There are many business applications of time series forecasting such as stock price prediction, sales forecasting, weather forecasting etc. A variety of machine learning models are applied in this task of time series forecasting. Every model has its own advantages and disadvantages. In this article, we will see a comparison between two time-series forecasting models – ARIMA model and LSTM RNN model. Both of these models are applied in stock price prediction to see the comparison between them.

**ARIMA Model**

The ARIMA model, or Auto-Regressive Integrated Moving Average model is fitted to the time series data for analyzing the data or to predict the future data points on a time scale. The biggest advantage of this model is that it can be applied in cases where the data shows evidence of non-stationarity.

The auto-regressive means that the evolving variable of interest is regressed on its own prior value and moving average indicates that the regression error is actually a linear combination of error terms whose values occurred contemporaneously and at various times in the past. The significance of integration in the ARIMA model is that the data values have been replaced with the difference between their values and the previous values

For more details on time series analysis using the ARIMA model, please refer to the following articles:-

- An Introductory Guide to Time Series Forecasting
- Time Series Modeling and Stress Testing – Using ARIMAX

**LSTM Recurrent Neural Network**

LSTM, or Long-Short-Term Memory Recurrent Neural Networks are the variants of Artificial Neural Networks. Unlike the feedforward networks where the signals travel in the forward direction only, in LSTM RNN, the data signals travel in backward directions as well as these networks have the feedback connections. The LSTM RNN is popularly used in time series forecasting. For more details on this model, please refer to the following articles:-

- How to Code Your First LSTM Network in Keras
- Hands-On Guide to LSTM Recurrent Neural Network For Stock Market Prediction.

Now, we will see a comparison of forecasting by both the above models. For implementation, we have used the historical prices of stocks to train and test our models. The historical values of stocks are downloaded by *nsepy *that is a python API.

**Implementation of Time Series Forecasting**

First of all, we need to import all the required libraries. *nsepy* must be installed using ‘*pip install nsepy*’ before importing it here. To use LSTM model, the TensorFlow must be installed as the TensorFlow backend is applied for LSTM model. The *pmdarima* must also be installed using ‘*pip install pmdarima*’ to use ARIMA model.

#Importing the libraries from nsepy import get_history as gh import datetime as dt from matplotlib import pyplot as plt from sklearn import model_selection from sklearn.metrics import confusion_matrix from sklearn.preprocessing import StandardScaler from sklearn.model_selection import train_test_split import numpy as np import pandas as pd from sklearn.preprocessing import MinMaxScaler from keras.models import Sequential from keras.layers import Dense from keras.layers import LSTM from keras.layers import Dropout from pmdarima import auto_arima import warnings from statsmodels.tsa.seasonal import seasonal_decompose from statsmodels.tsa.statespace.sarimax import SARIMAX

Once the libraries are installed, we need to fetch the data by passing the start date and the end date to the API function. The downloaded data will be preprocessed after that.

#Setting start and end dates and fetching the historical data start = dt.datetime(2013,1,1) end = dt.datetime(2019,12,31) stk_data = gh(symbol='SBIN',start=start,end=end) #Data Preprocessing stk_data['Date'] = stk_data.index data2 = pd.DataFrame(columns = ['Date', 'Open', 'High', 'Low', 'Close']) data2['Date'] = stk_data['Date'] data2['Open'] = stk_data['Open'] data2['High'] = stk_data['High'] data2['Low'] = stk_data['Low'] data2['Close'] = stk_data['Close']

Once we are ready with the dataset, we will fit the ARIMA model using the below code snippet and plot the result.

#####################ARIMA############################### # Ignore harmless warnings warnings.filterwarnings("ignore") # Fit auto_arima function to Stock Market Data stepwise_fit = auto_arima(data2['Close'], start_p = 1, start_q = 1, 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) # To print the summary stepwise_fit.summary() # Split data into train / test sets train = data2.iloc[:len(data2)-150] test = data2.iloc[len(data2)-150:] # Fit a SARIMAX model = SARIMAX(data2['Close'], order = (0, 1, 1), seasonal_order =(2, 1, 1, 12)) result = model.fit() result.summary() start = len(train) end = len(train) + len(test) - 1 # Predictions for one-year against the test set predictions = result.predict(start, end, typ = 'levels').rename("Predictions") # plot predictions and actual values predictions.plot(legend = True) test['Close'].plot(legend = True)

After visualizing the time-series plot using the ARIMA model, we will see the same analysis by LSTM model.

#############LSTM######################## train_set = data2.iloc[0:1333:, 1:2].values sc = MinMaxScaler(feature_range = (0, 1)) training_set_scaled = sc.fit_transform(train_set) X_train = [] y_train = [] for i in range(60, 1333): X_train.append(training_set_scaled[i-60:i, 0]) y_train.append(training_set_scaled[i, 0]) X_train, y_train = np.array(X_train), np.array(y_train) X_train = np.reshape(X_train, (X_train.shape[0], X_train.shape[1], 1)) #Defining the LSTM Recurrent Model regressor = Sequential() regressor.add(LSTM(units = 50, return_sequences = True, input_shape = (X_train.shape[1], 1))) regressor.add(Dropout(0.2)) regressor.add(LSTM(units = 50, return_sequences = True)) regressor.add(Dropout(0.2)) regressor.add(LSTM(units = 50, return_sequences = True)) regressor.add(Dropout(0.2)) regressor.add(LSTM(units = 50)) regressor.add(Dropout(0.2)) regressor.add(Dense(units = 1)) #Compiling and fitting the model regressor.compile(optimizer = 'adam', loss = 'mean_squared_error') regressor.fit(X_train, y_train, epochs = 15, batch_size = 32) #Fetching the test data and preprocessing testdataframe = gh(symbol='SBIN',start=dt.datetime(2018,5,23),end=dt.datetime(2018,12,31)) testdataframe['Date'] = testdataframe.index testdata = pd.DataFrame(columns = ['Date', 'Open', 'High', 'Low', 'Close']) testdata['Date'] = testdataframe['Date'] testdata['Open'] = testdataframe['Open'] testdata['High'] = testdataframe['High'] testdata['Low'] = testdataframe['Low'] testdata['Close'] = testdataframe['Close'] real_stock_price = testdata.iloc[:, 1:2].values dataset_total = pd.concat((data2['Open'], testdata['Open']), axis = 0) inputs = dataset_total[len(dataset_total) - len(testdata) - 60:].values inputs = inputs.reshape(-1,1) inputs = sc.transform(inputs) X_test = [] for i in range(60, 235): X_test.append(inputs[i-60:i, 0]) X_test = np.array(X_test) X_test = np.reshape(X_test, (X_test.shape[0], X_test.shape[1], 1)) #Making predictions on the test data predicted_stock_price = regressor.predict(X_test) predicted_stock_price = sc.inverse_transform(predicted_stock_price) #Visualizing the prediction plt.figure() plt.plot(real_stock_price, color = 'r', label = 'Close') plt.plot(predicted_stock_price, color = 'b', label = 'Prediction') plt.xlabel('Date') plt.legend() plt.show()

By comparing the two forecasting plots, we can see that the ARIMA model has predicted the closing prices very lower to the actual prices. This large variation in prediction can be seen at the majority of the places across the plot. But in the case of the LSTM model, the same prediction of closing prices can be seen higher than the actual value. But this variation can be observed at few places in the plot and majority of the time, the predicted value seems to be nearby the actual value. So we can conclude that, in the task of stock prediction, the LSTM model has outperformed the ARIMA model.

Finally, for more satisfaction, we will try to find out the Root Mean Squared Error (RMSE) in prediction by both the models.

######RMSE####### from sklearn.metrics import mean_squared_error from statsmodels.tools.eval_measures import rmse # RMSE for ARIMA model err_ARIMA = rmse(test["Close"], predictions) print('RMSE with ARIMA', err_ARIMA) #RMSE for LSTM Model err_LSTM = rmse(test["Close"], predicted_stock_price) print('RMSE with LSTM', err_LSTM)

Seeing the RMSEs, it is clear now that the LSTM model has the best performance in this task.