Wavelet Neural Networks

With Applications in Financial Engineering, Chaos, and Classification

Antonios K. Alexandridis, Achilleas D. Zapranis

• Éditeur: Wiley
• Année: 2014
• ISBN:
  9781118596296
• Édition: 1
• Sujet: Mathematik
• Sous-sujet: Mathematische Analyse

A step-by-step introduction to modeling, training, and forecasting using wavelet networks

Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification presents the statistical model identification framework that is needed to successfully apply wavelet networks as well as extensive comparisons of alternate methods. Providing a concise and rigorous treatment for constructing optimal wavelet networks, the book links mathematical aspects of wavelet network construction to statistical modeling and forecasting applications in areas such as finance, chaos, and classification.

The authors ensure that readers obtain a complete understanding of model identification by providing in-depth coverage of both model selection and variable significance testing. Featuring an accessible approach with introductory coverage of the basic principles of wavelet analysis, Wavelet Neural Networks: With Applications in Financial Engineering, Chaos, and Classification also includes:

• Methods that can be easily implemented or adapted by researchers, academics, and professionals in identification and modeling for complex nonlinear systems and artificial intelligence

• Multiple examples and thoroughly explained procedures with numerous applications ranging from financial modeling and financial engineering, time series prediction and construction of confidence and prediction intervals, and classification and chaotic time series prediction

• An extensive introduction to neural networks that begins with regression models and builds to more complex frameworks

• Coverage of both the variable selection algorithm and the model selection algorithm for wavelet networks in addition to methods for constructing confidence and prediction intervals

Ideal as a textbook for MBA and graduate-level courses in applied neural network modeling, artificial intelligence, advanced data analysis, time series, and forecasting in financial engineering, the book is also useful as a supplement for courses in informatics, identification and modeling for complex nonlinear systems, and computational finance. In addition, the book serves as a valuable reference for researchers and practitioners in the fields of mathematical modeling, engineering, artificial intelligence, decision science, neural networks, and finance and economics.

1
Machine Learning and Financial Engineering

Wavelet networks are a new class of networks that combine the classic sigmoid neural networks and wavelet analysis. Wavelet networks were proposed by Zhang and Benveniste (1992) as an alternative to feedforward neural networks which would alleviate the weaknesses associated with wavelet analysis and neural networks while preserving the advantages of each method.

Recently, wavelet networks have gained a lot of attention and have been used with great success in a wide range of applications, ranging from engineering; control; financial modeling; short-term load forecasting; time-series prediction; signal classification and compression; signal denoising; static, dynamic, and nonlinear modeling; to nonlinear static function approximation.

Wavelet networks are a generalization of radial basis function networks (RBFNs). Wavelet networks are hidden layer networks that use a wavelet for activation instead of the classic sigmoidal family. It is important to mention here that multidimensional wavelets preserve the “universal approximation” property that characterizes neural networks. The nodes (or wavelons) of wavelet networks are wavelet coefficients of the function expansion that have a significant value. In Bernard et al. (1998), various reasons were presented for why wavelets should be used instead of other transfer functions. In particular, first, wavelets have high compression abilities, and second, computing the value at a single point or updating a function estimate from a new local measure involves only a small subset of coefficients.

In statistical terms, wavelet networks are nonlinear nonparametric estimators. Moreover, the universal approximation property states that wavelet networks can approximate, to any degree of accuracy, any nonlinear function and its derivatives. The useful properties of wavelet networks make them an excellent nonlinear estimator for modeling, interpreting, and forecasting complex financial problems and phenomena when only speculation is available regarding the underlying mechanism that generates possible observations.

In the context of a globalized economy, companies that offer financial services try to establish and maintain their competitiveness. To do so, they develop and apply advanced quantitative methodologies. Neural networks represent a new and exciting technology with a wide range of potential financial applications, ranging from simple tasks of assessing credit risk to strategic portfolio management. The fact that neural and wavelet networks avoid a priori assumptions about the evolution in time of the various financial variables makes them a valuable tool.

The purpose of this book is to present a step-by-step guide for model identification of wavelet networks. A generally accepted framework for applying wavelet networks is missing from the literature. In this book we present a complete statistical model identification framework to utilize wavelet networks in various applications. More precisely, wavelet networks are utilized for time-series prediction, construction of confidence and prediction intervals, classification and modeling, and forecasting of chaotic time series in the context of financial engineering. Although our proposed framework is examined primarily for its use in financial applications, it is not limited to finance. It is clear that it can be adopted and used in any discipline in the context of modeling any nonlinear problem or function.

The basic introductory notions are presented below. Fist, financial engineering and its relationship to machine learning and wavelet networks are discussed. Next, research areas related to financial engineering and its function and applications are presented. The basic notions of wavelet analysis and of neural and wavelet networks are also presented. More precisely, the basic mathematical notions that will be needed in later chapters are presented briefly. Also, applications of wavelet networks in finance are presented. Finally, the basic aspects of the framework proposed for the construction of optimal wavelet networks are discussed. More precisely, model selection, variable selection, and model adequacy testing stages are introduced.

Financial Engineering

The most comprehensive definition of financial engineering is the following: Financial engineering involves the design, development, and implementation of innovative financial instruments and processes, and the formulation of creative solutions to problems of finance (Finnerty, 1988). From the definition it is clear that financial engineering is linked to innovation. A general definition of financial innovation includes not only the creation of new types of financial instruments, but the development and evolution of new financial institutions (Mason et al., 1995). Financial innovation is the driving force behind the financial system in fulfilling its primary function: the most efficient possible allocation of financial resources (Ζαπράνης, 2005). Investors, organizations, and companies in the financial sector benefit from financial innovation. These benefits are reflected in lower funding costs, improved yields, better management of various risks, and effective operation within changing regulations.

In recent decades the use of mathematical techniques and processes, derived from operational research, has increased significantly. These methods are used in various aspects of financial engineering. Methods such as decision analysis, statistical estimation, simulation, stochastic processes, optimization, decision support systems, neural networks, wavelet networks, and machine learning in general have become indispensable in several domains of financial operations (Mulvey et al., 1997).

According to Marshall and Bansal (1992), many factors have contributed to the development of financial engineering, including technological advances, globalization of financial markets, increased competition, changing regulations, the increasing ability to solve complex financial models, and the increased volatility of financial markets. For example, the operation of the derivatives markets and risk management systems is supported decisively by continuous advances in the theory of the valuation of derivatives and their use in hedging financial risks. In addition, the continuous increase in computational power while its cost is being reduced makes it possible to monitor thousands of market positions in real time to take advantage of short-term anomalies in the market.

In addition to their knowledge of economic and financial theory, financial engineers are required to possess the quantitative and technical skills ...

Table des matières

• Cover
• Titlepage
• Copyright
• Dedication
• Preface
• Chapter 1: Machine Learning and Financial Engineering
• Chapter 2: Neural Networks
• Chapter 3: Wavelet Neural Networks
• Chapter 4: Model Selection: Selecting the Architecture of the Network
• Chapter 5: Variable Selection: Determining the Explanatory Variables
• Chapter 6: Model Adequacy: Determining a Network's Future Performance
• Chapter 7: Modeling Uncertainty: From Point Estimates to Prediction Intervals
• Chapter 8: Modeling Financial Temperature Derivatives
• Chapter 9: Modeling Financial Wind Derivatives
• Chapter 10: Predicting Chaotic Time Series
• Chapter 11: Classification of Breast Cancer Cases
• Index
• End User License Agreement