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Stocks & Commodities V. 32:2 (10-15): Degree Of Complexity by Oscar G. Cagigas
Stocks & Commodities V. 32:2 (10-15): Degree Of Complexity by Oscar G. Cagigas
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Degree Of Complexity by Oscar G. Cagigas
Goodness, It Doesnt Fit
When designing trading systems, its easy to keep adding parameters or filters. But does the system perform better when its more complex? Heres how you can keep your system efficient and only add more when its necessary.
Although complex trading systems deliver good insample statistics, they inevitably fail when it comes to out-of-sample or real-time trading. In this article, I will present a simple theoretical model to show how important it is to keep complexity low when designing trading systems. As an example, I will show you a Donchian-based trading system that generates favorable in-sample statistics when its complexity is increased but deteriorates in the outof- sample tests as the complexity gradually increases. Theoretical model I am going to use a simple model that simulates an uptrend with some volatility. The model is as follows:
Price = C1*N + C2*sin(N) (1)
where:
N is the number of bars (the time variable) sin is the sine wave function C1 and C2 are coefficients that affect the slope of the rising price curve.
Basically, equation (1) is the sum of a straight line plus a sinusoidal wave. I have assigned the values of 10 and 40 to C1 and C2, respectively. In Figure 1 you can see a graphical representation of the price model.
After the price model is defined, I perform a polynomial interpolation of the model with the degree rising to three (from one). Polynomial interpolation finds a polynomial curve of the price variable that goes through the data points. The higher the degree of the polynomial, the more accurate.
The idea is to estimate the future behavior of the price model using a fit with increasing complexity. In Figure 2 you see the first, second, and third degrees of polynomial interpolations of the price model. As you can see, the three approaches look similar.
The goodness of fit R2 can be seen in the table in Figure 3. According to this table, the more complex polynomial, the third degree, has the best fit for the in-sample tests. It has the highest R2 value of 0.799.
Goodness, It Doesnt Fit
When designing trading systems, its easy to keep adding parameters or filters. But does the system perform better when its more complex? Heres how you can keep your system efficient and only add more when its necessary.
Although complex trading systems deliver good insample statistics, they inevitably fail when it comes to out-of-sample or real-time trading. In this article, I will present a simple theoretical model to show how important it is to keep complexity low when designing trading systems. As an example, I will show you a Donchian-based trading system that generates favorable in-sample statistics when its complexity is increased but deteriorates in the outof- sample tests as the complexity gradually increases. Theoretical model I am going to use a simple model that simulates an uptrend with some volatility. The model is as follows:
Price = C1*N + C2*sin(N) (1)
where:
N is the number of bars (the time variable) sin is the sine wave function C1 and C2 are coefficients that affect the slope of the rising price curve.
Basically, equation (1) is the sum of a straight line plus a sinusoidal wave. I have assigned the values of 10 and 40 to C1 and C2, respectively. In Figure 1 you can see a graphical representation of the price model.
After the price model is defined, I perform a polynomial interpolation of the model with the degree rising to three (from one). Polynomial interpolation finds a polynomial curve of the price variable that goes through the data points. The higher the degree of the polynomial, the more accurate.
The idea is to estimate the future behavior of the price model using a fit with increasing complexity. In Figure 2 you see the first, second, and third degrees of polynomial interpolations of the price model. As you can see, the three approaches look similar.
The goodness of fit R2 can be seen in the table in Figure 3. According to this table, the more complex polynomial, the third degree, has the best fit for the in-sample tests. It has the highest R2 value of 0.799.
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