The low-pass FIR filtering commonly used in the analysis of market data is the cause of inevitable changes in the original data. The desirable change, which is a rationale of such filtering, consists in smoothing the data. It is believed that this positive change enables a better estimation of market movements. On the other hand, the undesirable change in the original data consists in delaying the filter output data to such an extent that anticipations of future market movement are hardly possible. A tradeoff between the degree of desirable smoothing and undesirable delay provides a very little room for optimizing such filters, e.g., [1]. The aim of this paper is to determine the "best" non-causal smoothing FIR filters, which provide maximum of the return from the market. The assumed non-causality is obtained by advancing the output filter signal to compensate for the delay introduced by the a priori known filter. This way the smoothed data is not delayed with respect to the original data. Upon this assumption the following investment criterion is introduced: the long position is opened ( i.e. the shares or currency is bought) when the derivative of the filter output signal upwardly crosses zero. The position is closed ( i.e. the shares or currency is sold) when the derivative of the filter output signal downwardly crosses zero. The "best" filters are those which yield maximum return, irrespective of the length of filter impulse response. For the computation the data of one-minute quotations for the futures contracts on WIG 20, covering period of time from October 30,2001 thru June 16, 2003 were used. For this period of time the average transaction fee offered by brokers was between 10 -14 PLN. The computation were performed for the idealized case without including the transaction fee, and the more realistic case including the 12 PLN transaction fee. It was found, that in the idealized case practically all filters provide some return from the market. However, when the real transaction fee is included, only some of them provide positive return, whereas other generate loss.

References:

[1] Andrzej Dyka, Marek Kaźmierczak, Optymalna dolno-pasmowa filtracja danych rynkowych z użyciem filtru o skończonej odpowiedzi impulsowej Acta Physica Polonica B, Vol. 36, No8, 2005, 2487-2493

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