), 'seasonal_order': (0, 0,...	0.053497	(12, 1, 0)	(0, 0, 0, 0)	c
3	{'order': (12, 2, 0), 'seasonal_order': (0, 0,...	0.054425	(12, 2, 0)	(0, 0, 0, 0)	None
4	{'order': (12, 2, 0), 'seasonal_order': (0, 0,...	0.054425	(12, 2, 0)	(0, 0, 0, 0)	n
5	{'order': (12, 2, 0), 'seasonal_order': (0, 0,...	0.054500	(12, 2, 0)	(0, 0, 0, 0)	c
0	{'order': (12, 0, 0), 'seasonal_order': (0, 0,...	0.063656	(12, 0, 0)	(0, 0, 0, 0)	None
1	{'order': (12, 0, 0), 'seasonal_order': (0, 0,...	0.063656	(12, 0, 0)	(0, 0, 0, 0)	n
2	{'order': (12, 0, 0), 'seasonal_order': (0, 0,...	0.064095	(12, 0, 0)	(0, 0, 0, 0)	c

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