This study is an analysis of time series, such as quotes of financial instruments (stock prices,

currency pair values). Aim of the study is to develop an algorithm for the distribution of the

trend derivative estimator into two orthogonal components and determining their parameters

depending on the value of a time window and to test the statistical rate of return on investment

using these components. The purpose of the analysis of financial instruments is to predict

future changes in their prices and determine the profitability of potential investments. Given

the availability of testing various financial instruments, and thus the possibility of processing

their values using methods appropriate for time series analysis, this study attempts to develop

a computer algorithm to support investment decisions. The distribution of the trend derivative

estimator into two orthogonal components allows to determine four sets of input data,

indicating the beginning moments of the investment. Computations conducted for each of

these sets show that only for one of them the indicators of average profit, average income, and

investment efficiency adopt positive values, which indicates gaining some profits from the

investments. The computations were carried out for two different time series – DJIA index

and GBPUSD currency pair. This study demonstrates that there is a possibility of using the

distribution of the trend derivative for supporting trading decisions.

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