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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

model.predict(X)

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[0], train.shape[1])
    train_scaled = scaler.transform(train)
    # transform test
    test = test.reshape(test.shape[0], test.shape[1])
    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[0], 1, X.shape[1])
    model = Sequential()
    model.add(LSTM(neurons, batch_input_shape=(batch_size, X.shape[1], X.shape[2]), 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=[0], 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()
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  • $\begingroup$ scaling might be a problem if max / min values are not present in training samples. Then scaling an out-of-sample point might scale it wrongly $\endgroup$ – Nikos M. Apr 25 at 16:32
  • $\begingroup$ @NikosM. Thanks Nikos. Do you mean that I should removing scaling step or changing the min/max values? $\endgroup$ – Jasey Mon Apr 25 at 16:51
  • $\begingroup$ Scaling is useful to limit dynamic range, as long as min/max values are indeed known befopre-hand. This is my objection $\endgroup$ – Nikos M. Apr 25 at 19:43
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In order to predict the first out-of-sample datapoint you should take a sequence of the data and pass it to the LSTM model (example in pseudo-code):

pred = model.predict(X[-10:])

For the next predictions you'll have to include the current prediction into the data passed to the model.

X = X + [pred]
next_pred = model.predict(X)
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