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.




   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, Minsk, 1972.

   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 (Stanford University) and he named it Bootstrap. Due to his works this technology gained popularity and got wide application.


   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 Harward University (New York Times, 08.11.1988).

   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 London and New York was realized. The results of the forecasting were made available 15 – 20 hours before the actual values of the closing exchange rates were really formed on the FOREX.

   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.


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