(FOREX PREDICTION
PROJECT)

*Executive Summary*

Novel high
accuracy system predicting future rates of exchange in the Foreign Exchange
Market (FOREX) is offered. The project initiator is Prof. Leonid Peshes who is a specialist in the theory and practice of
reliability, accelerated life testing, technical and bio-cybernetics, the
analysis of the random processes and chaotic dynamic systems, pattern
recognition, intelligent systems and applied statistics.

*Object
*

FOREX is a giant
mechanism with a present daily turnover about USD 5 trillion which covers the
whole world. This currency amount grows 20-25 % each year. FOREX is a unique
market actively operating around the clock. It is the most dynamic, liquid,
accessible and quickly growing market. FOREX solely determines exchange rates
values for main convertible currencies. Currencies movement depends only on the
freely floating rates of exchange without any essential influence on the
governmental institutions and extraordinary events.

Important
advantage of FOREX comparatively with other markets is use of margin trades.
The margin trade means the possibility to buy and sell currencies when the full
money amount necessary for transaction is not available. To conclude the deal
the trader must deposit only an initial margin and then he may deal with the
currency volume, which exceeds the initial amount 50 – 200 times. Another FOREX
advantage is the possibility to make a profit at any direction of the exchange
rates change.

Fast currencies
movement, low cost and simplicity of realization of the transactions, high
liquidity allow considering FOREX as the most attractive object for business.
The principle of getting the profit from currency
trading which is considered here as an usual commodity is a very simple. A
trader repeatedly sells currencies that fall and buys currencies that rise. If these actions correspond to the actual trend in FOREX so each
such transaction will generate profit. An ability to predict the
exchange rates in accordance with the actual change of rates provides an
unlimited profit potential. FOREX is a basis for an
unique business, which makes it possible to take acute of the profit in the
shortest way: money makes money.

In this particular
project the developer (producer) and the consumer (buyer) is actually the same
entity. Taking into account this fact and also that FOREX is an open market
with free access and without any competitors’ counteractions it precludes the
necessity to look for the customers (buyers) and to spare much money, time and
effort usually required for marketing, promotion, public relations, sales etc.
in contrast to all other businesses.

As a
mathematical object FOREX represents a multivariate times series. It is a very
sophisticated historical process having dual nature. It is a random
non-stationary process with aftereffect and other features, which create
difficulties for its behavior forecasting. On the other hand it is a chaotic
(non-linear) dynamic process reflecting a collective psychology of the market
participants (mainly leaders). For each given short time interval of this
process exists a parameter – fractal which characterize the amount of previous
history (memory) influencing future value of the process which follows the
considered time period.

*Generic
Technology*

The development of the project is based on the generic original
multidimensional Bootstrap technology.
This data-based simulation resampling technique was
initially introduced at the end of 60-th by Prof. L. Peshes.
It was described in several his articles and the book “Fundamentals of
Accelerated Reliability Testing”, Science & Technics,

By using the resampling
procedure (multiple reproduction of the original sample in samples of the same
size with the identical statistical properties) it was obtained a solution of several tasks,
which were earlier inaccessible. In
particular the following problems were solved using this technique:

- definition of the required confidence intervals for any
characteristic of interest,

- selection of the adequate distribution function for the
observed sampled data securing serious
errors elimination in the use of
statistical models.

The software support for the new paradigm
was represented by the package known under the name PARUS (1968).

In 1979 this paradigm was newly discovered
by Prof. Bradley Efron (

The Bootstrap technology is capable to
consider the observed raw data as a pattern of investigation of the real
situation. By utilizing the automatic Bootstrap procedures this technology
allows to extract the necessary information and
knowledge mining in the required direction.

“ It gives us another way to
get empirical information in
circumstances that almost defy mathematical analysis. It is a nice way of
letting the data speak almost for themselves.” –said the world known
statistician Prof.
F. Mosteller from

This approach makes it possible to find a
highly accurate solution of the problem without any need to assume or impose a convenient
model that doesn't have a strong scientific basis. The Bootstrap theory offers
the most powerful and efficient implementation tool in a modern
statistical data analysis. It is a world breakthrough in the field of
statistics. The Bootstrap technique is the best applicable one for areas of activity
which accumulated great volumes of the actual data and which demand new
effective examination, classification, diagnostics, prediction etc. methods in
order to make authentic conclusion.

The most attractive application that ensures
maximal profit is a correct short-term prediction of exchange rates in the
FOREX. The chaos dynamic and fractal approach were successfully integrated in
the frame of the Bootstrap technique in this project.

The main advantages of the proposed
technology are:

1. Industrial technological
approach to data processing in the real-time mode.

2.
Automatic creation of the required knowledge bases on the observed actual data.

3.
Automatic generation and modification of inference engines.

4.
Ability of self-analysis, self-training and self-development in the course of
the system use.

5.
Natural empirical way of data presentation.

Novelty and originality of the prediction system
under consideration is determined
by the use of the principally new
patterns, methods, algoritms and know-how. It secures
its patentability and competitiveness.

*Proposed
Solution*

The input information for a prediction is
the historical data of
the exchange rates movements of the
major convertible currencies for the period
of last 15-20 years. This
original multivariate time series are exposed to some transformation and mapping into vector spaces with various dimensions. The values of the
components of each vector are
the values related to time intervals of identical duration. It is equal to the
prediction period (day, intraday, hour, half hour, quarter hour etc.) and
corresponding components define the state of the currency movements process
during the considered
time-interval.

Each vector is transformed into a new vector
whose components are the meanings (quantative,
qualification and qualitative) reflected by the most inherent peculiarities of the exchange rates behaviour for time intervals under consideration. These
values are determined accordingly to the specific set of functions. The new vector sequence and the serial numbers uniquely
conform to the initial vector time
series and serial numbers of the corresponding
vectors of both time series coincide.

As mentioned above it is important to
estimate duration of the previous history influencing the prediction – a fractal for
the time point immediately preceding the prediction period. If the investigated
time series are created by the dynamic chaotic system (non-linear dynamic
system), then a fractal
is characterized by some quantity
representing effective number of
freedom degrees or the immersion depth
which ensures uniquely prediction.

And if it is considered as a random vector
sequence (time series) a fractal is determined accordingly to the maximal
number of dependent vectors immediately preceding to
the prediction period. This number characterizes the aftereffect length (memory) of the
investigated random process on the forecast moment and determines the immersion depth for a
prediction.

For estimation of the mentioned fractal blocks are
tested consecutively. These blocks
consist of two, three, four and more last vectors of the new time series under
consideration. Initially the block consisting of two vectors (the last and before
last ones) is tested. All adjacent vectors pairs of this random sequence form the multivariate
empirical probability distribution. By means of selection the closest encirlement for the investigated pair of vectors the
empirical density of their joint distribution in the determined range of component values is estimated. This area
determines uniquely the subranges of these values
separately for each of the vectors of the tested pair. It allows to estimate in
them two
empirical corresponding densities. If the quotient of the product of the last
ones to the
joint density is close to one, so the vectors of the examined block are
independent (equality to one of the mentioned ratio is the independence
criterion).

In a similar way a block consisting of three
last vectors is tested. As a result the joint empirical densities for these three vectors and two last vectors and
also the individual densities for each of these vectors are estimated.
Appropriate relations for
the independence criterion are defined.

Densities estimated on this stage for the encirlement of the last and before last vectors and
together for this vectors pair are identical to the previous case but are
related to the more narrow range of their components change.

This testing process is fulfiled
identically also for the expanding blocks of last vectors (with length of
three, four etc.) of the considered time series. Until the
near neighbours may be found for him. The
calculated estimations
of the independence criterion for various lengths blocks in
various ranges of the corresponding vectors components change enable to
determine the required fractal.

To give the required prediction all blocks
(subsequences of adjacent vectors) having length equal to the found fractal are
grouped in the several sets. The rule of grouping is determined by the relative
change of exchange rates in the immediately following after the block vector of
the investigated time series. For example, blocks corresponding to the rate of
increase more than 0.1% are included into a group, corresponding to the rate of
decrease more than 0.1% are included into another group and blocks with
exchange rates change between -0.1% and
+0.1% are included into third group.

Using the near neighbours
for the block of the considered length consisting of last vectors of the
analyzed time series
which are present in every of the indicated sets the appropriate empiric density is estimated.
The selection
of sets defining the prediction is realized on the biggest value of the weighted estimates equal to the
product of corresponding densities on
their weighted coefficient, which
is directly proportional to the elements number in sets.

The reliability of the achieved conclusion is evaluated on the base of the Bootstrap
technique. For each of the sets, determining the prediction, 200-300
Bootstrap samples on its base are reproduced. The corresponding estimates calculated
by the mentioned above way for each of these Bootstrap samples make it
possible to realize the statistical
evaluation of the probability of the fixed prediction correctness.

*Feasibility
and Profit*

The
proposed project even being on the early stage of development allowed to show
the possibility of the essential increase of the forecast accuracy
comparatively to the existing means. On the base of the initial pilot
prototype several real time trial calculations were conducted with various
duration periods in the range 2 -–6 business weeks (10 – 30 business days). A
daily FOREX prediction of the closing price on the major markets in

Several Israeli
companies such as Koor Future Markets Ltd., Menorah
Insurance Company, Eventus
Ltd. etc. took part in the various time periods in appraisal of forecasts of
the USD respectively to three currencies: JPY, GBP, CHF (JPY/USD, USD/GBP, CHF/USD).
The success rate recorded for these experimental predictions was above 70 %.

For some of these time periods the net profit
was calculated and also the annual net profit was evaluated. This annual net
profit corresponding to each currency pair was about 250% and in the
implementation of transactions for pairs with the biggest predicted change the
net profit corresponds 480 %. We want to notice that the highest achievable
(hypothetical ideal) annual net profit corresponding to the transactions for
currency pairs with the biggest actual change of exchange rates might be 1100%.
The credit when the credit leverage is used will secure the net profit 50 –200
times more than the net profit respectively the own marging
of the trader.

To realize the
considered project the reliable software for the forecasting system should be
developed on the first stage (0.5 – 1.0 years). This
software must decrease the working time for predictions and increase their accuracy and
reliability, implement exchange rates’
predictions based on the combined pool of the hystorical
data for the currency pairs allowing to take into account the mutual influence
of these currencies trajectories’
movements (including pair USD/EUR), transition to the automatic
generation of predictions, possibility to predict in the Daily and Intraday
time frames, graphical representation and to provide the regular on-line
currency trading on FOREX. The
historical data for EUR till 2002 will be formed by means of the simulation on
the base of the European currencies which were replaced by EUR, first of all DEM.

On the second stage
(one year) it will be realised the further improvement of quality and
reliability of the system and the increase of the predictions accuracy, the
possibility to predict in the Hourly, Half-Hourly, Quarterly (15 min.) and
other shorter time frames representation, wide use.

The FOREX prediction project’s team consists
of the leading scientists and specialists in the fields of mathematics,
statistics,. computers and
management.