HMM in dynamic HAC models

Understanding the dynamics of high dimensional non-normal dependency structure is a challenging task. This research aims at attacking this problem by building up a hidden Markov model (HMM) for Hierarchical Archimedean Copulae (HAC), where the HAC represent a wide class of models for high dimensional dependency, and HMM is a statistical technique to describe time varying dynamics. HMM applied to HAC provide flexible modeling for high dimensional non Gaussian time series. Consistency results for both parameters and HAC structures are established in an HMM framework. The model is calibrated to exchange rate data with a VaR application, where the model’s performance is compared with other dynamic models, and in the second application we simulate rainfall process.Hidden Markov model, Hierarchical Archimedean Copulae, Multivariate Distribution

Hidden markov structures for dynamic copulae

This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Understanding the time series dynamics of a multi-dimensional dependency structure is a challenging task. Multivariate covariance driven Gaussian or mixed normal time varying models have only a limited ability to capture important features of the data such as heavy tails, asymmetry, and nonlinear dependencies. The present paper tackles this problem by proposing and analyzing a hidden Markov model (HMM) for hierarchical Archimedean copulae (HAC). The HAC constitute a wide class of models for multi-dimensional dependencies, and HMM is a statistical technique for describing regime switching dynamics. HMM applied to HAC flexibly models multivariate dimensional non-Gaussian time series.We apply the expectation maximization (EM) algorithm for parameter estimation. Consistency results for both parameters and HAC structures are established in an HMM framework. The model is calibrated to exchange rate data with a VaR application. This example is motivated by a local adaptive analysis that yields a time varying HAC model. We compare its forecasting performance with that of other classical dynamic models. In another, second, application, we model a rainfall process. This task is of particular theoretical and practical interest because of the specific structure and required untypical treatment of precipitation data.Peer Reviewe

Quantum dynamics of crystals of molecular nanomagnets inside a resonant cavity

It is shown that crystals of molecular nanomagnets exhibit enhanced magnetic relaxation when placed inside a resonant cavity. Strong dependence of the magnetization curve on the geometry of the cavity has been observed, providing evidence of the coherent microwave radiation by the crystals. A similar dependence has been found for a crystal placed between Fabry-Perot superconducting mirrors. These observations open the possibility of building a nanomagnetic microwave laser pumped by the magnetic field

Value premium and investor sentiment: Working paper series--11-02

There are two competing explanations for the value premium. One suggests that value premium is a compensation for risk, while the other implies that it is driven by investor sentiment. Previous empirical studies typically test these two competing explanations of value premium in isolation, which may lead to incorrect inferences. In this paper, we extend the literature by testing these two competing explanations of value premium in a joint fashion. We find that while value premium is correlated with investor sentiment, it shows very little correlation with the state of the economy. Based on this evidence, it is very difficult to argue that value premium is due to risk

Advanced methods for estimating the probability of informed trading

Grundlage dieser Dissertation ist ein Marktmodell, bei dem ein Market Maker mit informierten und uninformierten Marktteilnehmern handeln kann. Annahmegemäß betreten dabei informierte Händler den Markt nur an solchen Tagen, an denen preisrelevante (private) Informationen vorhanden sind. Käufe und Verkäufe werden jeweils als latente Punktprozesse mit zeitveränderlicher Intensität modelliert, wobei die Wartezeiten zwischen zwei Käufen bzw. Verkäufen einer Weibull-Verteilung entstammen. Zur Modellierung der erwarteten (bedingten) Durationen von Käufen und Verkäufen werden autoregressive Durationsmodelle (ACD - Modelle) verwendet. Die erwarteten Durationen fungieren schließlich als Scale-Parameter der Weibull-Verteilungen und sorgen somit für zeitveränderliche Intensitäten von Käufen und Verkäufen. Jeder Handelstag ist entweder durch das Fehlen von handelsrelevanten Informationen oder das Vorhandensein positiver oder negativer Nachrichten bei den informierten Händlern gekennzeichnet. Da die Art des Tages nicht beobachtbar ist, wird der entsprechende Prozess mit einem Hidden Markov Modell (HMM) beschrieben. Die Datengrundlage unserer Untersuchungen bilden Hochfrequenzdaten für insgesamt neun Automobilhersteller bzw. -zulieferer über einen Zeitraum von vier Jahren (2007 – 2010) und zwei Börsenplätzen (NYSE und Xetra). Die Modellparameter werden mit der Maximum-Likelihood-Methode geschätzt, was angesichts riesiger Datenmengen von über einer Million Durationen pro Datensatz schnelle und effiziente Algorithmen zur Berechnung der Likelihood erforderlich macht. Die Resultate der Modellschätzungen zeigen, dass das in diesem Kontext zur Schätzung derWahrscheinlichkeit von informiertem Handel erstmals verwendete HMM-Modell für den Großteil der Handelstage eine eindeutige Klassifizierung bezüglich des Informationsgehaltes möglich macht. Ferner erweist sich die bisher in der Literatur für die Durationen verwendete Exponentialverteilung im Gegensatz zur Weibullverteilung als nicht flexibel genug.The basis of this dissertation is a market model in which a market maker trades with informed and uninformed market participants. According to the model assumptions informed traders only enter the market on days with price-relevant (private) information. Buys and sells are modeled with latent point processes with time-varying intensities, where the waiting times between two consecutive buys or sells are assumed to follow a Weibull distribution. Autoregressive duration models (ACD models) are utilized to model the expected (conditional) durations of buys and sells. Those expected durations serve as scale parameters of the Weibull distributions and introduce the time-varying intensities of buys and sells. Each trading day is characterized by the presence or absence of price-relevant information. Furthermore, if there is private information, we differentiate between information with positive or negative direction. Since the state of a trading day is not observable, we model the corresponding process with a Hidden Markov Model (HMM). We use high-frequency transaction data over four years (2007 - 2010) and two marketplaces (NYSE and Xetra). All symbols in our datasource belong to the automobile sector. Model parameters are estimated by Maximum-Likelihood approach. The enormous size of data, with more than one million transactions per symbol, makes it crucial to have fast and efficient algorithms at hand to calculate the likelihood function. Empirical applications show that the HMM model, which is incorporated for the first time in this context of estimating the probability of informed trading, is able to clearly assign a state to the vast majority of trading periods. Moreover, the empirical results indicate that the typically used exponential distribution for durations is not flexible enough compared to the Weibull distribution

Phonon Bottleneck Effect Leads to Observation of Quantum Tunneling of the Magnetization and Butterfly Hysteresis Loops in (Et4N)3Fe2F9

A detailed investigation of the unusual dynamics of the magnetization of (Et4N)3Fe2F9 (Fe2), containing isolated [Fe2F9]3- dimers, is presented and discussed. Fe2 possesses an S=5 ground state with an energy barrier of 2.40 K due to an axial anisotropy. Poor thermal contact between sample and bath leads to a phonon bottleneck situation, giving rise to butterfly-shaped hysteresis loops below 5 K concomitant with slow decay of the magnetization for magnetic fields Hz applied along the Fe--Fe axis. The butterfly curves are reproduced using a microscopic model based on the interaction of the spins with resonant phonons. The phonon bottleneck allows for the observation of resonant quantum tunneling of the magnetization at 1.8 K, far above the blocking temperature for spin-phonon relaxation. The latter relaxation is probed by AC magnetic susceptibility experiments at various temperatures and bias fields. At H=0, no out-of-phase signal is detected, indicating that at T smaller than 1.8 K Fe2 does not behave as a single-molecule magnet. At 1 kG, relaxation is observed, occurring over the barrier of the thermally accessible S=4 first excited state that forms a combined system with the S=5 state.Comment: 10 pages, 10 figure

hand gesture modeling and recognition for human and robot interactive assembly using hidden markov models

Gesture recognition is essential for human and robot collaboration. Within an industrial hybrid assembly cell, the performance of such a system significantly affects the safety of human workers. This work presents an approach to recognizing hand gestures accurately during an assembly task while in collaboration with a robot co-worker. We have designed and developed a sensor system for measuring natural human-robot interactions. The position and rotation information of a human worker's hands and fingertips are tracked in 3D space while completing a task. A modified chain-code method is proposed to describe the motion trajectory of the measured hands and fingertips. The Hidden Markov Model (HMM) method is adopted to recognize patterns via data streams and identify workers' gesture patterns and assembly intentions. The effectiveness of the proposed system is verified by experimental results. The outcome demonstrates that the proposed system is able to automatically segment the data streams and recognize the gesture patterns thus represented with a reasonable accuracy ratio