How to Find parameters [p, d, q] value for ARIMA model in python?

Question

What is the correct way to predict p, d and q value for parameters for ARIMA model.

How Grid Search help to find these parameters?

How to make Non stationary data to stationary to apply ARIMA?

I have already referred this article

Answer 1

For grid Searching Method you can use an approach which is broken down into two parts:

1. Evaluate an ARIMA model.
   • Split the dataset into training and test sets.
   • Walk the time steps in the test dataset.
     • Train an ARIMA model.
     • Make a one-step prediction.
     • Store prediction; get and store actual observation.
   • Calculate error score for predictions compared to expected values

this the code:

# evaluate an ARIMA model for a given order (p,d,q)
def evaluate_arima_model(X, arima_order):
    # prepare training dataset
    train_size = int(len(X) * 0.66)
    train, test = X[0:train_size], X[train_size:]
    history = [x for x in train]
    # make predictions
    predictions = list()
    for t in range(len(test)):
        model = ARIMA(history, order=arima_order)
        model_fit = model.fit(disp=0)
        yhat = model_fit.forecast()[0]
        predictions.append(yhat)
        history.append(test[t])
    # calculate out of sample error
    error = mean_squared_error(test, predictions)
    return error

2. Evaluate sets of ARIMA parameters this is the code:

# evaluate combinations of p, d and q values for an ARIMA model
def evaluate_models(dataset, p_values, d_values, q_values):
    dataset = dataset.astype('float32')
    best_score, best_cfg = float("inf"), None
    for p in p_values:
        for d in d_values:
            for q in q_values:
                order = (p,d,q)
                try:
                    mse = evaluate_arima_model(dataset, order)
                    if mse < best_score:
                        best_score, best_cfg = mse, order
                    print('ARIMA%s MSE=%.3f' % (order,mse))
                except:
                    continue
    print('Best ARIMA%s MSE=%.3f' % (best_cfg, best_score)) 

For more details you can find in this link a tutorial, in which grid search ARIMA hyperparameters for a one-step rolling forecast is developped, https://machinelearningmastery.com/grid-search-arima-hyperparameters-with-python/