Entropy and Efficiency of the ETF Market

We investigate the relative information efficiency of financial markets by measuring the entropy of the time series of high frequency data. Our tool to measure efficiency is the Shannon entropy, applied to 2-symbol and 3-symbol discretisations of the data. Analysing 1-min and 5-min price time series of 55 Exchange Traded Funds traded at the New York Stock Exchange, we develop a methodology to isolate residual inefficiencies from other sources of regularities, such as the intraday pattern, the volatility clustering and the microstructure effects. The first two are modelled as multiplicative factors, while the microstructure is modelled as an ARMA noise process. Following an analytical and empirical combined approach, we find a strong relationship between low entropy and high relative tick size and that volatility is responsible for the largest amount of regularity, averaging 62% of the total regularity against 18% of the intraday pattern regularity and 20% of the microstructure

New procedures for testing whether stock price processes are martingales

We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale property of a stock price process can be tested based on the capital process of a betting strategy. In particular with high frequency Markov type strategies we find that martingale null hypotheses are rejected for many stock price processes

On the simplification of an examples-based controller with support vector machines

Examples-based controllers use historical data to evaluate local approximation models. Large data sets make it prohibitively expensive to evaluate the best control action in real time. Support vector machines (SVM) are known for their ability to identify the minimal set of data points needed to reconstruct an optimal decision surface. A successful application is presented: the simplification of a six-dimensional robotic controller. The SVM reduced the size of the data set to 5.3% of its original size while retaining 99.7% classification accuracy, thus leading the way to online implementation. The results indicate that SVM may be highly effective for the simplification of examples-based controllers

BIOINFORMATICS ORIGINAL PAPER Sequence analysis Identification of transcription factor binding sites with variable-order Bayesian networks

Motivation: We propose a new class of variable-order Bayesian network (VOBN) models for the identification of transcription factor binding sites (TFBSs). The proposed models generalize the widely used position weight matrix (PWM) models, Markov models and Bayesian network models. In contrast to these models, where for each position a fixed subset of the remaining positions is used to model dependencies, in VOBN models, these subsets may vary based on the specific nucleotides observed, which are called the context. This flexibility turns out to be of advantage for the classification and analysis of TFBSs, as statistical dependencies between nucleotides in different TFBS positions (not necessarily adjacent) may be taken into account efficiently—in a position-specific and context-specific manner. Results: We apply the VOBN model to a set of 238 experimentally verified sigma-70 binding sites in Escherichia coli. We find that the VOB