Explaining Danica v0.5 optimization choices - Volatility effect on the position of the optimum

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Written by Mikhail Kopytine   
Thursday, 14 January 2010 13:45
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Pearson correlation of predicted and  actual day-scale forex logarithmic returns (low, high, close) as a function of  the forecasting parameter.

Fig.2. Pearson correlation of predicted and actual day-scale logarithmic returns in low, high and close as a function of the forecasting parameter nicknamed Fred. The shaded bands indicate a measure of uncertainty, their boundaries mark one standard deviation (among the forex pairs considered) distance to the points. Back-testing simulations give the forecasting engine no access to the future data, direct or indirect. Significantly positive (and ideally, large) values correspond to quality forecasting. Note that the quantities at different Fred are not quite statistically independent, therefore the error bands should be understood as describing the uncertainty of the position of the curve at large rather than that of individual points.

The middle and half-width of the bands around the data points in Fig.2 represent the mean and standard deviation of the set of the individual Pearson correlation coefficients for the 6 major forex exchange rates, treated as independent measurements.

Pearson correlation of predicted and  actual day-scale forex logarithmic returns (CLOSE) as a function of  the forecasting parameter. Pearson correlation of predicted and  actual day-scale forex logarithmic returns (CLOSE) as a function of  the forecasting parameter.

Fig.3. Like Fig.2, with various cuts on the absolute magnitude (modulus) of the product from Fig.1 as explained in text below, including the case of no cut (top panel). Top panel presents the data for close from Fig.2, magnified.

Fig.3 is an attempt to quantify the impact of various volatility regimes into the overall performance figure. The colored data sets are obtained by applying symmetric cuts on the forecast-reality product as discussed above, the one of the type

abs(product) < cut

and calculating the Pearson correlation coefficient for the data that satisfies the cut. Because with increasing volatility, both the actual logarithmic returns (by definition) and the forecast ones increase, such a cut effectively limits volatility from above.

The positive net performance is seen to be largely created by high volatilities.

The study reveals that the higher Fred values (starting with perhaps 15) split the different volatility regimes in terms of performance. This is undesirable since low volatility regimes is where the market spends most of its time. Indeed there is no assurance that the recent extreme volatility will repeat itself.

This reminds me of the conclusions from the full trading system optimization (including the trade-idea selection and portfolio balancing components disabled in Danica) attempted in summer 2009: in the absence of Pearson data like Fig.2, I was led (by return/risk considerations) into the upper portion of Fred, to discover that the best "high Fred" systems traded almost exclusively during the peak of the financial panic.

Pearson correlation of predicted and  actual day-scale forex logarithmic returns (CLOSE) as a function of  the forecasting parameter. Pearson correlation of predicted and  actual day-scale forex logarithmic returns (CLOSE) as a function of  the forecasting parameter.

Fig.4. The area of interest in Fig.3, magnified.

While choosing the Fred position (the choice for v0.5 of the trading system is indicated by the green arrow in Fig.4) I was balancing the goal of having high "no cut" Pearson for "close", the goal of having high Pearson for "high" and "low" (there, product cuts like Fig.3 and 4 make little difference to the position of the maximum), and the goal of not getting in the area of too much variety in the behaviour of the colored data sets in Fig.3 and 4. What is currently believed to be a reasonable compromise is indicated by green arrow in Fig.4.

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Last Updated ( Wednesday, 14 April 2010 12:45 )
 

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