Ultra High Frequency Trigonometric Higher Order Neural Networks for Time Series Data Analysis

Ultra High Frequency Trigonometric Higher Order Neural Networks for Time Series Data Analysis

Ming Zhang (Christopher Newport University, USA)
Copyright: © 2009 |Pages: 31
DOI: 10.4018/978-1-59904-897-0.ch007
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Abstract

This chapter develops a new nonlinear model, Ultra high frequency Trigonometric Higher Order Neural Networks (UTHONN), for time series data analysis. Results show that UTHONN models are 3 to 12% better than Equilibrium Real Exchange Rates (ERER) model, and 4 – 9% better than other Polynomial Higher Order Neural Network (PHONN) and Trigonometric Higher Order Neural Network (THONN) models. This study also uses UTHONN models to simulate foreign exchange rates and consumer price index with error approaching 0.0000%.
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Introduction

Time series models are the most studied models in macroeconomics as well as in financial economics. Nobel Prize in Economic in 2003 rewards two contributions: nonstationarity and time-varying volatility. These contributions have greatly deepened our understanding of two central properties of many economic time series (Vetenskapsakademien, 2003). Nonstationarity is a property common to many macroeconomic and financial time series models. It means that a variable has no clear tendency to return to a constant value or a linear trend. Examples include the value of the US dollar expressed in Japanese yen and consumer price indices of the US and Japan. Granger (1981) changes the way of empirical models in macroeconomic relationships by introducing the concept of cointegrated variables. Granger and Bates (1969) research the combination of forecasts. Granger and Weiss (1983) show the importance of cointegration in the modeling of nonstationary economic series. Granger and Lee (1990) studied multicointegration. Granger and Swanson (1996) further develop multicointegration in studying of cointegrated variables. The first motivation of this chapter is to develop a new nonstationary data analysis system by using new generation computer techniques that will improve the accuracy of the analysis.

After Meese and Rogof’s (1983A, and 1983B) pioneering study on exchange rate predictability, the goal of using economic models to beat naïve random walk forecasts still remains questionable (Taylor, 1995). One possibility is that the standard economic models of exchange rate determination are inadequate, which is a common response of many professional exchange rate forecasters (Kiliam and Taylor, 2003; Cheung and Chinn, 1999). Another possibility is that linear forecasting models fail to consider important nonlinear properties in the data. Recent studies document various nonlinearities in deviations of the spot exchange rate from economic fundamentals (Balke and Fomby, 1997; Taylor and Peel, 2000; Taylor et al., 2001). Gardeazabal and Regulez (1992) study monetary model of exchange rates and cointegration for estimating, testing and predicting long run and short run nominal exchange rates. MacDonald and Marsh (1999) provide a cointegration and VAR (Vector Autoregressive) modeling for high frequency exchange rates. Estimating the equilibrium exchange rates has been rigorously studied (Williamson 1994). Ibrahima A. Elbradawi (1994) provided a model for estimating long-run equilibrium real exchange rates. Based on Elbradawi’s study, the average error percentage (error percentage = |error|/rate; average error percentage = total error percentage/n years) of long-run equilibrium real exchange rate is 14.22% for Chile (1968-1990), 20.06% for Ghana (1967-1990) and 4.73% for India (1967-1988). The second motivation for this chapter is to simulate actual exchange rate by developing new neural network models for improving prediction accuracy.

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Dedication
Table of Contents
Acknowledgment
Ming Zhang
Chapter 1
Ming Zhang
This chapter delivers general format of Higher Order Neural Networks (HONNs) for nonlinear data analysis and six different HONN models. This chapter... Sample PDF
Artificial Higher Order Neural Network Nonlinear Models: SAS NLIN or HONNs?
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Chapter 2
Adam Knowles, Abir Hussain, Wael El Deredy, Paulo G.J. Lisboa, Christian L. Dunis
Multi-Layer Perceptrons (MLP) are the most common type of neural network in use, and their ability to perform complex nonlinear mappings and... Sample PDF
Higher Order Neural Networks with Bayesian Confidence Measure for the Prediction of the EUR/USD Exchange Rate
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Chapter 3
Da Shi, Shaohua Tan, Shuzhi Sam Ge
Real-world financial systems are often nonlinear, do not follow any regular probability distribution, and comprise a large amount of financial... Sample PDF
Automatically Identifying Predictor Variables for Stock Return Prediction
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Chapter 4
John Seiffertt, Donald C. Wunsch II
As the study of agent-based computational economics and finance grows, so does the need for appropriate techniques for the modeling of complex... Sample PDF
Higher Order Neural Network Architectures for Agent-Based Computational Economics and Finance
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Chapter 5
Yuehui Chen, Peng Wu, Qiang Wu
Forecasting exchange rates is an important financial problem that is receiving increasing attention especially because of its difficulty and... Sample PDF
Foreign Exchange Rate Forecasting Using Higher Order Flexible Neural Tree
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Chapter 6
Yuehui Chen, Peng Wu, Qiang Wu
Artificial Neural Networks (ANNs) have become very important in making stock market predictions. Much research on the applications of ANNs has... Sample PDF
Higher Order Neural Networks for Stock Index Modeling
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Chapter 7
Ming Zhang
This chapter develops a new nonlinear model, Ultra high frequency Trigonometric Higher Order Neural Networks (UTHONN), for time series data... Sample PDF
Ultra High Frequency Trigonometric Higher Order Neural Networks for Time Series Data Analysis
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Chapter 8
Panos Liatsis, Abir Hussain, Efstathios Milonidis
The research described in this chapter is concerned with the development of a novel artificial higher order neural networks architecture called the... Sample PDF
Artificial Higher Order Pipeline Recurrent Neural Networks for Financial Time Series Prediction
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Chapter 9
Abir Hussain, Panos Liatsis
The research described in this chapter is concerned with the development of a novel artificial higherorder neural networks architecture called the... Sample PDF
A Novel Recurrent Polynomial Neural Network for Financial Time Series Prediction
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Chapter 10
David R. Selviah, Janti Shawash
Generalized correlation higher order neural network designs are developed. Their performance is compared with that of first order networks... Sample PDF
Generalized Correlation Higher Order Neural Networks for Financial Time Series Prediction
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Chapter 11
Godfrey C. Onwubolu
Real world problems are described by nonlinear and chaotic processes, which makes them hard to model and predict. This chapter first compares the... Sample PDF
Artificial Higher Order Neural Networks in Time Series Prediction
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Chapter 12
Rozaida Ghazali, Dhiya Al-Jumeily
This chapter discusses the use of two artificial Higher Order Neural Networks (HONNs) models; the Pi- Sigma Neural Networks and the Ridge Polynomial... Sample PDF
Application of Pi-Sigma Neural Networks and Ridge Polynomial Neural Networks to Financial Time Series Prediction
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Chapter 13
Edgar N. Sanchez, Alma Y. Alanis, Jesús Rico
In this chapter, we propose the use of Higher Order Neural Networks (HONNs) trained with an extended Kalman filter based algorithm to predict the... Sample PDF
Electric Load Demand and Electricity Prices ForecastingUsing Higher Order Neural Networks Trained by Kalman Filtering
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Chapter 14
Shuxiang Xu
Business is a diversified field with general areas of specialisation such as accounting, taxation, stock market, and other financial analysis.... Sample PDF
Adaptive Higher Order Neural Network Models and Their Applications in Business
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Chapter 15
Jean X. Zhang
This chapter proposes nonlinear models using artificial neural network models to study the relationship between chief elected official (CEO) tenure... Sample PDF
CEO Tenure and Debt: An Artificial Higher Order Neural Network Approach
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Chapter 16
Christian L. Dunis, Jason Laws, Ben Evans
This chapter investigates the soybean-oil “crush” spread, that is the profit margin gained by processing soybeans into soyoil. Soybeans form a large... Sample PDF
Modelling and Trading the Soybean-Oil Crush Spread with Recurrent and Higher Order Networks: A Comparative Analysis
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Chapter 17
Madan M. Gupta, Noriyasu Homma, Zeng-Guang Hou, Ashu M. G. Solo, Takakuni Goto
In this chapter, we aim to describe fundamental principles of artificial higher order neural units (AHONUs) and networks (AHONNs). An essential core... Sample PDF
Fundamental Theory of Artificial Higher Order Neural Networks
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Chapter 18
Jinde Cao, Fengli Ren, Jinling Liang
This chapter concentrates on studying the dynamics of artificial higher order neural networks (HONNs) with delays. Both stability analysis and... Sample PDF
Dynamics in Artificial Higher Order Neural Networks with Delays
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Chapter 19
Zhao Lu, Leang-san Shieh, Guanrong Chen
Aiming to develop a systematic approach for optimizing the structure of artificial higher order neural networks (HONN) for system modeling and... Sample PDF
A New Topology for Artificial Higher Order Neural Networks: Polynomial Kernel Networks
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Chapter 20
David R. Selviah
This chapter describes the progress in using optical technology to construct high-speed artificial higher order neural network systems. The chapter... Sample PDF
High Speed Optical Higher Order Neural Networks for Discovering Data Trends and Patterns in Very Large Databases
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Chapter 21
Zidong Wang, Yurong Liu, Xiaohui Liu
This chapter deals with the analysis problem of the global exponential stability for a general class of stochastic artificial higher order neural... Sample PDF
On Complex Artificial Higher Order Neural Networks: Dealing with Stochasticity, Jumps and Delays
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Chapter 22
Lei Zhang, Simeon J. Simoff, Jing Chun Zhang
This chapter introduces trigonometric polynomial higher order neural network models. In the area of financial data simulation and prediction, there... Sample PDF
Trigonometric Polynomial Higher Order Neural Network Group Models and Weighted Kernel Models for Financial Data Simulation and Prediction
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