# Mathematical modeling. Tasks of exchange rate forecasting

## Scientific approach

One of the most popular tasks of currency dealing and technical analysis of financial data is forecasting. In one form or another, people have faced forecasting tasks at all historical stages of civilization existence. However, until it was based on the following principles scientific approaches and methodsThe forecasts were made on the level of intuition, knowledge and experience of people. For example, folk omens.

The beginning of technical analysis is an attempt to systematize long-term observations of weather or human behavior. This was most often done in order to forecasts tasks on which people's very lives often depended.

Usually forecasting is associated with predicting future events, in particular, the values of time series. However, from the point of view of analytical technologies, forecasting can be considered more broadly. Practically, the determination of some unknown value by a set of related values can be considered as a task of exchange rate forecasting. Therefore, forecasting can be performed with the help of mathematical analysis tasks such as regression, classification and clustering. In terms of data analysis techniques, forecasting can be seen as the determination of some unknown quantity from a set of related values.

## Forecasting methods

All forecasting methods can be divided into three large groups: formalized, heuristic and complex.

–  Formalized methods allow obtaining quantitative indicators describing the state of some object or process as forecasts. It is assumed that the analyzed object or process has the property of inertness, i.e. in the future it will continue to develop in accordance with the same laws by which it developed in the past and exists in the present. The disadvantage of formalized methods is that only historical data can be used for forecasting (which is what uses technical analysis), which are within the evolutionary cycle of an object or process. Therefore, such methods are suitable only for operational and short-term forecasts. Formalized methods include extrapolation and regression methods, methods of mathematical statistics, factor analysis, etc.

–  Heuristic methods are based on the use of expert assessments. An expert (group of experts), relying on his/her knowledge in the subject area and practical experience, is able to predict qualitative changes in the behavior of the object or process under study. These methods are especially useful in cases when the behavior of objects and processes for which a forecast is required is characterized by a large degree of irregularity. While formalized methods (technical analysis) are used for operational and short-term forecasts due to their inherent limitations, heuristic methods (fundamental analysis) are more commonly used for medium-term and prospective.

–  Integrated forecasting uses a combination of formalized approach with expert assessments, which allows to achieve the best result. It follows unambiguously that at mathematical modeling of the forecasting problem It is necessary to use both technical and fundamental analysis of the exchange rate.

## Information collection methods

Methods of collecting information that will form the basis of the forecast may use special surveys, other forecasts, statistical analysis, and time series analysis, brainstorming methods, individual interviews with specialists, etc. Qualitative forecasting requires the following components:

- scientific analysis of these processes,
- Determining and analyzing cause-and-effect and other relationships between them,
- assessing the current situation and identifying the nodal issues that need to be addressed;
- An attempt to foresee the future of the organization in the conditions in which it will function, the problems that will arise and the challenges to overcome them;
- analysis and comparison of various options for the development of business processes in the organization, its personnel, production and scientific and technical potential.

Thus, forecasting refers to A scientific way of identifying the status and likely paths of development of the processes occurring on the financial markets. Forecasts can be developed in the form of qualitative characteristics, and in the simplest cases in the form of statements about the possibility or impossibility of occurrence of any event. These characteristics should include quantitative, point or interval estimates of indicators that characterize the processes and the degree of probability of their achievement.

## Heuristic methods

Earlier articles in this section considered mathematical modeling of the system of trend indicators of technical analysis. Now let us consider heuristic methods [1,2] based on the use of expert evaluations - FACTORS AFFECTING THE EXCHANGE RATE.

Mathematical modeling of the problem of forecasting money turnover - is one of the most important factors influencing the exchange rate of the national monetary unit. Money supplyAs a category, it has a structure that includes, in descending order of liquidity, the following components:

The concept of money supply used in exchange rate calculations is included in M2. The size of money supply is directly related to changes in the exchange rate. When the monetary policy of the state tightens, there is a reduction in the money supply in the country, which leads to a fall in prices and appreciation of the national currency. Thus, reduction of money supply by 1% leads, as a rule, to appreciation of the exchange rate by 1%. In the strategic context, the process of formation of the exchange rate of the national monetary unit with a certain degree of conventionality can be divided into two main stages.

Stage One. Formation of the real exchange rate reflecting the value of the national currency.
Second Stage. Formation of the market exchange rate reflecting the price of the national currency formed on the basis of the real exchange rate under the influence of market supply and demand.

This is possible both for a relatively stable economy of a single country and for an economy in a protracted socio-economic crisis. If we formalize the number of factors (in addition to the monetary circulation discussed above) of economic, political, structural, legal or psychological nature, directly or indirectly affecting the exchange rate of the national currency, their number reaches several dozens. The most significant of them (along with the amount of money supply) are: national income of the country, trade balance, discount rates, expected inflation rates.

The factors listed above can be categorized into the following groups:

1. Factors directly determining the dynamics of the exchange rate or constitutive factors. I.e. directly related to the process of international economic exchange: the gross national product of both countries involved in international exchange: balance of payments; internal and external supply of money; interest rates.
2. Factors affecting the constituent factors and thus having a regulating effect on the exchange rate mechanism. I.e. regulatory factors. Regulatory factors can be divided into government regulation factors and structural factors: structure of currency exchanges; banking structure of the country; communication infrastructure; seasonal factors; directions of foreign economic activity.
3. Factors arising when the economic system is taken out of dynamic equilibrium and therefore negatively affecting the dynamics of the exchange rate of the national monetary unit: crisis manifestations of the economy, political factors and psychological factors.
a. К crisis manifestations of the economy include: state budget deficit, money emission, inflation, monopoly prices, fulfillment of foreign currency inside the country functions of money: a) means of payment in full, b) means of accumulation, c) means of saving.
b. К political factors include the following: change of government representatives, political decisions entailing direct changes in the country's monetary system, the level of reliability in the management of the economic system and the degree of mutual understanding between economic and political structures in society.
c. К psychological factors include: expectation of inflation and devaluation of their national monetary unit, distrust of the national weak currency and fetishization of freely convertible currency, as a consequence of the first factor, lack of appropriate economic thinking among the population, as there are no well-designed programs of national economic recovery in the state due to ill-considered and hasty decisions of the executive authorities.

## Speculative factors

Factors not previously discussed are discussed below. They are: speculative operations; expectation of exchange rate changes.

The impact of speculative operations on the foreign exchange market can be divided into stabilizing and destabilizing.

In speculative transactions, which have the effect of stabilizing effect The change in the exchange rate of the national monetary unit can be represented as a sinusoidal curve deviating from the main trend of the exchange rate (trend). A change in the exchange rate subject to speculation is also a sinusoidal curve, but with a smaller amplitude. Currency is sold at the maximum price, exceeding the trend (as the main trend of the exchange rate), determined by the impact of factors that form the exchange rate. And it is bought at the minimum price, when this price becomes below the trend. As a result of changes in exchange rates, their values approach the trend. The actions of players following this scheme not only stabilize the situation on the currency market, but also bring them profit.

In speculative transactions, which have the effect of destabilizing effect to the currency market, the actions of players lead to an increase in the fluctuations of exchange rates relative to the trend. The currency is bought by players when the exchange rate is at a high level, thereby increasing the rate even more compared to the trend. It turns out that the currency is sold by players when the price of currency falls significantly, thereby lowering the rate even more exchange rate relative to the trend. As a result, players lose money from making these kinds of transactions in the foreign exchange market, buying foreign currency at a higher rate and selling it at a lower rate.

The thing is. currency market destabilization may affect the stability of the economy as a whole, first of all, the state of the financial market. Profit extraction is also possible from destabilizing operations on the currency market. For example, a player starts an operation to buy foreign currency (freely convertible currency) when the exchange rate reaches its maximum value, destabilizing the market and thereby provoking the other market players to increase demand for currency. But as soon as these players start buying up foreign currency on their own, deviating the exchange rate line even more from the trend, the market participant who provoked this situation stops operations on the currency market. When the foreign currency reaches its maximum value, he starts selling the accumulated currency at the maximum rate, gaining profit at the expense of the "provoked" players, who in this case lose their money and may go bankrupt. Thus, at their core, destabilizing operations on the va
However, there are a number of situations in which currency players who create destabilization in the currency market make profits that exceed, and sometimes significantly exceed, their losses.

The trend of exchange rate changes is significantly influenced by currency market participants' actionsbased on their expectations. Since foreign currency can act not only as a means of payment, but also as a means of accumulation (for example, the early US dollar in the economy of the Russian Federation), and can be used to purchase foreign financial assets, changes in exchange rates will affect the yield on these assets. Consequently, holders of such assets, in order to receive the highest income in the national currency, will try to estimate possible changes in the exchange rate in the future. However, if these expectations are not met, the demand for foreign currency will decrease. If the forecast is favorable, the demand for foreign currency will increase. As the world practice shows, the main reference points for participants of the foreign exchange market are: expected changes in the money supply; expected government policy, in particular, the policy affecting private owners of capital, consequences of official interventions in the foreign exchange market. For the above reasons, statements of political leaders, heads of financial authorities about changes in the economy can strengthen the inflationor change the attitude towards private property (confiscation, introduction of new taxes, all kinds of restrictive rules, etc.).

Academic institutions made attempts to build a mathematical model of exchange rate forecasting. However, each time these attempts were unsuccessful. According to experts, such a model should be based on the theory of purchasing power parity. Pro-forecasts of exchange rates, based on data on money supply and income, give significant discrepancies with reality. However, it is possible to forecast the trend component of the exchange rate.

LITERATURE
1. Morozov I.V., Fatkhullin R.R. FOREX: from simple to complex. M.: Omega-L, 2006.-536 pp.
2. Sobolev V.V. Currency dealing on financial markets / Yuzh.-Ros. gos. tehn. un. (NPI). - Novocherkassk, 2009. - 442 с.