I'm working on a time series forecasting problem using LSTM. The data is univariate and non-stationary. I followed this tutorial.
The data is processed as the following: First, the difference between each two consecutive time points is taken. Then, the data is formatted as a supervised learning problem by making the next time points as labels. Finally, scaling between 1 and -1 is performed. The processed data is then used to fit the LSTM model. The same processing steps are done with testing data to check the LSTM predicting. The inverse of the difference and scaling is performed to show the predicted values. Everything is ok and I got good results on the testing set. But the problem is when I want to predict the next time point which is out of sample. Suppose I have 100 data points, 70 points are used for training, 30 for testing, and I want to predict the point number 101 and so on. I tried to use
but it doesn't work. X can't simply be the last time point in the dataset, because the model should receive X as a sequence of the processed (differenced and scaled) data. I don't know what I should do to make the model predict the next (out of sample) points. Anyone can help, please?
Here is the code that I'm following:
from pandas import DataFrame from pandas import Series from pandas import concat from pandas import read_csv from pandas import datetime from sklearn.metrics import mean_squared_error from sklearn.preprocessing import MinMaxScaler from keras.models import Sequential from keras.layers import Dense from keras.layers import LSTM from math import sqrt from matplotlib import pyplot import numpy # date-time parsing function for loading the dataset def parser(x): return datetime.strptime('190'+x, '%Y-%m') # frame a sequence as a supervised learning problem def timeseries_to_supervised(data, lag=1): df = DataFrame(data) columns = [df.shift(i) for i in range(1, lag+1)] columns.append(df) df = concat(columns, axis=1) df.fillna(0, inplace=True) return df # create a differenced series def difference(dataset, interval=1): diff = list() for i in range(interval, len(dataset)): value = dataset[i] - dataset[i - interval] diff.append(value) return Series(diff) # invert differenced value def inverse_difference(history, yhat, interval=1): return yhat + history[-interval] # scale train and test data to [-1, 1] def scale(train, test): # fit scaler scaler = MinMaxScaler(feature_range=(-1, 1)) scaler = scaler.fit(train) # transform train train = train.reshape(train.shape, train.shape) train_scaled = scaler.transform(train) # transform test test = test.reshape(test.shape, test.shape) test_scaled = scaler.transform(test) return scaler, train_scaled, test_scaled # inverse scaling for a forecasted value def invert_scale(scaler, X, value): new_row = [x for x in X] + [value] array = numpy.array(new_row) array = array.reshape(1, len(array)) inverted = scaler.inverse_transform(array) return inverted[0, -1] # fit an LSTM network to training data def fit_lstm(train, batch_size, nb_epoch, neurons): X, y = train[:, 0:-1], train[:, -1] X = X.reshape(X.shape, 1, X.shape) model = Sequential() model.add(LSTM(neurons, batch_input_shape=(batch_size, X.shape, X.shape), stateful=True)) model.add(Dense(1)) model.compile(loss='mean_squared_error', optimizer='adam') for i in range(nb_epoch): model.fit(X, y, epochs=1, batch_size=batch_size, verbose=0, shuffle=False) model.reset_states() return model # make a one-step forecast def forecast_lstm(model, batch_size, X): X = X.reshape(1, 1, len(X)) yhat = model.predict(X, batch_size=batch_size) return yhat[0,0] # load dataset series = read_csv('shampoo-sales.csv', header=0, parse_dates=, index_col=0, squeeze=True, date_parser=parser) # transform data to be stationary raw_values = series.values diff_values = difference(raw_values, 1) # transform data to be supervised learning supervised = timeseries_to_supervised(diff_values, 1) supervised_values = supervised.values # split data into train and test-sets train, test = supervised_values[0:-12], supervised_values[-12:] # transform the scale of the data scaler, train_scaled, test_scaled = scale(train, test) # fit the model lstm_model = fit_lstm(train_scaled, 1, 3000, 4) # forecast the entire training dataset to build up state for forecasting train_reshaped = train_scaled[:, 0].reshape(len(train_scaled), 1, 1) lstm_model.predict(train_reshaped, batch_size=1) # walk-forward validation on the test data predictions = list() for i in range(len(test_scaled)): # make one-step forecast X, y = test_scaled[i, 0:-1], test_scaled[i, -1] yhat = forecast_lstm(lstm_model, 1, X) # invert scaling yhat = invert_scale(scaler, X, yhat) # invert differencing yhat = inverse_difference(raw_values, yhat, len(test_scaled)+1-i) # store forecast predictions.append(yhat) expected = raw_values[len(train) + i + 1] print('Month=%d, Predicted=%f, Expected=%f' % (i+1, yhat, expected)) # report performance rmse = sqrt(mean_squared_error(raw_values[-12:], predictions)) print('Test RMSE: %.3f' % rmse) # line plot of observed vs predicted pyplot.plot(raw_values[-12:]) pyplot.plot(predictions) pyplot.show()