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**Introduction.**

FOREX – is the abbreviation from the English words FOReign EXchange market.
Forex – is the largest financial market in the world, whose day turnover makes one and a half billion dollars.
In contrast to other financial markets, Forex has no central stock exchange. It functions by means of an electronic network (including the Internet),
whose units are banks, corporations and the private persons trading in currencies with each other. Absence of a central unit allows Forex market to work 24h/7days
[http://russian.mgforex.com/].

MG Financial Group(http://www.mgforex.com/)
- the leader of the Forex on-line technologies - has published the first version of its on-line trading platform (Deal Station) in April 1997.
This program allows traders to view currency rates, to make transactions and to trace open positions in real time mode.
The distinctive feature of DealStation is that it constantly refreshes all its information (continually).
The last development - DealStation 2000 is constructed on the basis of the newest technology "Push" Java which allows "to push" new information on a trader’s computer as soon as it becomes accessible.
One of competitors of the Deal Station is a program complex WinChart, which belongs to Straits Index company (http://www.straitsindex.com/).
One of the advantages of this program is an opportunity to study the elements of the technical analysis.

There are two approaches to the analysis of the currency market – fundamental and technical.
With the help of the fundamental analysis one can determine forces of supply and demand on the basis of financial and economic theories, which are based on the political-economical situation. The technical analysis examines trading rates and volumes on the basis of graphic representation of currency rates in time and it is directed on a tendency diagnosis in the future.
The technical analysis allows predicting exchange rates movements on the basis of the last trading rates and volumes data research.
This type of analysis relies on heuristic formulas for tracing the rate movement tendencies and allows to estimate opportunities for currency sale or currency purchases. Diagrams are: with 5-minute, 15-minute, 60-minute and 24 hour interval. Diagrams with a week and a month intervals are also applied. The last mentioned diagrams serve for an estimation of long-term tendencies.

**I. The examples of technical analysis.**

**1. 1. Levels of a relative minimum and maximum.**

Levels of a relative minimum and maximum are points where the diagram passes from decrease to increase and on the contrary (fig.1). The probability of exceeding these points is considered to be insignificant, therefore purchase or sale is more preferable at the moments of relative minima and maxima.

Fig.1.

**2. Direct lines and channels of the tendency.**

Direct lines are a simple, but powerful tool for trend revealation, i.e. the market tendencies.
They connect some consecutive maxima or minima which belong to some local trend.
Continuation of the line shows the most probable direction of the market movement in the future.
The channel represents a corridor of quotation changes and is defined as a part of a plane between the parallel straight linees constructed on maxima and on minima. Fig.2 represents the classical example of increase trend, but fig.3 gives an example of the channel localization.

Fig.2.

Fig.3.

**3. Current (dynamical) averages.**

Current average allows generalize trends and show the average price for a certain period of time.
Fig.4 contains three curves of average values, which depend on the period of averaging - a day, a week and a month.
There are three types of dynamic average indices: usual, linearly weighed and exponentially smoothed.
The exponential smoothing is considered to be more exact, from the probability of a prediction point of view, since it gives a greater weight to the rather recent data.
The usual average is counted up under the formula:

where **n**, for example, stands for the amount of days.

Fig.4.

**4. Bands.**

The Current average characterizes the process of the quotation changes on average.
To estimate statistics of local extremums (maxima and minima) according to the average,
one calculates an average square of deviations (RMS). Fig.5. represents an example of RMS diagrams,
which form the band. Thus RMS can serve as a measure of probability.
The formulas for calculation are represented below.

where **D*** - is a standard deviation, **n** is the amount of days,

Fig.5.

**I I. The elements of the probabilistic analysis of the Forex market.**

The stated above things illustrate the fact, that all efforts of the technical analysis are aimed at an estimation of the probability
of a forthcoming event. The technical analysis operates with the most important statistical characteristics - average, RMS,
statistics (moments) of higher orders. However, the actual probability remains unclaimed. At the same time, the probabilistic
analysis elements can be successfully used both for the calculation of probabilities, and as the graphic tool which is well known
to traders.

The results of the estimation researches of the quotation Forex market currencies probabilities are represented below.
These researches include the special software developing and the realization (on basis of the software) of the physical
simulation and the calculation of the probabilistic distributions of real exchange rates.

**1. The Simulation of distribution of DM quotations.**

Fig.6.

Fig.6 shows the modelling distribution of the daily diagram of the DM quotations.
There are three highlighted trends **a, b, c** on the diagram. Trends **a, b** are increasing, **c** is neutral.
The value of DM =1.8376 in a range of trend **b** determination is marked with a red mark. Fig.7 shows
a diagram of the distribution of probabilities. Right from the beginning it is necessary to note, that the trends represent
a regular mistake and basically they should be removed. However, in a context of accomplishing a task, they serve as a helpful
information. Fig.8 shows a smoothed curve of distribution of probabilities. From the analysis of distributions in fig.7 and fig.8 it
becomes clear that there is a visible trend division (localization).
It is not possible in the traditional technical analysis.

Fig.7.

Fig.8.

**2. The localization of trends of real distribution of quotations DM.**

Fig.9 shows the daily diagram of the DM quotations from the 30th of April 1997 until the 14th of June 1998.
The total amount is 297 reports. DM =1.7646 is marked with a red mark. Fig.11 and fig.12 show the diagrams of the probability
distribution. From the examination of the abovementioned diagrams it is clear that

Fig.9.

Fig.10.

Fig.11.

that the analyzable value belongs to the group of trends of the transition period, which goes from the low values
of quotations to the higher ones. The probability of getting into this group of trends is insignificant. For graphic calculation of
probabilities we shall transform distribution on fig.11 into the integral of probabilities, which is shown on fig.12.

fig.12.

From the examination of the above mentioned diagrams it is clear that the probability of DM quotations can be found within
the given interval **[1.6748; 1.7646]** and it makes about 30 %.

**3. The removal of "a regular mistake". **

To make a calculation of probabilities with the given (high) accuracy, we will need to remove the trends (fig.13).
By the way, the removal of trends is also practiced in traditional technical analysis. Fig. 14 shows required distribution of the
casual process probabilities of absolute quotation changes in fig.13. The appearance of distribution is a good evidence that the
analyzed, random process is normal or at least quasi- normal. To get stronger evidence it is necessary to apply the " chi-square".

fig.13.

fig.14.

If in the diagram belonging tî the fig.14 one counts up an integral of probabilities in an interval from **-0.0370 up to .0006**
(red mark), it will be equal to 0.1986. Thus, it is possible to assert, that the quotation change of DM in the
limits from **-0.0370 up to .0006** is expected with the probability about **20 %**. If we shall count up an integral
of probabilities for a symmetric DM interval, the general probability will be about **38 %**. The latter will allow to assert
that the change of DM quotations in an interval **[-0.0060; + 0.0060]** is necessary to expect with the
confidential probability of **62 %**.

**4. Application Markoff’s transitional probabilities.**

Processes of change of exchange rates are processes stochastic,
i.e. represent set both determined (trend) and casual events (fig.13, fig.14). The conclusion about expediency of application
Markoff’s transitional probabilities from here follows, which characterize process of transitions (for example, in time) random
variable **χ** from one condition **χ _{i}** in other condition

If to speak about process of change of quotations of currencies transitional probabilities it is conditional probabilities

Fig.15.

The basic property Markoff’s probabilities is memory of previous transitions. This property in a context of a considered problem can be formulated as follows: distribution of probabilities

The formulation of a real situation can look as follows. At the order of the trader there are data on 15-minute change of rate EURO/USD for the last 3 - 4 months. (for example, Bid Price). The sequence of values EURO/USD forms Markoff’s circuit

[ 4 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 5 25 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 1 29 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 7 27 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 8 49 20 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 21 67 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 6 26 2 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 1 5 2 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 1 5 1 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 8 2 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 1 9 1 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 5 6 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 5 48 8 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 7 17 3 1 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 16 2 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 5 2 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 3 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 17 4 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 54 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]. |

M-1 |

Σp_{i,j} = 1, |

j =0 |

where M - the greatest value of transitions in system EURO/USD. The appropriate matrix of transitive probabilities will look like:

[ .4444 .5556 0 0 0 0 0 0 0 0 0 . . . [ .1613 .8065 .0323 0 0 0 0 0 0 0 0 . . . [ 0 .027 .7838 .1892 0 0 0 0 0 0 0 . . . [ 0 0 .1667 .6429 .1905 0 0 0 0 0 0 . . . [ 0 0 0 .1026 .6282 .2564 .0128 0 0 0 0 . . . [ 0 0 0 0 .2234 .7128 .0638 0 0 0 0 . . . [ 0 0 0 0 0 .1765 .7647 .0588 0 0 0 . . . [ 0 0 0 0 0 0 .125 .625 .25 0 0 . . . [ 0 0 0 0 0 0 0 .1429 .7143 .1429 0 . . . . . . . . . . . . |

The condition of system EURO/USD at the present moment of time is equal to a vector of probabilities:

The condition of system EURO/USD in 15 minutes is described by expression and a vector:

= [0 0 0 .02292 .2996

*Decision Making.*
If as algorithm for the Decision Making we shall use search of a maximum of probability (.5766) the condition of quotation
EURO/USD will be former, since **i=5**.

Below the table of 15-minute predication (**Predict**) EURO/USD is submitted during 8 hours June, 11 2003.
The probability **Pmax** an expected condition **i**, is maximal for all transitions **j=>i,
j=0..M-1**.
In last column of the table values of mistakes of prediction (**Err [%]**) in percentage.

No. | Date | Real | Predict. | Pmax | Err [%] |
---|---|---|---|---|---|

1 | Wed Jun 11 04:39:43 2003 | 1.1677 | 0 | 0.00 | 100.00 |

2 | Wed Jun 11 04:54:47 2003 | 1.1672 | 1.1677 | 0.19 | -0.04 |

3 | Wed Jun 11 05:09:52 2003 | 1.1671 | 1.1672 | 0.45 | -0.01 |

4 | Wed Jun 11 05:24:57 2003 | 1.1671 | 1.1671 | 0.48 | 0.00 |

5 | Wed Jun 11 05:40:02 2003 | 1.1670 | 1.1671 | 0.52 | -0.01 |

6 | Wed Jun 11 05:55:06 2003 | 1.1659 | 1.1671 | 0.18 | -0.10 |

7 | Wed Jun 11 06:10:11 2003 | 1.1668 | 1.1670 | 0.33 | -0.02 |

8 | Wed Jun 11 06:25:16 2003 | 1.1673 | 1.1671 | 0.31 | 0.02 |

9 | Wed Jun 11 06:40:20 2003 | 1.1680 | 1.1677 | 0.15 | 0.03 |

10 | Wed Jun 11 06:55:25 2003 | 1.1673 | 1.1673 | 0.19 | 0.00 |

11 | Wed Jun 11 07:10:30 2003 | 1.1671 | 1.1677 | 0.16 | -0.05 |

12 | Wed Jun 11 07:25:35 2003 | 1.1675 | 1.1671 | 0.45 | 0.03 |

13 | Wed Jun 11 07:40:39 2003 | 1.1677 | 1.1675 | 0.15 | 0.02 |

14 | Wed Jun 11 07:55:44 2003 | 1.1675 | 1.1671 | 0.22 | 0.03 |

15 | Wed Jun 11 08:10:49 2003 | 1.1676 | 1.1675 | 0.17 | 0.01 |

16 | Wed Jun 11 08:25:54 2003 | 1.1712 | 1.1671 | 0.20 | 0.35 |

17 | Wed Jun 11 08:40:59 2003 | 1.1711 | 1.1713 | 0.19 | -0.02 |

18 | Wed Jun 11 08:56:03 2003 | 1.1715 | 1.1713 | 0.19 | 0.02 |

19 | Wed Jun 11 09:11:08 2003 | 1.1708 | 1.1715 | 0.20 | -0.06 |

20 | Wed Jun 11 09:26:13 2003 | 1.1705 | 1.1715 | 0.16 | -0.09 |

21 | Wed Jun 11 09:41:18 2003 | 1.1707 | 1.1701 | 0.42 | 0.05 |

22 | Wed Jun 11 09:56:24 2003 | 1.1715 | 1.1715 | 0.13 | 0.00 |

23 | Wed Jun 11 10:11:31 2003 | 1.1709 | 1.1715 | 0.21 | -0.05 |

24 | Wed Jun 11 10:24:41 2003 | 1.1727 | 1.1709 | 0.22 | 0.15 |

25 | Wed Jun 11 10:39:02 2003 | 1.1720 | 1.1725 | 0.12 | -0.04 |

26 | Wed Jun 11 10:54:07 2003 | 1.1723 | 1.1715 | 0.21 | 0.07 |

27 | Wed Jun 11 11:09:18 2003 | 1.1709 | 1.1715 | 0.11 | -0.05 |

28 | Wed Jun 11 11:24:23 2003 | 1.1708 | 1.1709 | 0.19 | -0.01 |

29 | Wed Jun 11 11:39:32 2003 | 1.1690 | 1.1715 | 0.14 | -0.21 |

30 | Wed Jun 11 11:54:42 2003 | 1.1698 | 1.1691 | 0.15 | 0.06 |

31 | Wed Jun 11 12:09:48 2003 | 1.1704 | 1.1701 | 0.37 | 0.03 |

32 | Wed Jun 11 12:24:54 2003 | 1.1707 | 1.1709 | 0.14 | -0.02 |

33 | Wed Jun 11 12:32:47 2003 | 1.1707 | 1.1715 | 0.12 | -0.07 |

Values of real quotations and values of predictions are illustrated with the help of the diagram (fig. 18), where

Fig.18.

The diagram of mistakes is shown on fig. 19, where

Fig.19.

The represented results of the probability distribution of currency quotations research for the market Forex show the following.

**a.** They allow to interprete the state of Forex market both as a graphic form of representation of probability distributions,
and as the numerical characteristics.

**b.** The represented numerical characteristics of the probability analysis (integrals of probabilities and confidential
probabilities) have generalizing character and can be used for a long-term forecasts. The software, in a context
of long-term forecasts, can be static i.e. to use some database of currency quotations. The software, in a context of
long-term forecasts, can be static i.e. use some database of currency quotations. The database can be refilled by a user
in a manual style. The static version development of such a program will take 2- 3 months. The dynamic version development
will take extra man-hours. The difference between the dynamic software and the static one is that for getting the currency
quotations in a real time the dynamic software has to contain an additional functional block. Example: