Some of my readers asked me about the inputs that worked best for applying NN to the eur/usd. The answer would be:

--> raw prices OHCL performed poor in general even if lags were introduced

--> technical indicators enhanced the explanatory power of the models ( the best result so far has been 84% trend accuracy)

--> financial ratios, we need to try to use them; a recent article for example included 24 ratios about the Canadian stock market

## Thursday, May 25, 2006

## Friday, May 19, 2006

### NN results...

Someone asked me to post the results... i want to give you an example of the potential profitability of NN if applied correctly... look at my post on moneytec:

link to the results

link to the results

## Sunday, May 14, 2006

### Reply to Zendini comments

Thanks a lot for you comment Zendini.. i really appreciate the fact that you decided to express your view on the subject...I still believe that NN have huge potential... i have recently read dozens of papers about empirical results starting from 1988... and i'm doing research on s&p500 data with very good results... I have also written a paper for a university project that i can't, unfortunately post on the blog for obvious reasons... so if you have doubts about the subject please refere to the following sources:

J. Loofbourrow & T. Loofbourrow, “Neural Networks for Trading”, AI in Finance (Special Report), 42-51

J. Zirilli, Financial Prediction Using Neural Networks, London, 1997, International Thompson Computer Press

A. Skabar & I. Cloete, Neural Networks, Financial Trading and the Efficient Markets Hypothesis, XXV Australasian Computer Science Conference 2002, Australian Computer Society, Inc.

Shaikh A. Hamid & Z. Iqbal, Using neural networks for forecasting volatility of S&P 500 Index futures prices, Journal of Business Research 57 (2004) 1116-1125.

K. Kohara, T.Ishikawa, Y.Fukuhara, Yukihiro Nakamura, Stock Price Prediction Using Prior Knowledge and Neural Networks, Intelligent Systems in Accounting, Finance and Management vol 6: 11-22, 1997

J. Kamruzzaman & R. Sarker, Comparing ANN Based Models with ARIMA for Prediction of Forex Rates.

G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control Holden-Day, San Francisco, CA

G. Zhang and M.Y. Hu, Neural Network Forecasting of the British Pound/USD Dollar Exchange Rate, “OMEGA; Int. Journal of Management Science, 26, pp 495-506, 1998

G. Deboeck, Trading on the Edge: Neural, Genetic and Fuzzy Systems for Chaotic Financial Markets

An-Sing Chen, Hazem Daouk, Mark T. Leung, Application of Neural Networks to an Emerging Financial Market: Forecasting and Trading the Taiwan Stock Index 2001

Wei Cheng, Lorry Wagner, Chien-Hua Lin, Forecasting the 30-year U.S. Treasury Bond with a System of Neural Networks,NeuroVe$t Journal, January/February 1996

S. Dutta and S. Sheckhar, Bond Rating: A Non-Conservative Application of Neural Networks, Proceedings of the IEEE International Conference on Neural Networks,1998, 2, 443-450

J. Moody and J. Utans, Architecture Selection Strategies for Neural Networks, In. A. P. Refenes, Ed., Neural Networks in the Capital Markets, Chichester, England, 1995, John Wiley & Sons, 277-300.

T. Lubecke, Kyung Doo Nam, R. Markland, C. Kwok, Combining Foreign Exchange Forecasts using Neural Networks, 1998, Global Finance Journal 9(1): 5-27

A. Fadlalla & Chien-Hua Lin, An Analysis of the Applications of Neural Networks in Finance, 2001, Interfaces 31: 4 July-August 2001 (pp. 112-122), Informs.

Have a nice day!

J. Loofbourrow & T. Loofbourrow, “Neural Networks for Trading”, AI in Finance (Special Report), 42-51

J. Zirilli, Financial Prediction Using Neural Networks, London, 1997, International Thompson Computer Press

A. Skabar & I. Cloete, Neural Networks, Financial Trading and the Efficient Markets Hypothesis, XXV Australasian Computer Science Conference 2002, Australian Computer Society, Inc.

Shaikh A. Hamid & Z. Iqbal, Using neural networks for forecasting volatility of S&P 500 Index futures prices, Journal of Business Research 57 (2004) 1116-1125.

K. Kohara, T.Ishikawa, Y.Fukuhara, Yukihiro Nakamura, Stock Price Prediction Using Prior Knowledge and Neural Networks, Intelligent Systems in Accounting, Finance and Management vol 6: 11-22, 1997

J. Kamruzzaman & R. Sarker, Comparing ANN Based Models with ARIMA for Prediction of Forex Rates.

G. E. P. Box and G. M. Jenkins, Time Series Analysis: Forecasting and Control Holden-Day, San Francisco, CA

G. Zhang and M.Y. Hu, Neural Network Forecasting of the British Pound/USD Dollar Exchange Rate, “OMEGA; Int. Journal of Management Science, 26, pp 495-506, 1998

G. Deboeck, Trading on the Edge: Neural, Genetic and Fuzzy Systems for Chaotic Financial Markets

An-Sing Chen, Hazem Daouk, Mark T. Leung, Application of Neural Networks to an Emerging Financial Market: Forecasting and Trading the Taiwan Stock Index 2001

Wei Cheng, Lorry Wagner, Chien-Hua Lin, Forecasting the 30-year U.S. Treasury Bond with a System of Neural Networks,NeuroVe$t Journal, January/February 1996

S. Dutta and S. Sheckhar, Bond Rating: A Non-Conservative Application of Neural Networks, Proceedings of the IEEE International Conference on Neural Networks,1998, 2, 443-450

J. Moody and J. Utans, Architecture Selection Strategies for Neural Networks, In. A. P. Refenes, Ed., Neural Networks in the Capital Markets, Chichester, England, 1995, John Wiley & Sons, 277-300.

T. Lubecke, Kyung Doo Nam, R. Markland, C. Kwok, Combining Foreign Exchange Forecasts using Neural Networks, 1998, Global Finance Journal 9(1): 5-27

A. Fadlalla & Chien-Hua Lin, An Analysis of the Applications of Neural Networks in Finance, 2001, Interfaces 31: 4 July-August 2001 (pp. 112-122), Informs.

Have a nice day!

## Tuesday, May 09, 2006

### Discussion board...

I'm thinking of creating a discussion board about NN and their application to financial markets... even though i got great feedback from readers of this blog i think we could try to discuss the issue together more often... could you please comment on this..

take care...

take care...

## Monday, May 08, 2006

### Limits and application of NN

"In principle, NNs can compute any computable function, i.e., they can do everything a normal digital computer can do (Valiant, 1988; Siegelmann and Sontag, 1999; Orponen, 2000; Sima and Orponen, 2001), or perhaps even more, under some assumptions of doubtful practicality (see Siegelmann, 1998, but also Hadley, 1999).

Practical applications of NNs most often employ supervised learning. For supervised learning, you must provide training data that includes both the input and the desired result (the target value). After successful training, you can present input data alone to the NN (that is, input data without the desired result), and the NN will compute an output value that approximates the desired result. However, for training to be successful, you may need lots of training data and lots of computer time to do the training. In many applications, such as image and text processing, you will have to do a lot of work to select appropriate input data and to code the data as numeric values.

In practice, NNs are especially useful for classification and function approximation/mapping problems which are tolerant of some imprecision, which have lots of training data available, but to which hard and fast rules (such as those that might be used in an expert system) cannot easily be applied. Almost any finite-dimensional vector function on a compact set can be approximated to arbitrary precision by feedforward NNs (which are the type most often used in practical applications) if you have enough data and enough computing resources.

To be somewhat more precise, feedforward networks with a single hidden layer and trained by least-squares are statistically consistent estimators of arbitrary square-integrable regression functions under certain practically-satisfiable assumptions regarding sampling, target noise, number of hidden units, size of weights, and form of hidden-unit activation function (White, 1990). Such networks can also be trained as statistically consistent estimators of derivatives of regression functions (White and Gallant, 1992) and quantiles of the conditional noise distribution (White, 1992a). Feedforward networks with a single hidden layer using threshold or sigmoid activation functions are universally consistent estimators of binary classifications (Faragó and Lugosi, 1993; Lugosi and Zeger 1995; Devroye, Györfi, and Lugosi, 1996) under similar assumptions. Note that these results are stronger than the universal approximation theorems that merely show the existence of weights for arbitrarily accurate approximations, without demonstrating that such weights can be obtained by learning.

Unfortunately, the above consistency results depend on one impractical assumption: that the networks are trained by an error (L_p error or misclassification rate) minimization technique that comes arbitrarily close to the global minimum. Such minimization is computationally intractable except in small or simple problems (Blum and Rivest, 1989; Judd, 1990). In practice, however, you can usually get good results without doing a full-blown global optimization; e.g., using multiple (say, 10 to 1000) random weight initializations is usually sufficient.

One example of a function that a typical neural net cannot learn is Y=1/X on the open interval (0,1). An open interval is not a compact set. With any bounded output activation function, the error will get arbitrarily large as the input approaches zero. Of course, you could make the output activation function a reciprocal function and easily get a perfect fit, but neural networks are most often used in situations where you do not have enough prior knowledge to set the activation function in such a clever way. There are also many other important problems that are so difficult that a neural network will be unable to learn them without memorizing the entire training set, such as:

* Predicting random or pseudo-random numbers.

* Factoring large integers.

* Determing whether a large integer is prime or composite.

* Decrypting anything encrypted by a good algorithm.

And it is important to understand that there are no methods for training NNs that can magically create information that is not contained in the training data.

Feedforward NNs are restricted to finite-dimensional input and output spaces. Recurrent NNs can in theory process arbitrarily long strings of numbers or symbols. But training recurrent NNs has posed much more serious practical difficulties than training feedforward networks. NNs are, at least today, difficult to apply successfully to problems that concern manipulation of symbols and rules, but much research is being done.

There have been attempts to pack recursive structures into finite-dimensional real vectors (Blair, 1997; Pollack, 1990; Chalmers, 1990; Chrisman, 1991; Plate, 1994; Hammerton, 1998). Obviously, finite precision limits how far the recursion can go (Hadley, 1999). The practicality of such methods is open to debate.

As for simulating human consciousness and emotion, that's still in the realm of science fiction. Consciousness is still one of the world's great mysteries. Artificial NNs may be useful for modeling some aspects of or prerequisites for consciousness, such as perception and cognition, but ANNs provide no insight so far into what Chalmers (1996, p. xi) calls the "hard problem":

Many books and articles on consciousness have appeared in the past few years, and one might think we are making progress. But on a closer look, most of this work leaves the hardest problems about consciousness untouched. Often, such work addresses what might be called the "easy problems" of consciousness: How does the brain process environmental stimulation? How does it integrate information? How do we produce reports on internal states? These are important questions, but to answer them is not to solve the hard problem: Why is all this processing accompanied by an experienced inner life?"

(source)

Practical applications of NNs most often employ supervised learning. For supervised learning, you must provide training data that includes both the input and the desired result (the target value). After successful training, you can present input data alone to the NN (that is, input data without the desired result), and the NN will compute an output value that approximates the desired result. However, for training to be successful, you may need lots of training data and lots of computer time to do the training. In many applications, such as image and text processing, you will have to do a lot of work to select appropriate input data and to code the data as numeric values.

In practice, NNs are especially useful for classification and function approximation/mapping problems which are tolerant of some imprecision, which have lots of training data available, but to which hard and fast rules (such as those that might be used in an expert system) cannot easily be applied. Almost any finite-dimensional vector function on a compact set can be approximated to arbitrary precision by feedforward NNs (which are the type most often used in practical applications) if you have enough data and enough computing resources.

To be somewhat more precise, feedforward networks with a single hidden layer and trained by least-squares are statistically consistent estimators of arbitrary square-integrable regression functions under certain practically-satisfiable assumptions regarding sampling, target noise, number of hidden units, size of weights, and form of hidden-unit activation function (White, 1990). Such networks can also be trained as statistically consistent estimators of derivatives of regression functions (White and Gallant, 1992) and quantiles of the conditional noise distribution (White, 1992a). Feedforward networks with a single hidden layer using threshold or sigmoid activation functions are universally consistent estimators of binary classifications (Faragó and Lugosi, 1993; Lugosi and Zeger 1995; Devroye, Györfi, and Lugosi, 1996) under similar assumptions. Note that these results are stronger than the universal approximation theorems that merely show the existence of weights for arbitrarily accurate approximations, without demonstrating that such weights can be obtained by learning.

Unfortunately, the above consistency results depend on one impractical assumption: that the networks are trained by an error (L_p error or misclassification rate) minimization technique that comes arbitrarily close to the global minimum. Such minimization is computationally intractable except in small or simple problems (Blum and Rivest, 1989; Judd, 1990). In practice, however, you can usually get good results without doing a full-blown global optimization; e.g., using multiple (say, 10 to 1000) random weight initializations is usually sufficient.

One example of a function that a typical neural net cannot learn is Y=1/X on the open interval (0,1). An open interval is not a compact set. With any bounded output activation function, the error will get arbitrarily large as the input approaches zero. Of course, you could make the output activation function a reciprocal function and easily get a perfect fit, but neural networks are most often used in situations where you do not have enough prior knowledge to set the activation function in such a clever way. There are also many other important problems that are so difficult that a neural network will be unable to learn them without memorizing the entire training set, such as:

* Predicting random or pseudo-random numbers.

* Factoring large integers.

* Determing whether a large integer is prime or composite.

* Decrypting anything encrypted by a good algorithm.

And it is important to understand that there are no methods for training NNs that can magically create information that is not contained in the training data.

Feedforward NNs are restricted to finite-dimensional input and output spaces. Recurrent NNs can in theory process arbitrarily long strings of numbers or symbols. But training recurrent NNs has posed much more serious practical difficulties than training feedforward networks. NNs are, at least today, difficult to apply successfully to problems that concern manipulation of symbols and rules, but much research is being done.

There have been attempts to pack recursive structures into finite-dimensional real vectors (Blair, 1997; Pollack, 1990; Chalmers, 1990; Chrisman, 1991; Plate, 1994; Hammerton, 1998). Obviously, finite precision limits how far the recursion can go (Hadley, 1999). The practicality of such methods is open to debate.

As for simulating human consciousness and emotion, that's still in the realm of science fiction. Consciousness is still one of the world's great mysteries. Artificial NNs may be useful for modeling some aspects of or prerequisites for consciousness, such as perception and cognition, but ANNs provide no insight so far into what Chalmers (1996, p. xi) calls the "hard problem":

Many books and articles on consciousness have appeared in the past few years, and one might think we are making progress. But on a closer look, most of this work leaves the hardest problems about consciousness untouched. Often, such work addresses what might be called the "easy problems" of consciousness: How does the brain process environmental stimulation? How does it integrate information? How do we produce reports on internal states? These are important questions, but to answer them is not to solve the hard problem: Why is all this processing accompanied by an experienced inner life?"

(source)

## Monday, May 01, 2006

### Book about NN by Smith

Today i will start reading a new book by Murray Smith called "NN for statistical modeling". The book is about backpropagation, which is supposed to be the most widely used and studied method in the NN community.The book was published in 1996 and seems to be a rather understandable one combining theoretical and practical issues. I will keep you informed about it.

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