Bayesian analysis of wandering vector models for displaying ranking data

In a process of examining k objects, each judge provides a ranking of them. The aim of this paper is to investigate a probabilistic model for ranking data - the wandering vector model. The model represents objects by points in a d-dimensional space, and the judges are represented by latent vectors emanating from the origin in the same space. Each judge samples a vector from a multivariate normal distribution; given this vector, the judge's utility assigned to an object is taken to be the length of the orthogonal projection of the object point onto the judge vector, plus a normally distributed random error. The ordering of the k utilities given by the judge determines the judge's ranking. A Bayesian approach and the Gibbs sampling technique are used for parameter estimation. The method of computing the marginal likelihood proposed by Chib (1995) is used to select the dimensionality of the model. Simulations are done to demonstrate the proposed estimation and model selection method. We then analyze the Goldberg data, in which 10 occupations are ranked according to the degree of social prestige.published_or_final_versio

An R package for analyzing and modeling ranking data

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Fast ML estimation for the mixture of factor analyzers via an ECM algorithm

In this brief, we propose a fast expectation conditional maximization (ECM) algorithm for maximum-likelihood (ML) estimation of mixtures of factor analyzers (MFA). Unlike the existing expectation-maximization (EM) algorithms such as the EM in Ghahramani and Hinton, 1996, and the alternating ECM (AECM) in McLachlan and Peel, 2003, where the missing data contains component-indicator vectors as well as latent factors, the missing data in our ECM consists of component-indicator vectors only. The novelty of our algorithm is that closed-form expressions in all conditional maximization (CM) steps are obtained explicitly, instead of resorting to numerical optimization methods. As revealed by experiments, the convergence of our ECM is substantially faster than EM and AECM regardless of whether assessed by central processing unit (CPU) time or number of iterations. © 2008 IEEE.published_or_final_versio

Combining Technical Trading Rules Using Parallel Particle Swarm Optimization based on Hadoop

Technical trading rules have been utilized in the stock markets to make profit for more than a century. However, no single trading rule can ever be expected to predict the stock price trend accurately. In fact, many investors and fund managers make trading decisions by combining a bunch of technical indicators. In this paper, we consider the complex stock trading strategy, called Performance-based Reward Strategy (PRS), proposed by [1]. Instead of combining two classes of technical trading rules, we expand the scope to combine the seven most popular classes of trading rules in financial markets, resulting in a total of 1059 component trading rules. Each component rule is assigned a starting weight and a reward/penalty mechanism based on rules' recent profit is proposed to update their weights over time. To determine the best parameter values of PRS, we employ an improved time variant particle swarm optimization (TVPSO) algorithm with the objective of maximizing the annual net profit generated by PRS. Due to a large number of component rules and swarm size, the optimization time is significant. A parallel PSO based on Hadoop, an open source parallel programming model of MapReduce, is employed to optimize PRS more efficiently. The experimental results show that PRS outperforms all of the component rules in the testing period.published_or_final_versio

Accumulator pricing

Accumulator is a highly path dependant derivative structure that has been introduced as a retail financial product in recent years and becomes very popular in some Asian cities with its speculative nature. Despite its popularity, its pricing formula is not well known especially when there is a barrier structure. When the barrier in an accumulator contract is applied continuously, this paper obtains exact analytic pricing formulae for immediate settlement and for delay settlement. For discrete barrier, we also obtain analytic formulae which can approximate the fair price of an accumulator under both settlement methods. Through Monte Carlo simulation, we show that the approximation is highly satisfactory. With price formulae in close forms, this paper further explains how to price the product fairly to fit into its zero-cost structure. The analytic formulae also help in computing the Greeks of an accumulator which are documented in this paper. An asymmetry can be observed here that when the buyer is suffering a loss, risk characteristics like delta and vega are substantially larger than when the buyer is enjoying a profit. This means that losing buyers will be more vulnerable to price changes and volatility changes than winning buyers. This is consistent with another observation in the paper that the value at risk for the buyer can be several times larger than that of the seller. © 2009 IEEE.published_or_final_versionThe IEEE Symposium on Computational Intelligence for Financial Engineering (CIFEr) 2009, Nashville, TN., 30 March-2 April 2009. In Proceedings of the CIFEr, 2009, p. 72-7

Complex stock trading strategy based on particle swarm optimization

Technical Session 1B - Advanced Algorithmic Trading – I: no. 41Trading rules have been utilized in the stock market to make profit for more than a century. However, only using a single trading rule may not be sufficient to predict the stock price trend accurately. Although some complex trading strategies combining various classes of trading rules have been proposed in the literature, they often pick only one rule for each class, which may lose valuable information from other rules in the same class. In this paper, a complex stock trading strategy, namely weight reward strategy (WRS), is proposed. WRS combines the two most popular classes of trading rules-moving average (MA) and trading range break-out (TRB). For both MA and TRB, WRS includes different combinations of the rule parameters to get a universe of 140 component trading rules in all. Each component rule is assigned a start weight and a reward/penalty mechanism based on profit is proposed to update these rules’ weights over time. To determine the best parameter values of WRS, we employ an improved time variant Particle Swarm Optimization (PSO) algorithm with the objective of maximizing the annual net profit generated by WRS. The experiments show that our proposed WRS optimized by PSO outperforms the best moving average and trading range break-out rules.postprin

On Buffered Threshold Garch Models

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Testing for the Buffered Autoregressive Processes

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Analyzing ranking data using decision tree

Ranking/preference data arises from many applications in marketing, psychology and politics. We establish a new decision tree model for the analysis of ranking data by adopting the concept of classification and regression tree [2]. We modify the existing splitting criteria, Gini and entropy, which can precisely measure the impurity of a set of ranking data. Two types of impurity measures for ranking data are introduced, namely n-wise and top-k measures. Minimal cost-complexity pruning is used to find the optimum-sized tree. In model assessment, the area under the ROC curve (AUC) is applied to evaluate the tree performance. The proposed methodology is implemented to analyze a partial ranking dataset of Inglehart's items collected in the 1993 International Social Science Programme survey. Change in importance of item values with country, age and level of education are identified.postprintThe European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD 2008), Antwerp, Belgium, 15-19 September 2008. In Proceedings of ECML PKDD 2008, p. 139-15

Bilinear probabilistic principal component analysis

Probabilistic principal component analysis (PPCA) is a popular linear latent variable model for performing dimension reduction on 1-D data in a probabilistic manner. However, when used on 2-D data such as images, PPCA suffers from the curse of dimensionality due to the subsequently large number of model parameters. To overcome this problem, we propose in this paper a novel probabilistic model on 2-D data called bilinear PPCA (BPPCA). This allows the establishment of a closer tie between BPPCA and its nonprobabilistic counterpart. Moreover, two efficient parameter estimation algorithms for fitting BPPCA are also developed. Experiments on a number of 2-D synthetic and real-world data sets show that BPPCA is more accurate than existing probabilistic and nonprobabilistic dimension reduction methods.published_or_final_versio