Optimization of parameters

Let's look at how to optimize the parameters of the models.

AR model

import statsmodels.tsa.api as smtsa
aic=[] 
for ari in range(1, 3): 
 obj_arima = smtsa.ARIMA(ts_log_diff, order=(ari,2,0)).fit(maxlag=30, method='mle', trend='nc') 
 aic.append([ari,2,0, obj_arima.aic])
print(aic)

[[1, 2, 0, -76.46506473849644], [2, 2, 0, -116.1112196485397]]

Therefore, our model parameters are p=2, d=2, and q=0 in this scenario for the AR model, as the AIC for this combination is the least.

ARIMA model

Even for the ARIMA model, we can optimize the parameters by using the following code:

import statsmodels.tsa.api as smtsa
aic=[] 
for ari in range(1, 3): 
     for maj in range(1,3): 
        arima_obj = smtsa.ARIMA(ts_log, order=(ari,1,maj)).fit(maxlag=30, method='mle', trend='nc') 
        aic.append([ari,1, maj, arima_obj.aic])
print(aic)

The following is the output you get by executing the preceding code:

[[1, 1, 1, -242.6262079840165], [1, 1, 2, -248.8648292320533], [2, 1, 1, -251...