SARIMAX Model (sarima + Exogenous variable).py

#Continuing with our Sarima Model we will be adding an exogenous variable (thus SARIMAX)
#returning to the forecasting portion of our last model 

data = pd.read_csv('https://raw.githubusercontent.com/selva86/datasets/master/a10.csv', parse_dates=['date'], index_col='date')
#same dataset as before, which belongs to selva86 on github.

from statsmodels.tsa.seasonal import seasonal_decompose
from dateutil.parser import parse

result_mul = seasonal_decompose(data['value'][-36:],   
                                model='multiply', 
                                extrapolate_trend='freq')

seasonal_index = result_mul.seasonal[-12:].to_frame()
seasonal_index['month'] = pd.to_datetime(seasonal_index.index).month


data['month'] = data.index.month
df = pd.merge(data, seasonal_index, how='left', on='month')
df.columns = ['value', 'month', 'seasonal_index']
df.index = data.index  

import pmdarima as pm

#Actual Model
sxmodel = pm.auto_arima(df[['value']], exogenous=df[['seasonal_index']],
                           start_p=1, start_q=1,
                           test='adf',
                           max_p=3, max_q=3, m=12,
                           start_P=0, seasonal=True,
                           d=None, D=1, trace=True,
                           error_action='ignore',  
                           suppress_warnings=True, 
                           stepwise=True)

sxmodel.summary()

Fit ARIMA: order=(1, 0, 1) seasonal_order=(0, 1, 1, 12); AIC=536.818, BIC=556.362, Fit time=2.083 seconds
Fit ARIMA: order=(0, 0, 0) seasonal_order=(0, 1, 0, 12); AIC=626.061, BIC=635.834, Fit time=0.033 seconds
Fit ARIMA: order=(1, 0, 0) seasonal_order=(1, 1, 0, 12); AIC=598.004, BIC=614.292, Fit time=0.682 seconds
Fit ARIMA: order=(0, 0, 1) seasonal_order=(0, 1, 1, 12); AIC=613.475, BIC=629.762, Fit time=0.510 seconds
Fit ARIMA: order=(1, 0, 1) seasonal_order=(1, 1, 1, 12); AIC=559.530, BIC=582.332, Fit time=3.129 seconds
(...Truncated...)
Fit ARIMA: order=(3, 0, 0) seasonal_order=(0, 1, 0, 12); AIC=556.094, BIC=575.639, Fit time=0.260 seconds
Fit ARIMA: order=(3, 0, 0) seasonal_order=(0, 1, 2, 12); AIC=531.502, BIC=557.562, Fit time=2.375 seconds
Fit ARIMA: order=(3, 0, 0) seasonal_order=(1, 1, 2, 12); AIC=nan, BIC=nan, Fit time=nan seconds
Total fit time: 30.781 seconds

n_periods = 24
fitted, confint = sxmodel.predict(n_periods=n_periods, 
                                  exogenous=np.tile(seasonal_index.value, 2).reshape(-1,1), 
                                  return_conf_int=True)

index_of_fc = pd.date_range(data.index[-1], periods = n_periods, freq='MS')


fitted_series = pd.Series(fitted, index=index_of_fc)
lower_series = pd.Series(confint[:, 0], index=index_of_fc)
upper_series = pd.Series(confint[:, 1], index=index_of_fc)


plt.plot(data['value'])
plt.plot(fitted_series, color='green')
plt.fill_between(lower_series.index, 
                 lower_series, 
                 upper_series, 
                 color='k', alpha=.15)

plt.title("Nate's SARIMAX Model")
plt.show()