Introduction

Market of FOREX (FOReign EXchange market) is the interbank market of exchange of one currencies on other, formed in 1971, when international trade passed from the fixed currency exchanges rates to floating ones. A market is the aggregate of transactions of agents of currency market on the exchange of the stipulated sums of monetary item of one country on currency of other on-course concerted upon the certain date. Contracts consist at the market of FOREX, mainly, with the purpose of game on the difference of rates of exchange. At an exchange an one currency exchange rate in relation to other concerns very simply: by demand and supply is exchange which both sides agree to.

Main feature of currency market of Forex, bringing over to him shallow players, is possibility of purchase and sale of foreign currencies in default of at the trader of all sum necessary for the finance of transaction. Brokers providing services of marginal trade require bringing of mortgage deposit and enable to the client to accomplish operations of purchase-sale of currencies on sums, in 40 – 50, sometimes in 100 times greater, than the borne deposit. The risk of losses is laid on a client, a deposit insures a broker.

The profitableness of investing at this market depends on the change of quotations of currencies. The currency market of Forex attracts investors by the quickness of finance of transaction and additional bank service – crediting of transactions with a credit shoulder from 1:1 to 1:1000.

Moving of capital is the engine of currency market of Forex between the states, economic indicators of leading countries of world, political, psychological factors and also technical analysis.

    Relevance of the theme

Developed theme there is quite actual, the because volumes of operations of world currency market grow constantly, that related to development of international trade abolition of currency limitations in many countries. In addition, presently, when Ukraine prepares to the entry in WTO, exchange trade becomes for our country by the very widespread and perspective type of activity, which causes the necessity of leading researches in area of forecasting of conduct of the prices exchanges graphs. These researches will help to build exact prognoses applying, in obedience to recommendations, one or another model of class of ARIMA.

Choosing correct strategy of conduct, a trader, at a relatively small deposit (how was mentioned higher), can make handsome profit during the short period of time. For the choice of correct strategy of conduct, a trader must make the statistical analysis of the present prices graphs, execute the short-term prognosis of conduct of the prices graphs on the nearest bars and to define, whether the turn of market will not happen on the nearest bars. As the prices graphs in reality are transients, creation of such model which will be adequate to the constantly changing market situation is needed.

In-process this as a prognosis model the regressive model of ARIMA is chosen. ARIMA-processes are the class of stochastic processes in-use for the analysis of temporal rows. Models allow getting exact prognoses, leaning only against the information contained in prehistory of the forecast rows of the prices graphs. These models behave to the class of linear models and can well describe both stationary and unstationary temporal rows. In addition, analyzing the scientific publications of the last decade it is possible to see that in the overwhelming amount of works on prognostication by classic methods ARIMA is used exactly, as the most grounded and reliable algorithm (from statistical).

    Goals and objectives of the work

The goal of this work is determination of the best model from the great number of models of ARIMA for construction of short-term prognosis of conduct of the prices graphs for the different values of temporal window of prognostication, also determination of the most suitable model for realization of prognosis on the certain areas of the price graph. Thus, purpose of this work is choice of prognosis model of ARIMA depending on the size of temporal window of realization of prognosis and in-use criterion, formulation of high-quality recommendations on the choice and use of model on the basis of quantitative estimations.

Picture. 1 - Schematic description of implementation of forecasting the prices graphs by the ARIMA models with different sets of parameters. (Animation consists of 12 frames, 10 cicles)

Forecasting by the models of ARIMA is successfully carried out long time already enough, but the novelty of this work consists of leadthrough of complex analysis of advantages and lacks of the use of concrete model from the class of ARIMA depending on the folded market situation. For this purpose prognostication is in-process conducted by the different models of ARIMA (models with the different sets of parameters). An executions sequence is following: to identify a model, I.e. to define the amount of parameters of different type, which are in a model, estimate model parameters, explore model adequacy and on the basis of model to build a prognosis, after to define the best prognosis model.

    Model selection criterions

In-process model which allow carrying out the most high-quality forecast, concerns by two criteria. The criteria of choice the best model are following: maximization value of probability of realization correct forecast, which is calculated for each of models ARIMA with different set of parameters separately for the forecasting with different values of temporal window ( m1 = 15 and m2 = 30 ), and minimization of root-sum-square uncertainty of forecasting.

The value of probability is calculating in following way:

,

where
k_i – the number of cases, when the forecasted value deviates from the real no more than ± 2 σ,
n – general number of forecasted value.

After the calculation of all values , we should find the maximal one from them () and exactly the model with set of parameters nomber i is consider the best model according to this criterion. During work for realization of short-term forecasting based on real data of fluctuations of exchange rates, the ARIMA (p,d,q) model is used for the different values of temporal window and forecast is carried out on a next bar (on one value ahead), and the got results are compared between itself.

Minimization of middle quadratic error of the prognosis got by a certain model is the second criterion of choice of the most suitable model. The value of root-sum-square error is calculated in following way:

,

where
y_j – real data
– data, got as a consequence of forecasting using model number i.

After the calculation of all values , we should find the minimal one from them () and exactly the model with set of parameters nomber i is consider the best model according to this criterion. During work for realization of short-term forecasting based on real data of fluctuations of exchange rates, the ARIMA (p,d,q) model is used for the different values of temporal window and forecast is carried out on a next bar (on one value ahead), and the got results are compared between itself.

    Research results

For formulation of qualitative recommendations as for using of ARIMA model with the certain sets of parameters on the different areas of the price graph, the comparative analysis of short-term forecasting implemented with help of different models. On a picture 2 is represented the price graph of currency exchanges rates of the EUR-USD market of Forex from 01.05.2002 to 18.09.2002 (100 values)

Picture.2 - Prices graphics of Forex 01.05.2002-18.09.2002

The temporal window m = 30 is chosen and forecasting is carried out on a 1 bar ahead. From present real data was built a corridor ± 2 σ. On the real moment forecasting is executed by the models of ARIMA (1,0,0) and ARIMA (0,0,1), which, in fact, are the models of autoregressive AR(1) and moving average MA(1) accordingly. On a picture 3 the got values of short-term prognosis are represented by the indicated models.

Picture.3 - Forecasting by models ARIMA(1,0,0) и ARIMA(0,0,1)

Conducting testing on accordance to the 1st criterion, the following results were got:
The values of probabilities are accordingly and , The values of probabilities are accordingly equal and, thereby, in obedience to the criterion of maximization probability of adequate forecast, the model ARIMA(1,0,0) is considered the best.
It is visible from the graph, that

• on this area of the price graph the model ARIMA (1,0,0) gives more accurate forecast, than ARIMA (0,0,1).
• both models expressly enough predict the turn of market (change the trend’s direction)
• both models stop to give an adequate data, when the turn of market have place - this position requires further detailed analysis, possibly, it is necessary to change the value of temporal window and to repeat a forecasting
• the sharp change of market situation is reflected by these models with some delay
• the model of moving average gives an adequate prognosis in less than 50% cases and strongly different from the real information, possibly because it gives identical weight both to more new prices and more old, although more logical would be to consider new prices are more important, because reflects a market situation more near to the present moment.

    Conclusion

Forecasting with larger value of temporal window gives more accurate result, because forecasting by ARIMA models is executed by the analysis of information which is contained in prehistory of temporal row, and the more value of temporal window the plenty of information is present for implementation of analysis and construction of high-quality forecasts.

Advantages of ARIMA models:

• Approach of Box-Jenkins to the analysis of temporal rows is a very powerful instrument for construction of accurate forecasts with small distance of forecasting.
• ARIMA models are flexible enough and can describe the wide spectrum of descriptions of temporal rows which meet in practice.

Disadvantages of ARIMA models:

• It is necessary to have a great number of basic data
• There is no simple method of adjustment of parameters of ARIMA models, – when new information is attracted, a model has to be almost fully reconstructed.
• Also for estimations one or another model is used, and it means the presence of model risk in calculations. Therefore it is necessary to do periodic verification of adequacy of the applied model.
• So, the general weakness of forecasting with these models consists in that all of them regardless of the applied methods of calculation use historical information. And if conditions at the market (for example, correlation between assets) have changed sharply, these changes will be taken into account only through the certain interval of time. And to this moment of prediction will be improper.

Afore-named factors result in that these models work well in the case of stable markets condition and stop adequately reflecting the conduct of prices, when there are the substantial changes at the markets.

As a result of work a conclusion will be done about the rules of application ARIMA model with different sets of parameters for realization short-term forecasting at the market FOREX and will be developed some recommendations for adjustment by the traders their strategy of the conduct and effective management of assets.

At present moment the work is developing, researches in full size are not completed yet, completion of the project is planned by December 2007.

It is in-process planned to conduct the analysis of forecasting of the prices graphs with the different value of temporal window by the following models:

• (1,0,0) – autoregressive function;
• (0,1,0) – moving average;
• (1,0,1) – the combined model of autoregressive and moving average;
• (0,1,1) – exponential average;
• (1,1,1) – transient with linear trend

    References

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