#Set initial values and some bounds
ps = range(0, 5)
d = 1
qs = range(0, 5)
Ps = range(0, 5)
D = 1
Qs = range(0, 5)
s = 5

#Create a list with all possible combinations of parameters
parameters = product(ps, qs, Ps, Qs)
parameters_list = list(parameters)
len(parameters_list)

# Train many SARIMA models to find the best set of parameters
def optimize_SARIMA(parameters_list, d, D, s):
    """
        Return dataframe with parameters and corresponding AIC

        parameters_list - list with (p, q, P, Q) tuples
        d - integration order
        D - seasonal integration order
        s - length of season
    """

    results = []
    best_aic = float('inf')

    for param in tqdm_notebook(parameters_list):
        try: model = sm.tsa.statespace.SARIMAX(data.CLOSE, order=(param[0], d, param[1]),
                                               seasonal_order=(param[2], D, param[3], s)).fit(disp=-1)
        except:
            continue

        aic = model.aic

        #Save best model, AIC and parameters
        if aic < best_aic:
            best_model = model
            best_aic = aic
            best_param = param
        results.append([param, model.aic])

    result_table = pd.DataFrame(results)
    result_table.columns = ['parameters', 'aic']
    #Sort in ascending order, lower AIC is better
    result_table = result_table.sort_values(by='aic', ascending=True).reset_index(drop=True)

    return result_table

result_table = optimize_SARIMA(parameters_list, d, D, s)

#Set parameters that give the lowest AIC (Akaike Information Criteria)
p, q, P, Q = result_table.parameters[0]

best_model = sm.tsa.statespace.SARIMAX(data.CLOSE, order=(p, d, q),
                                       seasonal_order=(P, D, Q, s)).fit(disp=-1)

print(best_model.summary())