All right. Let's do an experiment. On a piece of paper draw 7 -8 vertical bars of different length. Using your eyes only draw a line through them that in your opinion would fairly represent their combined center of gravity. Then measure the bars and using EXCEL calculate a linear regression line of those bars. See for yourself that your eyes are incredibly precise. This is one of our incredible abilities. Otherwise we as humans would not survive!
Can linear regression analysis really predict the future?
- Thread starter tradrejoe
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Much of AI borrows from literal physiology provided by nature and evolution in our brains (think perceptrons, neural nets).
Why do we try to mimic biology? Because elements that we naturally use, such as the perceptron (neuron) and hebbian networks are remarkably adept at functions like regression, content addressable recall, and learning from past experience. I completely agree that our minds evolved for survival, with prediction being one of the key advantages.
The mind is still remarkably far more advanced than simple AI models, but as we increase complexity and size of our physical and algorithmic models, I don't doubt they will approach much of the mind's capabilities.
Feel free to look up the analogy between the perceptron and neuron (which it is modeled after), and its well known capability to perform regression.
Quote from dtrader98:
Nice!
Here are some links to support it.
http://www.pnas.org/content/101/12/4286.figures-only?cited-by=yes&legid=pnas;101/12/4286
http://www.youtube.com/watch?v=vbNDNkvzzuk
If what you're saying is true why do we need computers to do regression analysis with stock prices? Can't one just become accustomed to the "inertia" of price and other traders and trade by eye or by "feel" as we do when we drive cars? We don't need computer models or high level math in order to drive, why do we need it to trade? Doesn't this describe what traders already know about mean reversion and breakout trading strategies, buying when traders are anxious to buy and selling when buyers dry up and feel nervious holding?
I'm not an expert on such things, so I walked across the street to talk to my neighbor who happens to be a neurologist.
Here's what he said: A linear regression model is based on probabilities, a distribution of outcomes around the mean. The human mind, on the other hand, works largely in a deterministic fashion. To use the previous example, he said that if the lines on the road jumped around like stock prices we would all be very bad drivers. He said there is a HUGE difference between visually fitting a line to a known set of historical points and predicting an unknown future data set based on prior historical results. He said that the human mind is quite easily fooled by "non-deterministic events" (e.g. price movements in the stock market).
Here's what he said: A linear regression model is based on probabilities, a distribution of outcomes around the mean. The human mind, on the other hand, works largely in a deterministic fashion. To use the previous example, he said that if the lines on the road jumped around like stock prices we would all be very bad drivers. He said there is a HUGE difference between visually fitting a line to a known set of historical points and predicting an unknown future data set based on prior historical results. He said that the human mind is quite easily fooled by "non-deterministic events" (e.g. price movements in the stock market).
Don't want to get into an argument about it (draw your own conclusions), but it is well known in the neurophysiology community that the brain organizes activity in a chaotic manner looking for attractor regions that minimize energy states. Much the same way that AI (including regression) systems optimize solutions. Over time and based upon experience the connections will reorganize themselves based upon activity (persistance) in neighboring networks, in an effort to adapt to their external (and constantly) changing environment. As we get older, this plasticity abates. Part of the reason humans suffer from extrapolating too many patterns falsely into the future (much like Rorschach tests) is due to their particular tendency to overestimate based upon their personal experience (see behavioral bias studies/taleb for laymen behavioral finance), and their built in (genetic) predisposition to need to formulate and generalize models to predict the world around them for survival.
The ability of the mind to reach a decision is far more probabalistic than deterministic IMO. Just think about how chaos operates; one small perturbation will change the trajectory of an initial path very quickly, the brain signals operate much the same way. We know this from all kinds of studies, particularly from dynamics of EEG patterns . At any given instance, your mind will have all kinds of unexpected perturbations causing it to seek the lowest energy attractor based upon prior experience. You can think of falling into a local basin rather than global as a result, again, that is more probabilistic, depending on initial conditions.
Ask him if he thinks the mind operates in a deterministic, chaotic, or random fashion. If he's a neurologist, I would be surprised that he does not pick chaotic. I can point to an entire field of study dedicated to this phenomena.
If he agrees it is chaotic, then ask whether chaos is more of a probabilistic or deterministic phenomena; I think he will re-state his conclusion given that framework.
BTW, did you know that heart signals are purposely chaotic as a robustness measure for survival (why is that?).
Deterministic patterns are a signature of something very wrong (seizure, tachycardia). The body tends to optimize most of its parts using similar fashion (including the mind).
The lines on the road don't jump around, it is the moving objects in your periphery that jump around. Your mind is a highly sophisticated control system that allows you to adapt and react very quickly to such changing events. It's just like the simulators you used in drivers ed to train your mind.
He is spot on about being fooled by randomness.
"Patterns are the fool's gold of the financial markets. The power of chance suffices to create spurious patterns that...for all the world appear predictable and bankable... They are the inevitable consequence of the human need to find patterns in the patternless." Benoit Mandelbrot
This over-tendency to of the mind to try to fit spurious patterns is precisely why we need computational intelligence to help augment our decisions. Unlike human minds, which by their very nature, attempt to arrive at subjective conclusions based on their ability to extrapolate and generalize-- computer algorithms allow us to process all of the data in a more robust statistical manner.
Thanks Maestro, I found something similar, a trading simulation of the Soybean and Crush Spread: http://www.ljmu.ac.uk/BLW/BLW_Facultytopleveldocs/Soybean_Crush_Spread.pdf . Basically they tested several neural network algorithms for predicting the spread value. According to the paper, Higher Order Neural Networks (HONN) performed the best by generating a 23.99% trading return during back testing, hedge fund level return! The HONN network they described used up to 3rd order lags and combinations of 1st to 3rd order lags in a Logit Regression. A generalized HONN network is described in this paper: http://clgiles.ist.psu.edu/papers/AO-1987-nn_invariance.pdf .
For training, the spread values from 1/1/95 to 8/17/01 were used as input and the spread values from 8/20/01 to 4/25/03 were used as actual output to be predicted. A 440x7 beta coefficient matrix was generated to minimized the prediction error. Then, this beta matrix was used in combination with 1/1/95 to 4/25/03 data (basically the training + testing) to predict yet another 440-points-timeseries further out into the future between 8/20/01 to 5/25/03 to generate the 23.99% return.
It worked probably because the smaller time period for training was a "minimiature version" of the larger time period. But can we generally make the assumption that if we "zoom out" on the time scale, the larger time frame replicates the behavior of smaller time frames within it? Does this assumption remind you of Fibonacci analysis? In other words, can we always make the assumption that history will repeat itself?
You know, it would be a great exercise to apply this trading simulation to a long only strategy involving synthetic asset formed by less correlated assets that have net positive return over time (such as equity plus commodities). If the assumption about history repeating itself is correct, then the market neutral Soybean and Crush Spread will not be tradable any more at some point in the future as its value converges to zero and there will be no more noise to trade.
What is the probability that the "random walk" of index/stock/futures prices is just that, "random", i.e. 100% random, 100% of the time?
IMHO: 0 - null, zero.
Why? Because it's the result of interaction between human beings, or programs written by human beings.
And human beings, especially when assembled in large groups, tend to react to events in very specific ways, and to repeat their behaviour over time when presented the same events, the same data.
Now, not being 100% random 100% of the time does not mean that it's 100% deterministic, 100% of the time. I think we'd certainly know this if it were to be true. And it just can't be this way, otherwise there would simply be no market, since all participants would have the same opinion at the same time.
The true challenge in trading (esp day trading) is to find those windows of opportunities where a market has reached a specific point, a "déjà vu" configuration to which market participants will tend to react the same (or similar enough) way over time. And to avoid entering any position otherwise. Patience, etc...
No way on earth that e.g. double-tops or double-bottoms on specific price levels where congestion happened in a recent past are solely due to randomness. Happen way too often for it to be fully random.
Just my 0.2 cents.
IMHO: 0 - null, zero.
Why? Because it's the result of interaction between human beings, or programs written by human beings.
And human beings, especially when assembled in large groups, tend to react to events in very specific ways, and to repeat their behaviour over time when presented the same events, the same data.
Now, not being 100% random 100% of the time does not mean that it's 100% deterministic, 100% of the time. I think we'd certainly know this if it were to be true. And it just can't be this way, otherwise there would simply be no market, since all participants would have the same opinion at the same time.
The true challenge in trading (esp day trading) is to find those windows of opportunities where a market has reached a specific point, a "déjà vu" configuration to which market participants will tend to react the same (or similar enough) way over time. And to avoid entering any position otherwise. Patience, etc...
No way on earth that e.g. double-tops or double-bottoms on specific price levels where congestion happened in a recent past are solely due to randomness. Happen way too often for it to be fully random.
Just my 0.2 cents.