Pairote Sattayatham

GB-splines of arbitrary order

Explicit formulae and recurrence relations for the calculation of generalized B-splines (GB-splines) of arbitrary order are given. We derive main properties of GB-splines and their series, i.e. partition of unity, shape-preserving properties, invariance with respect to ane transformations, etc. It is shown that such splines have the variation diminishing property and are Chebyshevian splines. c 1999 Elsevier Science B.V. All rights reserved.

On periodic solutions of nonlinear evolution equations in Banach spaces

We prove an existence result for T -periodic solutions to nonlinear evolution equations of the form

Weighted k-means for density-biased clustering

Clustering is a task of grouping data based on similarity. A popular k-means algorithm groups data by firstly assigning all data points to the closest clusters, then determining the cluster means. The algorithm repeats these two steps until it has converged. We propose a variation called weighted k-means to improve the clustering scalability. To speed up the clustering process, we develop the reservoir-biased sampling as an efficient data reduction technique since it performs a single scan over a data set. Our algorithm has been designed to group data of mixture models. We present an experimental evaluation of the proposed method.

Classification of invariant solutions of the Boltzmann equation

An isomorphism of the Lie algebras L11 admissible by the full Boltzmann kinetic equation with an arbitrary differential cross section and by the Euler gas dynamics system of equations with a general state equation is set up. The similarity is also proved between extended algebras L12 admissible by the same equations for specified power-like intermolecular potentials and for polytropic gas. This allows the solution of the problem of classification of the full Boltzmann equation invariant H-solutions using an optimal system of subalgebras known for the Euler system. Representations of essentially different H-solutions of the spatially inhomogeneous Boltzmann equation with one and two independent invariant variables in the explicit form are obtained on this basis.

Relaxed controls for a class of strongly nonlinear delay evolution equations

Abstract Relaxed controls for a class of strongly nonlinear delay evolution equations are investigated. Existence of solutions of strongly nonlinear delay equations is proved and properties of original and relaxed trajectories are discussed. The existence of optimal relaxed controls and relaxation result are also presented. For illustration, two examples are given.

Density-biased clustering based on reservoir sampling

Clustering is a task of grouping data based on similarity. A popular k-means algorithm groups data by firstly assigning all data points to the closest clusters, then determining the cluster means. The algorithm repeats these two steps until it has converged. We propose a variation called weighted k-means to improve the clustering scalability. To speed up the clustering process, we develop the reservoir-biased sampling as an efficient data reduction technique since it performs a single scan over a data set. Our algorithm has been designed to group data of mixture models. We present an experimental evaluation of the proposed method.

Stock Trading Using PE Ratio Based on Bayesian Inference

The Price Earnings (PE) ratio is one of the most widely applied tool for the firm valuation in a security market. Unfortunately, recent academic developments in financial econometrics and machine learning have rarely looked at this tool. In the paper, we propose to formalize a process of fundamental PE ratio estimation by employing Dynamic Bayesian Network (DBN) methodology. Forward-backward inference and Expectation Maximization (EM) parameter estimation algorithms are derived with respect to our proposed DBN structure. A simple but practical trading strategy is invented based on the result of Bayesian inference. We make stock trading experiments using Thai stocks and American stocks, respectively. Extensive experiments show that our trading strategy statistically outperforms the buy-and-hold strategy.

Value at risk estimation under stochastic volatility models using adaptive PMCMC methods

ABSTRACT In this paper, we propose a value-at-risk (VaR) estimation technique based on a new stochastic volatility model with leverage effect, nonconstant conditional mean and jump. In order to estimate the model parameters and latent state variables, we integrate the particle filter and adaptive Markov Chain Monte Carlo (MCMC) algorithms to develop a novel adaptive particle MCMC (A-PMCMC) algorithm. Comprehensive simulation experiments based on three stock indices and two foreign exchange time series show effectiveness of the proposed A-PMCMC algorithm and the VaR estimation technique.

Forecasting Volatility and Price of the SET50 Index Using the Markov Regime Switching

Abstract In this paper, we forecast the volatility and price of SET50 Index using the Markov Regime Switching GARCH (MRS-GARCH) models. These models allow volatility to have different dynamics according to unobserved regime variables. The main purpose of this paper is to find out whether the MRS-GARCH models are an improvement on the GARCH type models in terms of modeling and forecast volatility and price of the SET50 Index. The MRS-GARCH under the GED distribution is best performance model for the SET50 Index volatility. Moreover, we forecast closing price of SET50 Index, we found the MRS-GARCH under t-distribution with two degree of freedoms model is perform best.

Relaxed Control for a Class of Strongly Nonlinear Impulsive Evolution Equations

Relaxed control for a class of strongly nonlinear impulsive evolution equations is investigated. Existence of solutions of strongly nonlinear impulsive evolution equations is proved and properties of original and relaxed trajectories are discussed. The existence of optimal relaxed control and relaxation results are also presented. For illustration, one example is given.