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

This chapter develops a new nonlinear model, Ultra high frequency siGmoid and Trigonometric Higher Order Neural Networks (UGT-HONN), for data pattern recognition. UGT-HONN includes Ultra high frequency siGmoid and Sine function Higher Order Neural Networks (UGS-HONN) and Ultra high frequency siGmoid and Cosine functions Higher Order Neural Networks (UGC-HONN). UGS-HONN and UGC-HONN models are used to recognition data patterns. Results show that UGS-HONN and UGC-HONN models are better than other Polynomial Higher Order Neural Network (PHONN) and Trigonometric Higher Order Neural Network (THONN) models, since UGS-HONN and UGC-HONN models to recognize data pattern with error approaching 0.0000%.

New open box and nonlinear system model of Ultra High Frequency Sigmoid and Sine Artificial Higher Order Neural Network (UGS-HONN) is presented in this paper. A new learning algorithm for UGS-HONN is also developed from this study. A time series data modeling system, UGS-HONN Simulator, is built based on the UGS-HONN system models too. Test results show that average error of UGS-HONN system models are closing to zero (10-6). The average errors of Polynomial Higher Order Neural Network (PHONN), Trigonometric Higher Order Neural Network (THONN), and Sigmoid polynomial Higher Order Neural Network (SPHONN) models are from 2.8128% to 4.9076%. It means that UGS-HONN system models are 2.8128% to 4.9076% better than PHONN, THONN and SPHONN models.

Business is a diversified field with general areas of specialisation such as accounting, taxation, stock market, and other financial analysis. Artificial Neural Networks (ANN) have been widely used in applications such as bankruptcy prediction, predicting costs, forecasting revenue, forecasting share prices and exchange rates, processing documents and many more. This chapter introduces an Adaptive Higher Order Neural Network (HONN) model and applies the adaptive model in business applications such as simulating and forecasting share prices. This adaptive HONN model offers significant advantages over traditional Standard ANN models such as much reduced network size, faster training, as well as much improved simulation and forecasting errors, due to their ability to better approximate complex, non-smooth, often discontinuous training data sets. The generalisation ability of this HONN model is explored and discussed.

The data in the real world are complex and varied. When we apply artificial neural networks to simulate the real-world commerce data through simple functions, accuracy could become problematic. To overcome this issue, we could choose Higher Order Neural Network (HONN) models, which can simulate a data set very accurately. This paper has developed a new open-box HONN model with fractional functions, called a Fractional High Frequency Cosine and Sine HONN (FHFCSHONN) model. FHFCSHONN structure and learning algorithm formulas are studied too. This paper also built a new software package called a FHFCSHONN simulator. Based on the commerce data testing results, the FHFCSHONN model's average error is 0.6980%, while the other three HONN model average errors are 4.0160%, 4.2370%, and 4.3556% respectively.

An Artificial Neural Network (ANN) works by creating connections between different processing elements (artificial neurons). ANNs have been extensively used for Data Mining, which extracts hidden patterns and valuable information from large databases. This paper introduces a new adaptive Higher Order Neural Network (HONN) model and applies it in data mining tasks such as determining breast cancer recurrences and predicting incomes base on census data. An adaptive hyperbolic tangent function is used as the neuron activation function for the new adaptive HONN model. The paper compares the new HONN model against a Multi-Layer Perceptron (MLP) with the sigmoid activation function, an RBF Neural Network with the Gaussian activation function, and a Recurrent Neural Network (RNN) with the sigmoid activation function. Experimental results show that the new adaptive HONN model offers several advantages over conventional ANN models such as better generalisation capabilities as well as abilities in handling missing values in a dataset.

Business is a diversified field with general areas of specialisation such as accounting, taxation, stock market, and other financial analysis. Artificial Neural Networks (ANNs) have been widely used in ap- plications such as bankruptcy prediction, predicting costs, forecasting revenue, forecasting share prices and exchange rates, processing documents and many more. This chapter introduces an Adaptive Higher Order Neural Network (HONN) model and applies the adaptive model in business applications such as simulating and forecasting share prices. This adaptive HONN model offers significant advantages over traditional Standard ANN models such as much reduced network size, faster training, as well as much improved simulation and forecasting errors, due to their ability to better approximate complex, non-smooth, often discontinuous training data sets. The generalisation ability of this HONN model is explored and discussed.

This paper introduces an adaptive Higher Order Neural Network (HONN) model and applies it in data mining such as simulating and forecasting government taxation revenues. The proposed adaptive HONN model offers significant advantages over conventional Artificial Neural Network (ANN) models such as much reduced network size, faster training, as well as much improved simulation and forecasting errors. The generalization ability of this HONN model is explored and discussed. A new approach for determining the best number of hidden neurons is also proposed.

This chapter introduces multi-polynomial higher order neural network models (MPHONN) with higher accuracy. Using Sun workstation, C++, and Motif, a MPHONN simulator has been built. Real-world data cannot always be modeled simply and simulated with high accuracy by a single polynomial function. Thus, ordinary higher order neural networks could fail to simulate complicated real-world data. But MPHONN model can simulate multi-polynomial functions and can produce results with improved accuracy through experiments. By using MPHONN for financial modeling and simulation, experimental results show that MPHONN can always have 0.5051% to 0.8661% more accuracy than ordinary higher order neural network models.

In this paper, a new discrete time identification scheme for a singularly perturbed nonlinear system using recurrent high order multi-time scale neural network is presented. The high-order neural network (HONN) is known for its simple structure and powerful nonlinearity approximation property, which make it more suitable for modeling the singularly perturbed nonlinear systems than the multi-layer neural network [10]. An on-line identification scheme—optimal bounded ellipsoid (OBE) algorithm is developed for the recurrent high order neural network (RHONN) model. By adaptively changing the learning rate, the on-line identification scheme can achieve faster convergence compared to the other widely used learning schemes, such as backpropagation. Simulation results are presented to demonstrate the effectiveness of the proposed algorithm.

This paper estimates the equilibrium real effective exchange rate and determine the level of exchange rate misalignment in Sierra Leone, for the period 1980 to 2018. The paper utilizes the behavioral equilibrium exchange rate methodology within the Johansen maximum likelihood framework to estimate the long run equilibrium real effective exchange rate. The unit root test result shows that all the variables are integrated of order one, whilst the cointegration test establishes the existence of one cointegrating vector as evidenced by both the Trace and Maximum Eigen Statistics. The normalized long run results reveal that openness, government expenditure and money supply were the most significant determinants of the real effective exchange rate in the long run. Furthermore, the findings reveal that the real effective exchange rate experienced sustained deviation from the long run equilibrium real effective exchange rate during the study period, with episodes of overvaluation and undervaluation. Specifically, the real effective exchange rate was overvalued by 3.69 percent during the period between 1980-1985; undervalued by 1.8 percent between 1986-1997, and overvalued by 0.9 percent between 1998-2004, Thus, the paper reveals episodes of misalignment of the real effective exchange rate. Based on these findings, the study recommends that, the monetary authorities should ensure stability of the exchange rate and maintain price stability, through sterilization of capital flows as well as contain money growth within the statutory limit.

This chapter proposes a theoretical framework for parallel implementation of Deep Higher Order Neural Networks (HONNs). First, we develop a new partitioning approach for mapping HONNs to individual computers within a master-slave distributed system (a local area network). This will allow us to use a network of computers (rather than a single computer) to train a HONN to drastically increase its learning speed: all of the computers will be running the HONN simultaneously (parallel implementation). Next, we develop a new learning algorithm so that it can be used for HONN learning in a distributed system environment. Finally, we propose to improve the generalisation ability of the new learning algorithm as used in a distributed system environment. Theoretical analysis of the proposal is thoroughly conducted to verify the soundness of the new approach. Experiments will be performed to test the new algorithm in the future.

Time series forecasting gets much attention due to its impact on many practical applications. Higher-order neural network with recurrent feedback is a powerful technique which used successfully for forecasting. It maintains fast learning and the ability to learn the dynamics of the series over time. In general, the most used recurrent feedback is the network output. However, no much attention has been paid to use network error instead of the network output. For that, in this paper, we propose a novel model which is called Ridge Polynomial Neural Network with Error Feedback (RPNN-EF) that combines the properties of higher order and error feedback recurrent neural network. Three signals have been used in this paper, namely heat wave temperature, IBM common stock closing price and Mackey–Glass equation. Simulation results show that RPNN-EF is significantly faster than other RPNN-based models for one-step ahead forecasting and its forecasting performance is more significant than these models for multi-step ahead forecasting.

The detection of gaussian signals with unknown correlation coefficient, ρ s is considered. A strategy for designing high order neural networks (HONN) in composite hypothesis test is proposed. A HONN trained with ρ s varying uniformly in [0, 1] is considered to approximate the Average Likelihood Ratio (ALR). In order to compare the suitability of the approximation, a sub-optimal solution based on constrained generalized likelihood ratio is used. A study of the computational cost is carried out. Results show that a HONN is able to approximate the ALR with a low computational cost.

Multiresolution locally expanded HONN for handwritten numeral recognition

The motivation for this article is to check whether neural network models have remained a superior method for forecasting the EUR/USD exchange rate during the financial crisis of 2007–2009. Alternative neural network architectures (Multi-Layer Perceptron (MLP), Recurrent Neural Network and Higher Order Neural Network (HONN)) are benchmarked against a random walk and a traditional ARMA model, and evaluated in terms of statistical accuracy and through a trading simulation on daily data over the period from January 2000 to February 2009, the period from August 2007 to February 2009, providing the out-of-sample testing period. Transaction costs and a confirmation filter devised to reduce false signals and thus also reduce losses and transaction costs were also taken into consideration. It is shown that the HONN structure gives the overall best results on a simple trading simulation; however, for an advanced trading simulation with a confirmation filter, the MLP outperforms all other models on most performance measures. On the whole, the results show that neural networks are still able to produce forecasts that yield a positive return and are superior to those of linear and more traditional models, with respect to both trading performance and statistical accuracy, even under very volatile market conditions.