Advanced Algorithmic Trading Strategies
In its Matlab implementation, ANFIS is a training routine for Sugeno-type FIS based on adaptive generalized neural networks. ANFIS uses a hybrid-learning algorithm to identify parameters. It applies a combination of the least-squares (LS) method and the backpropagation gradient descent algorithm for training FIS membership function parameters to emulate a given training data set.
Among economists, the random walk hypothesis, now referred to as the weak form of the Efficient Markets Hypothesis, is fairly generally accepted. Some, like Andrew Lo, director of the MIT Laboratory for Financial Engineering, have argued that because of investor irrationality, asset prices display some momentum over time. But this claim remains controversial, as does the performance of algorithmic trading strategies designed to exploit such patterns. Even the skeptics agree that any violations of the weak form of the hypothesis are subtle and hard to exploit.
The second computer package that will be used in this book is Maple. This is a symbolic algebra system. It not only performs numerical calculations but also manipulates mathematical symbols. In effect, it obligingly does the mathematics for you. There are other similar packages available, such as Matlab, Derive and Mathcad, and most of the Maple examples and exercises given in this book can be tackled just as easily using these packages instead. This is not the place to show you the full power of Maple, but hopefully the examples given in this book will give you a flavour of what can be achieved, and why it is such a valuable tool in mathematical modelling.
The research described here still very much represents work in progress - currently under the aegis of a research fellowship awarded under the Goal Environmental Change Programme of the ESRC. The author is indebted to David Waxman who operationalised for 'Matlab' software (version 4.2c.1) the 'diversity optimisation' procedure developed by the author. Without David's invaluable input, the illustrative analysis described in the final section of this paper would have been prohibitively difficult to perform on a spreadsheet. Without implicating them in any way in the shortcomings, the author is also especially grateful for many thoughtful general comments on the manuscript by Chris Freeman, Keith Pavitt, Ed Steinmueller and Nick von Tunzelman and for discussions over the years on various specific issues arising in this study to colleagues at SPRU and further afield, especially David Fisk (on fuzzy logic and ignorance), Sylvan Katz (on complexity and power law relations), Gordon MacKerron...
We conclude this section by describing the use of a computer package to solve optimization problems. Although a spreadsheet could be used to do this, by tabulating the values of a function, it cannot handle the associated mathematics. A symbolic computation system such as Maple, Matlab, Mathcad or Derive can not only sketch the graphs of functions, but also differentiate and solve algebraic equations. Consequently, it is possible to obtain the exact solution using one of these packages. In this book we have chosen to use Maple.
In the Parallel ANFIS-NN prototypes, several ANFIS systems work in parallel and feed their first-stage cost estimates to a neural network that merges these first-stage estimates and produces as output the final estimate of the cost. We developed and discuss here systems where each ANFIS simultaneously takes either two or three variables as inputs, namely Parallel-ANFIS-NN1 and Parallel-ANFIS-NN2. Once again, the best results were always obtained by using Gaussian type membership functions, either gaussmf, gauss2mf, or gbell in Matlab's language. The neural networks developed for the two- and three-input ANFIS were very similar to each other, and both use logsig for the transfer functions in both layers of the backprop networks.
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