Optimization of representation for extracting knowledge from ultra-high frequency time series

Order Book Commonalities and Bond Return Predictability

An experimental approach to the study of limit order books lies in the availability of data. Most of the results presented in this book - in any case, those we have produced ourselves - use the Thomson Reuters Tick History (TRTH) database. All exchange-traded assets worldwide are present in the TRTH database, where they are identified by their Reuters Identification Code (RIC). Similar to most historical databases directly provided by the exchanges, the TRTH data come into the form of two separate files, a trade file recording all transactions, and an event file recording every change in the limit order book. Some very specific information, such as traders’ identities, cannot be publicly disclosed for obvious confidentiality reasons, but in theory, one could reconstruct the sequence of order arrivals of all types using this trade and event files. After explaining the algorithm used for the processing of limit order book data, we describe the specific data sets that have been used at various places in this book. That way, our results can be reproduced, extended and, of course, challenged, based on the very same data sets we have used. Limit Order Book Data Processing Because one cannot distinguish market orders from cancellations just by observing changes in the limit order book (the “event” file), and since, the timestamps of the “trade” and “event” files are asynchronous , we use a matching procedure to reconstruct the order book events. In a nutshell, we proceed as follows for each stock and each trading day: 1. Parse the “event” file to compute order book state variations: • If the variation is positive (volume at one or more price levels has increased), then label the event as a limit order. • If the variation is negative (volume at one or more price levels has decreased), then label the event as a “likely market order”. • If no variation—this happens when there is just a renumbering in the field “Level” that does not affect the state of the book—do not count an event. 2. Parse the “trade” file and for each trade: • Compare the trade price and volume to likely market orders whose timestamps are in, where t Tr is the trade timestamp and Δ t is a predefined, market-dependent time window.

The primary difficulty of obtaining useful information from gamma-gamma coincidence spectra is the process of determining which spectral features are useful for drawing a conclusion. This is especially true for dense and complicated coincidence spectra, such as those of fission products from irradiated uranium samples. A set of binary classification support vector machine algorithms was trained with supervised learning on gamma-gamma coincidence data from irradiated uranium samples of natural, low, and high-enriched uranium. The resulting model will be capable of classifying uranium samples into the correct enrichment regime (natural, low, or high) based on their gamma-gamma coincidence spectra. Current results with the binary classification support vector machines indicate a 92% classification accuracy. This eliminates the need for a spectral analyst to parse through the data and manually determine which spectral features are indicative of enrichment. The basis functions used by the model to make classification decisions can also inform the analyst of less obvious spectral features that are indicative of enrichment. Ongoing work to improve classification accuracy is discussed.

Limit order books and liquidity around scheduled and non-scheduled announcements: Empirical evidence from NASDAQ Nordic

Non-Parametric Prediction of the Mid-Price Dynamics in a Limit Order Book

Since Kalman Filter was first developed by Kalman (1960), it has been widely used in engineering, statistics and econometrics. Filtering is different from forecasting as forecasting is made for predicting the future while filtering aims the estimation of unobservable parameters in the same period. For techniques as Kalman filters, on one hand, it can help to filter away the “noisy order”, revealing the true state of limit order book. On the other hand, it can be also use for prediction of state for next time step. In this paper, we estimate the limit order book using gamma distribution. Then each order book snapshot can be described using four parameters. After that, the basic filter is introduced with applications to disclose the pattern in limit order book.

The modeling of the limit order book is directly related to the assumptions on the behavior of real market participants. This paper is two-fold. We first present empirical findings that lay the ground for two improvements to these models. The first one is concerned with market participants by adding the additional dimension of informed market makers, whereas the second, and maybe more original one, addresses the race in the book between informed traders and informed market makers leading to different shapes of the order book. Namely, we build an agent-based model for the order book with four types of market participants: informed trader, noise trader, informed market makers and noise market makers. We build our model based on the Glosten–Milgrom approach and the most recent Huang–Rosenbaum–Saliba approach. We introduce a parameter capturing the race between informed liquidity traders and suppliers after a new information on the fundamental value of the asset. We then derive the whole “static” limit order book and its characteristics, namely, the bid-ask spread and volumes available at each level price- from the interactions between the agents and compare it with the pre-existing model. We then discuss the case where noise traders have an impact on the fundamental value of the asset and extend the model to take into account many kinds of informed market makers.

ABSTRACTIn this article, we take an algorithmic approach to solve the problem of optimal execution under time-varying constraints on the depth of a limit order book (LOB). Our algorithms are within the resilience model proposed by Obizhaeva and Wang (2013) with a more realistic assumption on the order book depth; the amount of liquidity provided by an LOB market is finite at all times. For the simplest case where the order book depth stays at a fixed level for the entire trading horizon, we reduce the optimal execution problem into a one-dimensional root-finding problem which can be readily solved by standard numerical algorithms. When the depth of the order book is monotone in time, we apply the Karush-Kuhn-Tucker conditions to narrow down the set of candidate strategies. Then, we use a dichotomy-based search algorithm to pin down the optimal one. For the general case, we start from the optimal strategy subject to no liquidity constraints and iterate over execution strategy by sequentially adding more constraints to the problem in a specific fashion until primal feasibility is achieved. Numerical experiments indicate that our algorithms give comparable results to those of current existing convex optimization toolbox CVXOPT with significantly lower time complexity.

Prediction of protein secondary structures is an important problem in bioinformatics and has many applications. The recent trend of secondary structure prediction studies is mostly based on the neural network or the support vector machine (SVM). The SVM method is a comparatively new learning system which has mostly been used in pattern recognition problems. In this study, SVM is used as a machine learning tool for the prediction of secondary structure and several encoding schemes, including orthogonal matrix, hydrophobicity matrix, BLOSUM62 substitution matrix, and combined matrix of these, are applied and optimized to improve the prediction accuracy. Also, the optimal window length for six SVM binary classifiers is established by testing different window sizes and our new encoding scheme is tested based on this optimal window size via sevenfold cross validation tests. The results show 2% increase in the accuracy of the binary classifiers when compared with the instances in which the classical orthogonal matrix is used. Finally, to combine the results of the six SVM binary classifiers, a new tertiary classifier which combines the results of one-versus-one binary classifiers is introduced and the performance is compared with those of existing tertiary classifiers. According to the results, the Q3 prediction accuracy of new tertiary classifier reaches 78.8% and this is better than the best result reported in the literature.

This paper investigates whether the combination of airborne hyperspectral imagery (Aisa EAGLE II) and image classification methods (MLC, SVM) using feature extraction can discriminate among species and clones of energy trees. The trees examined have similar morphological traits due to limitation of detection. The image classification was applied on a spectrally selected and transformed (PCA, MNF) dataset. A binary tree SVM classifier was developed in accordance with the principle of SVM, based on the Jeffries-Matusita (JM) separability measure of selected classes. The adaptive binary tree SVM on MNF-transformed dataset provided more accurate results than applied MLC and multiclass SVM methods. The primary outcome of this study was a comparison of support vector machines (SVM) classification methods to evaluate species or clones of energy plants. In this paper, an adaptive binary tree SVM classifier (ABTSVM) is proposed to increase the accuracy of subspecies level.

The Predictive Power of Limit Order Book for Future Volatility, Trade Price, and Speed of Trading

Order Aggressiveness and Order Book Dynamics

In this paper we show how to reconstruct the limit order book of the 30 stocks constituting the DAX30 index based on the trading protocol of the Xetra Trading System at the Frankfurt Stock Exchange. The algorithm used is innovative as it captures all trading phases, including auctions, and delivers a reconstruction of the orderbook either from a trader’s view or a supervisory view including hidden volume as well.Based on the rebuilt order book, liquidity dynamics are examined. In contrats to findings for dealer markets, past market returns play a minor role in the determination of liquidity and liquidity commonality in Xetra, a pure limit order book market. Consequently, we provide evidence that liquidity provision by multiple sources in Xetra mitigates systemic liquidity risk introduced by the interrelation of return and liquidity.

This paper builds on the landmark contribution of Glosten (1994) by treating the determination of limit order supply schedules as an exercise in asset pricing theory with the possible sizes of incoming market orders as the value-relevant states of nature, yielding an analogue of the Fundamental Theorem of Asset Pricing. State prices and price impact prove to be proportional to the slope of the book and simple nonparametric and semiparametric models for limit order book dynamics arise when the price of order flow risk is constant over time, providing a comprehensive and coherent framework for organizing limit order book data.

We show that the liquidity provided by an individual stock's limit order book comoves significantly with the market aggregate limit order book liquidity. A closer look at the inside and outside liquidity provided by different parts of limit order book suggests that inside liquidity is mainly influenced by market volatility, while idiosyncratic volatility has a larger impact on outside liquidity. Hence, limit order book inside liquidity exhibits higher commonality than outside liquidity. We also show that the comovement between the stock‐level and market‐aggregate limit order book liquidity measures is related to the commonality in the overall stock market liquidity.