The use of Karhunen-Loeve filters to predict the behavior of the currency market

Abstract

One of the tasks of trading is to predict the behavior of the price of currency market transactions in order to timely enter into an agreement. The purpose of the article is to describe a proposed forecasting technique adapted for the implementation in the popular platform NinjaTrader. The forecast is based on the analysis of data provided in the Karhunen-Loeve representation using the logit model. The article describes an original and highly effective procedure for the synthesis of Karhunen-Loeve filters for statistical ensembles characterized by grouping its members around a limited (up to 103) number of typical representatives. The proposed procedure for constructing a basis provides a 102A·1012 fold reduction in the computational cost for the synthesis of Karhunen-Loeve filters for a specified type of statistical signal ensembles, which makes such a synthesis feasible. Described are programs that implement the construction of the basis, the creation and training of a logit model and the forecasting. It is demonstrated how the application of data analysis in the constructed basis with the help of a logit model can provide an acceptable level of reliability for a forecast intended for practical application.