STOCK
MARKET PREDICTION USING NEURAL NETWORKS
by
Dr. Valentin Steinhauer
Disclaimer:
No liability assumed
for
accuracy ,
completeness of the methods and other information in this
tutorial.
Short description
Here are
considered two complementary directions:
one - time
series prediction, the second
- Bollinger Bands method.
Why are they selected?
In the quiet time
the harmonicas
laws prevail and at this point
are good a
time series prediction.
This method (from
different sources) allows
a prediction up and down in the stock market values
with about
52%-53%
probability, 50% -50% is, don’t
forget, random.
Second
direction (Bollinger Bands) is from
completely different area:
the stock market nervousness.
When prices fall or
grow too much
compared to earlier times,
then there
is often a turning point.
Statistics of positive predictions
in this case are better.
But the cases do not occur
as often, and it will be required
waiting.
Time series prediction
in stock market
Time series prediction plays a big
role in economics. The stock market courses, as well as the consumption of energy
can be predicted to be able to make decisions. This tutorial shows one possible
approach how neural networks can be used for this kind of prediction. It extends
the Neuroph tutorial called "Time
Series Prediction",
that
gives a good theoretical base for prediction.
Used
for
our purposes, the time
sequence is observing
variable. Variable
observed at discrete
time intervals. The analysis of
time series includes a description
of the process or phenomenon, which
generates a sequence. To predict
the time series, it is necessary
to present the behavior
of the process in the
form of a mathematical model that
can be extended in the future.
To do this, the model is
a good representation of observations
in any local segment
of time close to the present.
Usually there is no need
to have a model that would represent
a very old observations,
as they probably will not characterize
the moment. Also there is no
need to submit observations
in the distant future, je
after a time interval that is greater
than the horizon.
Once the correct
model will be created
to handle the temporal
sequence, we can develop appropriate
means of prediction.
To show how it works, we trained the
network with the DAX (German stock index) data – for a month (03.2009: from
02th to 30) - to predict the value at 31.03.2009. As a strategy we take the
sequences from 4 days to predict each 5th day. In the training set 5th day is
the supervised value. The data DAX can be downloaded from the following URL
(one of the possibilities):
http://download.finance.yahoo.com/d/quotes.csv?s=^GDAXI&f=sl1d1t1c1ohgv&e=.cs
TrainingSetGetter is available for
download as a part of NetBeans project, however it is only the hard coded example
data with normalization . Also the
first step is the normalization of the training data in area (0-1). The
following formula offers it as follows:
Norm.value = 0.8 (value – v1) /
(v2 – v1) + 0.1,
Here 0.8 and 0.1 are the
values to correct data set from limits 0 and 1, v2 is the maximum value * expander
and v1 – minimum value/expander. The normalization plays important role in preparation
of data for network training. This “expander” coefficient is entered for compression
or stretching at a normalization. In each case of
a prediction it is desirable to select this coefficient from control points.
Next, the network topology is defined:
what type of network, how many layers and how many neurons per layer are used.
Actually, there is no rule for this, and usually it is determined experimentaly.
However the common type of network used for prediction is a
multi layer perceptron. A recommendation is to have 2n+1 nodes for
hidden-layer, where n is the number of the input nodes. The output layer has
only one node in this case.
The good results were obtained
with the following topology and parameter set: maxIteration=10000, maxerror=0.0001
and the training set is organized as follows:
public
DataSet getTrainingSet(int n, int m) {
trainingSet
= new DataSet(n, m);
……………………………………….
trainingSet.addRow(in,
out);
……………………………………….
and
corresponding network is:
int
maxIterations = 10000;
NeuralNetwork neuralNet = new
MultiLayerPerceptron(4, 9, 1);
((LMS) neuralNet.getLearningRule()).setMaxError(0.0001);
((LMS) neuralNet.getLearningRule()).setMaxIterations(maxIterations);
neuralNet.learn(trainingSet);
At this point, we are ready to train
and test the network. For testing we'll use prepared data set in which the DAX
data are given from the 27,28,29 and 30.03.09 to
predict the value at 31.03.09
neuralNet.setInput(test);
neuralNet.calculate();
double[]
networkOutput = neuralNet.getOutput();
double
predictedNormalized = networkOutput[0] ;
Since the network is initialised with
random weight values, the test results will differ from a calculation to calculation.
After five tests it came out with the following prediction - results for 03.31.2009:
4084.61; 4081.28; 4073.08; 4075.22; 4087.42.
The duration time was 3 sec ( 2 CPU, 3.3Ghz,
2GB Ram, WinXP).
That
is so called a committee - a collection of different neural
networks, that together present the example, with
“expander” 1.30D. It gives a much better
result compared to other neural networks procedures. The value which was official
announced on that day is 4084.76.
Therefore
in
direction of obtaining better quantitative results is changing the sequence
of calculations, which we carried out in previous example. We can use concurrent
calculations to create the committee. The committee tends not only to
a stability but it also allows an effective relative
control of training conditions. Relative scattering of the results from committee
is the figure of merit in this case. To create the concurrency we used the
jetlang package.
The committee includes the following
modules in the example: Actor, Channels, Message and it will be controlled from
the Main module.
The periodic signals
prevail in this model ( postulate ). Which periodic
signal is major? Where is the under fitting or over fitting of perceptron? Is
it possible to automatically predict in this model?
We'll show an algorithm with auto-correction which demonstrates some basic development
ideas ("a biggest harmonicas wave"):
1.
We have more than one
sequence of calculations ( see "committee")
2.
The main circle gives the
variation of number of points (N) in the window of time prediction. A head period
is determined by N in every variation from "a biggest harmonicas wave". The
number of hidden layers is 2*N+1 automatic. As figure of merit will be used
the R = ∑ | |F_{obs}| - |F_{calc}| | /
∑ |F_{obs}| , so called
R-factor
through full time series data.
3.
For each N will be variety
the training sets: the elements will be removed
consecutively to achieve the minimum of R-factor and to achieve the optimal
relationship between the under fitting and over fitting.
4.
The middle value through
committee is the result of this simple automatic flow.
How good is this model
"a biggest harmonicas wave" for your tasks, you should decide yourself. The
simple DAX tests showed good mathematical results.
This
filtering of the model
are similar
to the human
sleep: trainings models are
maximally reduced, but when the recognition
is improved.
By time series
prediction the best
results
were
obtained when analyzing the
grow and fall of
stock values,
not for a
prognosis of values
yourself.
Bollinger Bands in
stock market with Neuroph
Bollinger Bands
is invented by John Bolliger.^{ }Bollinger Bands indicate a variation
of price of a financial instrument over time.
The exit for borders of bands conducts
with a high probability to return to bands. And the main difficulty is to find:
when does occur the return? To predict this return
we use Neuroph. Bollinger Bands reflects degree of nervousness and are well
suitable for not stabile stock market. You can read more about the Bollinger
Bands in other documents [
Wiki,
for example] . We will us concentrate on the using technique with Neuroph.
The main parameters for
Bollinger Bands are
As the test data will
be used DAX.
Consider the training
work of this method
as an example.
In a prepared
file, which contains the values
of
Dax for one day
with a 5
minute intervals will be search for
situation going beyond the
value of the average. To average
it is detected number of
21 last
values experimentally. The output
is 1, if the
current value of
Dax is upper 2
sigma average
or below
2 sigma from
average and in the 15 min is the behavior correct, in other cases it is 0. “Correct”
means the value returns to the band. The sigma is the standard deviation
and it will be calculated in the method “standardAbweichung” dynamically.
The algorithm is implemented in the
program BollingerAnalyze see
the appendix (project package). The normalization is
similar to that shown
above, see the “normalize”
method in the BollingerAnalyze.java.
In the
training program
will be
estimated (in order to control) the frequency of correct operation
of the method: how many cases
are right from all cases. You can
try other parameters for your coals. Using the
trained network is shown
in the method getRecommendation.
The method gives 1 or -1 if you have Bollinger Bands situation (up or down)
and in 15 minutes will
return DAX in the band. In a bad case it is 0 or the value can
not be predicted.
Of course a big
problem is
to obtain the values
in
real time. However, this is
an organizational problem and it
may be made with the dynamic
Neuroph value recognition from images
in real time probably.
The message
after the training and test is as the follow:
extremes
number = 4707 bollingers extremes number.
= 1006 full number of points = 21136 defects = 1. In the case “defects” means
how many bollinger situation were not correct predicted.
Finally,
two important factors in predicting
problems - possibilities and
interests of people who make and
use prediction. Ideally,
the historical information is analyzed
automatically, and the forecast
is a manager
for a possible modification.
The introduction of an expert in
the forecasting process is important,
but it requires the cooperation of
experienced managers. Next
forecast sent
to managers, who use it
to make decisions. And even if
they say the weather
is just talk,
they can get real benefits
from its use.
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