Disliked{quote} Can you explain this sentence much better please? Preferably with mathematical proof. Predicting the next price is exactly the same thing as predicting the next return since the return is the difference between two consecutive prices. Based on the price a lin.reg. model will simply predict the continuity of a straight line; while based on price return it will predict the continuation of the mean of this series, which is nothing else than the slope of the straight line. Also taking the difference of the signal increases the variance of the...Ignored
First Example
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Closing prices = 1.2510, 1.2520, 1.2530, 1.2540 Example in terms of prices: (inputs) 1.2520, 1.2530 -> (target) 1.2540 Example in terms of returns: (inputs) 0.0010, 0.0010 -> (target) 0.0010
Now for the second example:
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Closing prices = 1.2210, 1.2220, 1.2230, 1.2240 Example in terms of prices: (inputs) 1.2220, 1.2230 -> (target) 1.2240 Example in terms of returns: (inputs) 0.0010, 0.0010 -> (target) 0.0010
It is easy to see that both examples are exactly equal in terms of returns while in terms of absolute prices they are very different. A machine learning algorithm training using these two examples will give you one result when training based on prices and another when training based on returns (remember that we train using all examples). The return calculation in fact reduces the amount of information, enough to make the above two examples exactly the same, while they remain different from an absolute price point of view. Suppose you now need to make a prediction with prices:
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Closing prices = 1.2700, 1.2710, 1.2720 inputs using closing prices: (inputs) 1.2710, 1.2720 inputs using returns: (inputs) 0.0010, 0.0010
I believe it is easy to see how the case using returns would be able to make a better prediction.
But don't take my word for it! Train a machine learning algorithm using prices or using returns, you will get very different results (this is what I have always experienced). Perhaps I am very poor at expressing what I want here, making your own experiments using prices/returns will probably be much more enlightening than reading my (possibly not so clear) explanations.
It is also a pity that you haven't been able to reproduce my results. Perhaps there are some minor nuances that we haven't pin pointed that make our implementations fundamentally different. If you ever happen to get access to the Asirikuy programming framework do let me know and I will be glad to share code for any implementation you want so you can reproduce my exact results (other readers who have access to the framework can also ask for code here, I'll be happy to post it on the thread).