Suppose you had an idea for a trading method. To find out if it had any validity you'd probably create a set of rules and backtest the idea. Even if the results look good, how do you know it's worth pursuing? One idea is to test each variable for correllation and dependency.
For example, suppose I want to create a daytrading system using support and resistance. I'm thinking of using the pivot point work done by so many people. For those new to this, a pivot point for tomorrow = (today's high + low + close)/3. R1 or first resistance would indicate an area where an upmove might stop and turn (r1 = (2*pvt) - Low). S1 or first support would indicate an area where a downmove might stop and turn (s1 = (2*pvt)-high).
My system might say buy at s1 (because it's a support point and sell at r1 because it's a resistance point).If the results are promising, how can I have more confidence in trading this?
r1 and s1 are prediction points of possible highs and lows. A simple test is to use the r1 and s1 and check to see how close they correllate with tomorrow's high and low. In this example, I tested the SP market from 1996 - 2002 and did a simple correllation test in excel. r1 correllated to the next day high at .998909. Likewise s1 correllated to the next day low at .99839. These numbers sound impressive, however to find out if they are really good, we need to do another test using a variable that these should beat if the idea is sound. In this instance, I've chosen to use the open of tomorrow as a prediction for the high and low. This will help desribe how much better than a random point, r1 and s1 are. A correllation test performed using the open verus the high resulted in .999174. Likewise checking the correllation of the open versus low had a correllation of .999113. In both cases the open was more closely correllated to the high and low than r1 and s1. In this case, I could safely exclude r1 and s1 as possible variables to be used for creating a support and resistance trading model. (One interesting side note was the correllation between s1 and tomorrow's open was .999184 and the correllation between r1 and tomorrow's open was .999174. These might have some value at predicting whether tomorrow will start as an up or down day).
Had that test done well, I would've moved on to do a test for dependency. Two types of dependency are typically found in time series. This first is deterministic. That is, for every point, we can predict with 100% accuracy the next point based on some parameter. For instance we could have a table with switch on/off represented by 1 = on and 0 = off. Next to it could be a table of light on and light off. After a brief check we'd find that when switch = 1, light = on. While we can dream about finding this type of dependency, it's not likely to be found in the markets. The other type of dependency is called stochastic dependency. It's based upon the idea that exact predictions are impossible and must be replaced by the idea that future values have a probability distribution based on a knowledge of past values.
Since this post is so long, I'll just add a link to a paper on this topic for those interested in more detail. I'll come back to this with a example for doing stochastic dependency tests when I have more time.
http://www.math.ethz.ch/~mcneil/ftp/pitfalls.pdf
For example, suppose I want to create a daytrading system using support and resistance. I'm thinking of using the pivot point work done by so many people. For those new to this, a pivot point for tomorrow = (today's high + low + close)/3. R1 or first resistance would indicate an area where an upmove might stop and turn (r1 = (2*pvt) - Low). S1 or first support would indicate an area where a downmove might stop and turn (s1 = (2*pvt)-high).
My system might say buy at s1 (because it's a support point and sell at r1 because it's a resistance point).If the results are promising, how can I have more confidence in trading this?
r1 and s1 are prediction points of possible highs and lows. A simple test is to use the r1 and s1 and check to see how close they correllate with tomorrow's high and low. In this example, I tested the SP market from 1996 - 2002 and did a simple correllation test in excel. r1 correllated to the next day high at .998909. Likewise s1 correllated to the next day low at .99839. These numbers sound impressive, however to find out if they are really good, we need to do another test using a variable that these should beat if the idea is sound. In this instance, I've chosen to use the open of tomorrow as a prediction for the high and low. This will help desribe how much better than a random point, r1 and s1 are. A correllation test performed using the open verus the high resulted in .999174. Likewise checking the correllation of the open versus low had a correllation of .999113. In both cases the open was more closely correllated to the high and low than r1 and s1. In this case, I could safely exclude r1 and s1 as possible variables to be used for creating a support and resistance trading model. (One interesting side note was the correllation between s1 and tomorrow's open was .999184 and the correllation between r1 and tomorrow's open was .999174. These might have some value at predicting whether tomorrow will start as an up or down day).
Had that test done well, I would've moved on to do a test for dependency. Two types of dependency are typically found in time series. This first is deterministic. That is, for every point, we can predict with 100% accuracy the next point based on some parameter. For instance we could have a table with switch on/off represented by 1 = on and 0 = off. Next to it could be a table of light on and light off. After a brief check we'd find that when switch = 1, light = on. While we can dream about finding this type of dependency, it's not likely to be found in the markets. The other type of dependency is called stochastic dependency. It's based upon the idea that exact predictions are impossible and must be replaced by the idea that future values have a probability distribution based on a knowledge of past values.
Since this post is so long, I'll just add a link to a paper on this topic for those interested in more detail. I'll come back to this with a example for doing stochastic dependency tests when I have more time.
http://www.math.ethz.ch/~mcneil/ftp/pitfalls.pdf
