Interdependence between Greece and other European stock markets: A comparison of wavelet and VMD copula, and the portfolio implications

The interdependence of Greece and other European stock markets and the subsequent portfolio implications are examined in wavelet and variational mode decomposition domain. In applying the decomposition techniques, we analyze the structural properties of data and distinguish between short and long term dynamics of stock market returns. First, the GARCH-type models are fitted to obtain the standardized residuals. Next, different copula functions are evaluated, and based on the conventional information criteria and time varying parameter, Joe-Clayton copula is chosen to model the tail dependence between the stock markets. The short-run lower tail dependence time paths show a sudden increase in comovement during the global financial crises. The results of the long-run dependence suggest that European stock markets have higher interdependence with Greece stock market. Individual country’s Value at Risk (VaR) separates the countries into two distinct groups. Finally, the two-asset portfolio VaR measures provide potential markets for Greece stock market investment diversification.

Diversification when it hurts? The joint distributions of real estate and equity markets

Much of the literature on the construction of mixed asset portfolios and the case for property as a risk diversifier rests on correlations measured over the whole of a given time series. Recent developments in finance, however, focuses on dependence in the tails of the distribution. Does property offer diversification from equity markets when it is most needed - when equity returns are poor. The paper uses an empirical copula approach to test tail dependence between property and equity for the UK and for a global portfolio. Results show strong tail dependence: in the UK, the dependence in the lower tail is stronger than in the upper tail, casting doubt on the defensive properties of real estate stocks.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Band-tail shape and transport near the metal-insulator transition in Si-doped

In the present work, an infrared light-emitting diode is used to photodope molecular-beam-epitaxy-grown Si: Al0.3Ga0.7As, a well-known persistent photoconductor, to vary the effective electron concentration of samples in situ. Using this technique, we examine the transport properties of two samples containing different nominal doping concentrations of Si [1 x 10(19) cm(-3) for sample 1 (S1) and 9 x 10(17) cm(-3) for sample 2 (S2)] and vary the effective electron density between 10(14) and 10(18) cm(-3). The metal-insulator transition for S1 is found to occur at a critical carrier concentration of 5.7 x 10(16) cm(-3) at 350 mK. The mobilities in both samples are found to be limited by ionized impurity scattering in the temperature range probed, and are adequately described by the Brooks-Herring screening theory for higher carrier densities. The shape of the band tail of the density of states in Al0.3Ga0.7As is found electrically through transport measurements. It is determined to have a power-law dependence, with an exponent of -1.25 for S1 and -1.38 for S2.

Extended cusp-like regions and their dependence on the Polar orbit, seasonal variations, and interplanetary conditions

Extended cusp-like regions (ECRs) are surveyed, as observed by the Magnetospheric Ion Composition Sensor (MICS) of the Charge and Mass Magnetospheric Ion Composition Experiment (CAMMICE) instrument aboard Polar between 1996 and 1999. The first of these ECR events was observed on 29 May 1996, an event widely discussed in the literature and initially thought to be caused by tail lobe reconnection due to the coinciding prolonged interval of strong northward IMF. ECRs are characterized here by intense fluxes of magnetosheath-like ions in the energy-per-charge range of _1 to 10 keV e_1. We investigate the concurrence of ECRs with intervals of prolonged (lasting longer than 1 and 3 hours) orientations of the IMF vector and high solar wind dynamic pressure (PSW). Also investigated is the opposite concurrence, i.e., of the IMF and high PSW with ECRs. (Note that these surveys are asking distinctly different questions.) The former survey indicates that ECRs have no overall preference for any orientation of the IMF. However, the latter survey reveals that during northward IMF, particularly when accompanied by high PSW, ECRs are more likely. We also test for orbital and seasonal effects revealing that Polar has to be in a particular region to observe ECRs and that they occur more frequently around late spring. These results indicate that ECRs have three distinct causes and so can relate to extended intervals in (1) the cusp on open field lines, (2) the magnetosheath, and (3) the magnetopause indentation at the cusp, with the latter allowing magnetosheath plasma to approach close to the Earth without entering the magnetosphere.

Nonparametric tail risk, macroeconomics and stock returns: predictability and risk premia

This paper proposes a new novel to calculate tail risks incorporating risk-neutral information without dependence on options data. Proceeding via a non parametric approach we derive a stochastic discount factor that correctly price a chosen panel of stocks returns. With the assumption that states probabilities are homogeneous we back out the risk neutral distribution and calculate five primitive tail risk measures, all extracted from this risk neutral probability. The final measure is than set as the first principal component of the preliminary measures. Using six Fama-French size and book to market portfolios to calculate our tail risk, we find that it has significant predictive power when forecasting market returns one month ahead, aggregate U.S. consumption and GDP one quarter ahead and also macroeconomic activity indexes. Conditional Fama-Macbeth two-pass cross-sectional regressions reveal that our factor present a positive risk premium when controlling for traditional factors.

Valence band tail states in disordered superlattices embedded in wide parabolic AlGaAs well

Optical properties of intentionally disordered multiple quantum well (QW) system embedded in a wide AlGaAs parabolic well were investigated by photoluminescence (PL) measurements as functions of the laser excitation power and the temperature. The characterization of the carriers localized in the individual wells was allowed due to the artificial disorder that caused spectral separation of the photoluminescence lines emitted by different wells. We observed that the photoluminescence peak intensity from each quantum well shifted to high energy as the excitation power was increased. This blue-shift is associated with the filling of localized states in the valence band tail. We also found that the dependence of the peak intensity on the temperature is very sensitive to the excitation power. The temperature dependence of the photoluminescence peak energy from each QW was well fitted using a model that takes into account the thermal redistribution of the localized carriers. Our results demonstrate that the band tails in the studied structures are caused by alloy potential fluctuations and the band tail states dominate the emission from the peripheral wells. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730769]

Ultra-low concentrations of naloxone selectively antagonize excitatory effects of morphine on sensory neurons, thereby increasing its antinociceptive potency and attenuating tolerance/dependence during chronic cotreatment.

Ultra-low picomolar concentrations of the opioid antagonists naloxone (NLX) and naltrexone (NTX) have remarkably potent antagonist actions on excitatory opioid receptor functions in mouse dorsal root ganglion (DRG) neurons, whereas higher nanomolar concentrations antagonize excitatory and inhibitory opioid functions. Pretreatment of naive nociceptive types of DRG neurons with picomolar concentrations of either antagonist blocks excitatory prolongation of the Ca(2+)-dependent component of the action potential duration (APD) elicited by picomolar-nanomolar morphine and unmasks inhibitory APD shortening. The present study provides a cellular mechanism to account for previous reports that low doses of NLX and NTX paradoxically enhance, instead of attenuate, the analgesic effects of morphine and other opioid agonists. Furthermore, chronic cotreatment of DRG neurons with micromolar morphine plus picomolar NLX or NTX prevents the development of (i) tolerance to the inhibitory APD-shortening effects of high concentrations of morphine and (ii) supersensitivity to the excitatory APD-prolonging effects of nanomolar NLX as well as of ultra-low (femtomolar-picomolar) concentrations of morphine and other opioid agonists. These in vitro studies suggested that ultra-low doses of NLX or NTX that selectively block the excitatory effects of morphine may not only enhance the analgesic potency of morphine and other bimodally acting opioid agonists but also markedly attenuate their dependence liability. Subsequent correlative studies have now demonstrated that cotreatment of mice with morphine plus ultra-low-dose NTX does, in fact, enhance the antinociceptive potency of morphine in tail-flick assays and attenuate development of withdrawal symptoms in chronic, as well as acute, physical dependence assays.