This page contains a Flash digital edition of a book.
TRADING SYSTEMS by Dr. Daniel Fernández PhD


COMMODITIES


FX


Currency pairs: A look through the fractal dimension


Te key to the existence of predictability in financial time series is the presence of characteristics that are both persistent and distinct from those of a random walk. It is not enough for a time series to be either different from a random walk or constant in character as neither would allow for


the systematic extraction


of profit from the market. If a time series is constant in character but equal to a random walk then no useful predictions can be made while if the character of the series is different from that of a random walk but oscillates widely the possibility to extract any


Te first problem we face when attempting to evaluate deviations from a random walk is how to measure such deviations. Te family of measurements related to Chaos theory, such as the Lyapunov exponent, Hurst exponent and fractal


benefit is also voided. Trough this article we will use the fractal dimension to explore how the character of 16 Forex financial series changes through time as well as how we can infer from this information which series are the most suitable for the finding of historically profitable algorithmic trading strategies.


dimension are particularly useful for this purpose as not only do they provide a measurement of how a series deviates from a random walk but they also hint at the qualitative properties


that change within the


series when such deviations happen. On this article we will be using the fractal dimension for our study as its calculation is computationally cheap and the deviations are associated with the fractality within a series which is related with series complexity and the existence of patterns which are immediately relevant to potentially profitable trading.


FX TRADER MAGAZINE January - March 2017 43


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