TRADING SYSTEMS Difference between efficient and real series 20
This means that
all 15 10 5 0 Pair Figure 2
is significantly different from the mean value expected from efficient time series created using bootstrapping with replacement.
0.15
time series follow a b e h a v i o r that would not be expected if there was a complete lack of predictable p a tte r n s w i t h i n the data. Figure 2 sho ws how the
di f ference b e t w e e n
0.12 0.09 0.06
Figure 3 0.03
500 1000 Window Size 1500
the fractal dimension for the real and random series compares for each symbol. Symbols with a higher di f ference are ex p e ct e d to deviate more from a perfectly efficie n t series while l o w e r differences are ex p e ct e d to lead to more efficie n t symbols. In
EURUSD AUDUSD GBPUSD EURJPY GBPJPY USDJPY USDCAD EURCAD USDCHF EURAUD AUDCHF AUDCAD GBPAUD CHFJPY CADJPY EURCHF
2000
FX
all cases the value found in the real series differs by more than 15% from the values expected from random series, showing that all these 16 series deviate significantly from random behavior. Note that the most liquid
symbols lowest deviations
Aſter establishing that the mean fractal dimension does deviate from an efficient case we can now look at how the fractal dimension slices are distributed and how this changes for different slice sizes. The standard deviation of the distribution of fractal dimensions is particularly interesting since a lower standard deviation implies that the character of the series remains more constant through time.
Since predictability
requires both a deviation from randomness and a persistence of the character of this behavior through time we
expect that
series for which the deviation is lower will be more suitable for the creation of historically profitable algorithmic trading strategies.
Figure 3 shows how the standard deviation for the fractal dimension changes as a function of the slice size for the different currency pairs under study. The EUR/USD, USD/ JPY and USD/CHF show the
FX TRADER MAGAZINE January - March 2017 45 also have the
Fractal dimension StdDev USDCHF
EURUSD USDJPY
AUDCHF AUDUSD CADJPY GBPUSD
EURAUD EURCAD
GBPAUD EURJPY GBPJPY CHFJPY
AUDCAD USDCAD EURCHF
Difference (%)
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