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Trading strategies intended for high frequency trading in Forex markets are executed by cutting-edge automated trading systems. Such systems implement algorithmic trading strategies and are configured with predefined optimized parameters in order to generate entry and exit orders and execute trades on trading platforms. Three high-frequency automated trading systems were developed in the current research, using the MACD (oscillator), the SMA (moving average) and the PIVOT points (price crossover) technical indicators. The systems traded on hourly time frames, employing historical data of closing prices and the parameter optimization for each system was done using the d-Backtest PS method over weekly periods. With this work we intend to extend the methods of parameter selection for automated trading systems in high frequency trading. Through this research and the interpretation and evaluation of its results, we conclude that backtesting parameters' optimization, especially through the d-Backtest PS method, is much more profitable than the default values of the parameters and that the optimization of parameters yields the highest profits through the implementation of restrictive relationships among them. It is also observed that the selection of the most profitable parameters of a trading system can be unrestricted, rendering the validation of the minor divergence occurring among slightly varying prices redundant. Meanwhile, other conclusions that can be drawn are that the most profitable classification system employed by the d-Backtest PS method is calibrated by means of two validation periods and that the most efficient profitability ratio between historical data period and validation period is 6:1 (in- and out-of-the-sample ratio). [ABSTRACT FROM AUTHOR]

Back testing process is widely used today in forecasting experiments tests. This method is to calculate the profitability of a trading system, applied to specific past period. The data which are used, correspond to that specific past period and are called “historical data” or “training data”. There is a plethora of trading systems, which include technical indicators, trend following indicators, oscillators, control indicators of price level, etc. It is common nowadays for calculations of technical indicator values to be used along with the prices of securities or shares, as training data in fuzzy, hybrid and support vector machine/regression (SVM/SVR) systems. Whether the data are used in fuzzy systems, or for SVM and SVR systems training, the historical data period selection on most occasions is devoid of validation (In this research we designate historical data as training data). We substantiate that such an expert trading system, has a profitability edge—with regard to future transactions—over currently applied trading strategies that merely implement parameters’ optimization. Thus not profitable trading systems can be turned into profitable. To that end, first and foremost, an optimal historical data period must be determined, secondarily a parameters optimization computation must be completed and finally the right conditions of parameters must be applied for optimal parameters’ selection. In this new approach, we develop an integrated dynamic computation algorithm, called the “d-BackTest PS Method”, for selection of optimal historical data period, periodically. In addition, we test conditions of parameters and values via back-testing, using multi agent technology, integrated in an automated trading expert system based on Moving Average Convergence Divergence (MACD) technical indicator. This dynamic computation algorithm can be used in Technical indicators, Fuzzy, SVR and SVM and hybrid forecasting systems. The outcome crystalizes in an autonomous intelligent trading system. [ABSTRACT FROM AUTHOR]

In this paper we study the boundedness, the persistence, the attractivity and the stability of the positive solutions of the nonlinear difference equation xn+1 = α + (xn-1p / xnq), n = 0,1,..., where α, p, q ∈(0, ∞) and x-1, x0 ∈ (0, ∞). Moreover we investigate the existence of a prime two periodic solution of the above equation and we find solutions which converge to this periodic solution. [ABSTRACT FROM AUTHOR]

In this paper we study the boundedness, the persistence, the attractivity and the stability of the positive solutions of the nonlinear difference equation xn+1 = α + (xn-1p / xnq), n = 0,1,..., where α, p, q ∈(0, ∞) and x-1, x0 ∈ (0, ∞). Moreover we investigate the existence of a prime two periodic solution of the above equation and we find solutions which converge to this periodic solution. [ABSTRACT FROM AUTHOR]

We consider the following system of Lyness-type difference equations: x1(n + 1) = (akxk(n) + bk)/ xk-1(n - 1), x2(n + 1) = (a1x1(n) + b1)/xk(n - 1), xi(n + 1) = (ai-1xi-1(n) + bi-1)/xi-2(n-1), i = 3, 4,...,k, where ai, bi, i = 1, 2,...,k, are positive constants, k ≥ 3 is an integer, and the initial values are positive real numbers. We study the existence of invariants, the boundedness, the persistence, and the periodicity of the positive solutions of this system. [ABSTRACT FROM AUTHOR]