## Time Series Prediction with Convolutional Neural Networks and Keras

A convolutional neural network (CNNs) is a type of network that has recently
gained popularity due to its success in classification problems (e.g. image recognition
or time series classification) . One of the working examples how to use Keras CNN for time series can be found at this link. This example allows to predict for single time series and multivariate time series.

Running the code from this link, it was noticed that sometimes the prediction error has very high value, may be because optimizer gets stuck in local minimum. (See Fig1. The error is on axis Y and is very high for run 6) So I updated the script to run several times and then remove results with high error. (See Fig2 The Y axis showing small error values). Here is the summary of all changes:

• Created multiple runs that can allow to filter bad results based on error. Training CNN is running 10 times and for each run error data and some other associated data is saved. Error is calculated as square root of sum if squared errors for last 10 predictions during the training.
• Added also plot to see error over multiple runs.
• In the end of script added one plot that showing errors for each run (See Fig1.) , and another plot showing errors only for runs that did not have high error (See Fig2.).

Below is the full code

``````
#!/usr/bin/env python
"""
This code is based on convolutional neural network model from below link
gist.github.com/jkleint/1d878d0401b28b281eb75016ed29f2ee
"""

from __future__ import print_function, division

import numpy as np
from keras.layers import Convolution1D, Dense, MaxPooling1D, Flatten
from keras.models import Sequential
from keras.models import model_from_json

import matplotlib.pyplot as plt
import csv

__date__ = '2017-06-22'

error_total =[]
result=[]
i=0

def make_timeseries_regressor(window_size, filter_length, nb_input_series=1, nb_outputs=1, nb_filter=4):
""":Return: a Keras Model for predicting the next value in a timeseries given a fixed-size lookback window of previous values.

The model can handle multiple input timeseries (`nb_input_series`) and multiple prediction targets (`nb_outputs`).

:param int window_size: The number of previous timeseries values to use as input features.  Also called lag or lookback.
:param int nb_input_series: The number of input timeseries; 1 for a single timeseries.
The `X` input to ``fit()`` should be an array of shape ``(n_instances, window_size, nb_input_series)``; each instance is
a 2D array of shape ``(window_size, nb_input_series)``.  For example, for `window_size` = 3 and `nb_input_series` = 1 (a
single timeseries), one instance could be ``[, , ]``. See ``make_timeseries_instances()``.
:param int nb_outputs: The output dimension, often equal to the number of inputs.
For each input instance (array with shape ``(window_size, nb_input_series)``), the output is a vector of size `nb_outputs`,
usually the value(s) predicted to come after the last value in that input instance, i.e., the next value
in the sequence. The `y` input to ``fit()`` should be an array of shape ``(n_instances, nb_outputs)``.
:param int filter_length: the size (along the `window_size` dimension) of the sliding window that gets convolved with
each position along each instance. The difference between 1D and 2D convolution is that a 1D filter's "height" is fixed
to the number of input timeseries (its "width" being `filter_length`), and it can only slide along the window
dimension.  This is useful as generally the input timeseries have no spatial/ordinal relationship, so it's not
meaningful to look for patterns that are invariant with respect to subsets of the timeseries.
:param int nb_filter: The number of different filters to learn (roughly, input patterns to recognize).
"""
model = Sequential((
# The first conv layer learns `nb_filter` filters (aka kernels), each of size ``(filter_length, nb_input_series)``.
# Its output will have shape (None, window_size - filter_length + 1, nb_filter), i.e., for each position in
# the input timeseries, the activation of each filter at that position.
Convolution1D(nb_filter=nb_filter, filter_length=filter_length, activation='relu', input_shape=(window_size, nb_input_series)),
MaxPooling1D(),     # Downsample the output of convolution by 2X.
Convolution1D(nb_filter=nb_filter, filter_length=filter_length, activation='relu'),
MaxPooling1D(),
Flatten(),
Dense(nb_outputs, activation='linear'),     # For binary classification, change the activation to 'sigmoid'
))
# To perform (binary) classification instead:
return model

def make_timeseries_instances(timeseries, window_size):
"""Make input features and prediction targets from a `timeseries` for use in machine learning.

:return: A tuple of `(X, y, q)`.  `X` are the inputs to a predictor, a 3D ndarray with shape
``(timeseries.shape - window_size, window_size, timeseries.shape or 1)``.  For each row of `X`, the
corresponding row of `y` is the next value in the timeseries.  The `q` or query is the last instance, what you would use
to predict a hypothetical next (unprovided) value in the `timeseries`.
:param ndarray timeseries: Either a simple vector, or a matrix of shape ``(timestep, series_num)``, i.e., time is axis 0 (the
row) and the series is axis 1 (the column).
:param int window_size: The number of samples to use as input prediction features (also called the lag or lookback).
"""
timeseries = np.asarray(timeseries)
assert 0 < window_size < timeseries.shape
X = np.atleast_3d(np.array([timeseries[start:start + window_size] for start in range(0, timeseries.shape - window_size)]))
y = timeseries[window_size:]
q = np.atleast_3d([timeseries[-window_size:]])
return X, y, q

def evaluate_timeseries(timeseries, window_size):
"""Create a 1D CNN regressor to predict the next value in a `timeseries` using the preceding `window_size` elements
as input features and evaluate its performance.

:param ndarray timeseries: Timeseries data with time increasing down the rows (the leading dimension/axis).
:param int window_size: The number of previous timeseries values to use to predict the next.
"""
filter_length = 5
nb_filter = 4
timeseries = np.atleast_2d(timeseries)
if timeseries.shape == 1:
timeseries = timeseries.T       # Convert 1D vectors to 2D column vectors

nb_samples, nb_series = timeseries.shape
print('\n\nTimeseries ({} samples by {} series):\n'.format(nb_samples, nb_series), timeseries)
model = make_timeseries_regressor(window_size=window_size, filter_length=filter_length, nb_input_series=nb_series, nb_outputs=nb_series, nb_filter=nb_filter)
print('\n\nModel with input size {}, output size {}, {} conv filters of length {}'.format(model.input_shape, model.output_shape, nb_filter, filter_length))
model.summary()

error=[]

X, y, q = make_timeseries_instances(timeseries, window_size)
print('\n\nInput features:', X, '\n\nOutput labels:', y, '\n\nQuery vector:', q, sep='\n')
test_size = int(0.01 * nb_samples)           # In real life you'd want to use 0.2 - 0.5
X_train, X_test, y_train, y_test = X[:-test_size], X[-test_size:], y[:-test_size], y[-test_size:]
model.fit(X_train, y_train, nb_epoch=25, batch_size=2, validation_data=(X_test, y_test))

# serialize model to JSON
model_json = model.to_json()
with open("model"+str(i)+".json", "w") as json_file:
json_file.write(model_json)
# serialize weights to HDF5
model.save_weights("model"+str(i)+".h5")
print("Saved model to disk")
global i
i=i+1

pred = model.predict(X_test)
print('\n\nactual', 'predicted', sep='\t')
error_curr=0
for actual, predicted in zip(y_test, pred.squeeze()):
print(actual.squeeze(), predicted, sep='\t')
tmp = actual-predicted
sum_squared = np.dot(tmp.T , tmp)
error.append ( np.sqrt(sum_squared) )
error_curr=error_curr+ np.sqrt(sum_squared)
print('next', model.predict(q).squeeze(), sep='\t')
result.append  (model.predict(q).squeeze())
error_total.append (error_curr)
print (error)

'''
-----
RETURNS:
A matrix with the file contents
'''

vals = []
with open(fn, 'r') as csvfile:
for row in tsdata:
vals.append(row)

# removing title row
vals = vals[1:]
y = np.array(vals).astype(np.float)
return y

def main():
"""Prepare input data, build model, eval uate."""
np.set_printoptions(threshold=25)
ts_length = 1000
window_size = 50
number_of_runs=10
error_max=200

print('\nSimple single timeseries vector prediction')
timeseries = np.arange(ts_length)                   # The timeseries f(t) = t
# enable below line to run this time series
#evaluate_timeseries(timeseries, window_size)

print('\nMultiple-input, multiple-output prediction')
timeseries = np.array([np.arange(ts_length), -np.arange(ts_length)]).T      # The timeseries f(t) = [t, -t]
# enable below line to run this time series
##evaluate_timeseries(timeseries, window_size)

print('\nMultiple-input, multiple-output prediction')
timeseries = np.array([np.arange(ts_length), -np.arange(ts_length), 2000-np.arange(ts_length)]).T      # The timeseries f(t) = [t, -t]
# enable below line to run this time series
#evaluate_timeseries(timeseries, window_size)

print (timeseries)

for i in range(number_of_runs):
evaluate_timeseries(timeseries, window_size)

error_total_new=[]
for i in range(number_of_runs):
if (error_total[i] < error_max):
error_total_new.append (error_total[i])

plt.plot(error_total)
plt.show()
print (result)

plt.plot(error_total_new)
plt.show()
print (result)

best_model=np.asarray(error_total).argmin(axis=0)
print ("best_model="+str(best_model))

json_file = open('model'+str(best_model)+'.json', 'r')
json_file.close()

# load weights into new model