Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Reducible Diffusions with Time-Varying Transformations with Application to Short-Term Interest Rates

Reducible diffusions (RDs) are nonlinear transformations of analytically solvable Basic Diffusions (BDs). Hence, by construction RDs are analytically tractable and flexible diffusion processes. Existing literature on RDs has mostly focused on time-homogeneous transformations, which to a significant extent fail to explore the full potential of RDs from both theoretical and practical points of view. In this paper, we propose flexible and economically justifiable time variations to the transformations of RDs. Concentrating on the Constant Elasticity Variance (CEV) RDs, we consider nonlinear dynamics for our time-varying transformations with both deterministic and stochastic designs. Such time variations can greatly enhance the flexibility of RDs while maintaining sufficient tractability of the resulting models. In the meantime, our modeling approach enjoys the benefits of classical inferential techniques such as the Maximum Likelihood (ML). Our application to the UK and the US short-term interest rates suggests that from an empirical point of view time-varying transformations are highly relevant and statistically significant. We expect that the proposed models can describe more truthfully the dynamic time-varying behavior of economic and financial variables and potentially improve out-of-sample forecasts significantly.

Constructing networks of continuous-time velocity-based models

A conventional local model (LM) network consists of a set of affine local models blended together using appropriate weighting functions. Such networks have poor interpretability since the dynamics of the blended network are only weakly related to the underlying local models. In contrast, velocity-based LM networks employ strictly linear local models to provide a transparent framework for nonlinear modelling in which the global dynamics are a simple linear combination of the local model dynamics. A novel approach for constructing continuous-time velocity-based networks from plant data is presented. Key issues including continuous-time parameter estimation, correct realisation of the velocity-based local models and avoidance of the input derivative are all addressed. Application results are reported for the highly nonlinear simulated continuous stirred tank reactor process.

Efficient Evaluation of Multidimensional Time-Varying Density Forecasts

We propose two simple evaluation methods for time varying density forecasts of continuous higher dimensional random variables. Both methods are based on the probability integral transformation for unidimensional forecasts. The first method tests multinormal densities and relies on the rotation of the coordinate system. The advantage of the second method is not only its applicability to any continuous distribution but also the evaluation of the forecast accuracy in specific regions of its domain as defined by the user’s interest. We show that the latter property is particularly useful for evaluating a multidimensional generalization of the Value at Risk. In simulations and in an empirical study, we examine the performance of both tests.

Adaptive calibration of a three-microphone system for acoustic waveguide characterization under time-varying conditions

The pressure and velocity field in a one-dimensional acoustic waveguide can be sensed in a non-intrusive manner using spatially distributed microphones. Experimental characterization with sensor arrangements of this type has many applications in measurement and control. This paper presents a method for measuring the acoustic variables in a duct under fluctuating propagation conditions with specific focus on in-system calibration and tracking of the system parameters of a three-microphone measurement configuration. The tractability of the non-linear optimization problem that results from taking a parametric approach is investigated alongside the influence of extraneous measurement noise on the parameter estimates. The validity and accuracy of the method are experimentally assessed in terms of the ability of the calibrated system to separate the propagating waves under controlled conditions. The tracking performance is tested through measurements with a time-varying mean flow, including an experiment conducted under propagation conditions similar to those in a wind instrument during playing.

Time-Varying Liquidity and Momentum Profits

A basic intuition is that arbitrage is easier when markets are most liquid. Surprisingly, we find that momentum profits are markedly larger in liquid market states. This finding is not explained by variation in liquidity risk, time-varying exposure to risk factors, or changes in macroeconomic condition, cross-sectional return dispersion, and investor sentiment. The predictive performance of aggregate market illiquidity for momentum profits uniformly exceed that of market return and market volatility states. While momentum strategies are unconditionally unprofitable in US, Japan, and Eurozone countries in the last decade, they are substantial following liquid market states.

A time-domain approach to the analysis and modeling of on-body propagation characteristics using synchronized measurements at 2.45 GHz

Modeling of on-body propagation channels is of paramount importance to those wishing to evaluate radio channel performance for wearable devices in body area networks (BANs). Difficulties in modeling arise due to the highly variable channel conditions related to changes in the user's state and local environment. This study characterizes these influences by using time-series analysis to examine and model signal characteristics for on-body radio channels in user stationary and mobile scenarios in four different locations: anechoic chamber, open office area, hallway, and outdoor environment. Autocorrelation and cross-correlation functions are reported and shown to be dependent on body state and surroundings. Autoregressive (AR) transfer functions are used to perform time-series analysis and develop models for fading in various on-body links. Due to the non-Gaussian nature of the logarithmically transformed observed signal envelope in the majority of mobile user states, a simple method for reproducing the failing based on lognormal and Nakagami statistics is proposed. The validity of the AR models is evaluated using hypothesis testing, which is based on the Ljung-Box statistic, and the estimated distributional parameters of the simulator output compared with those from experimental results.

Body shadowing mitigation using differentiated LOS/NLOS channel models for RSSI-based Monte Carlo personnel localization

Research into localization has produced a wealth of algorithms and techniques to estimate the location of wireless network nodes, however the majority of these schemes do not explicitly account for non-line of sight conditions. Disregarding this common situation reduces their accuracy and their potential for exploitation in real world applications. This is a particular problem for personnel tracking where the user's body itself will inherently cause time-varying blocking according to their movements. Using empirical data, this paper demonstrates that, by accounting for non-line of sight conditions and using received signal strength based Monte Carlo localization, meter scale accuracy can be achieved for a wrist-worn personnel tracking tag in a 120 m indoor office environment. © 2012 IEEE.

Iterative Multiuser Detection and Decoding for DS-CDMA System With Space-Time Linear Dispersion

This paper considers a Q-ary orthogonal direct-sequence code-division multiple-access (DS-CDMA) system with high-rate space-time linear dispersion codes (LDCs) in time-varying Rayleigh fading multiple-input-multiple-output (MIMO) channels. We propose a joint multiuser detection, LDC decoding, Q-ary demodulation, and channel-decoding algorithm and apply the turbo processing principle to improve system performance in an iterative fashion. The proposed iterative scheme demonstrates faster convergence and superior performance compared with the V-BLAST-based DS-CDMA system and is shown to approach the single-user performance bound. We also show that the CDMA system is able to exploit the time diversity offered by the LDCS in rapid-fading channels.

Incorporating Higher Moments into Value at Risk Forecasting

Value-at-risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a simple approach to forecasting of a portfolio VaR. We employ the Gram-Charlier expansion (GCE) augmenting the standard normal distribution with the first four moments, which are allowed to vary over time. In an extensive empirical study, we compare the GCE approach to other models of VaR forecasting and conclude that it provides accurate and robust estimates of the realized VaR. In spite of its simplicity, on our dataset GCE outperforms other estimates that are generated by both constant and time-varying higher-moments models.

Dynamic Density Forecasts for Multivariate Asset Returns

We propose a simple and flexible framework for forecasting the joint density of asset returns. The multinormal distribution is augmented with a polynomial in (time-varying) non-central co-moments of assets. We estimate the coefficients of the polynomial via the Method of Moments for a carefully selected set of co-moments. In an extensive empirical study, we compare the proposed model with a range of other models widely used in the literature. Employing a recently proposed as well as standard techniques to evaluate multivariate forecasts, we conclude that the augmented joint density provides highly accurate forecasts of the “negative tail” of the joint distribution.

Speaker Recognition In Noisy Conditions With Limited Training Data

In this paper we present a novel method for performing speaker recognition with very limited training data and in the presence of background noise. Similarity-based speaker recognition is considered so that speaker models can be created with limited training speech data. The proposed similarity is a form of cosine similarity used as a distance measure between speech feature vectors. Each speech frame is modelled using subband features, and into this framework, multicondition training and optimal feature selection are introduced, making the system capable of performing speaker recognition in the presence of realistic, time-varying noise, which is unknown during training. Speaker identi?cation experiments were carried out using the SPIDRE database. The performance of the proposed new system for noise compensation is compared to that of an oracle model; the speaker identi?cation accuracy for clean speech by the new system trained with limited training data is compared to that of a GMM trained with several minutes of speech. Both comparisons have demonstrated the effectiveness of the new model. Finally, experiments were carried out to test the new model for speaker identi?cation given limited training data and with differing levels and types of realistic background noise. The results have demonstrated the robustness of the new system.

The association between glucose lowering drug use and mortality among breast cancer patients with type 2 diabetes.

This study assessed the association between glucose-lowering drug (GLD) use, including metformin, sulphonylurea derivatives and insulin, after breast cancer diagnosis and breast cancer-specific and all-cause mortality. 1763 breast cancer patients, diagnosed between 1998 and 2010, with type 2 diabetes were included. Cancer information was retrieved from English cancer registries, prescription data from the UK Clinical Practice Research Datalink and mortality data from the Office of National Statistics (up to January 2012). Time-varying Cox regression models were used to calculate HRs and 95 % CIs for the association between GLD use and breast cancer-specific and all-cause mortality. In 1057 patients with diabetes before breast cancer, there was some evidence that breast cancer-specific mortality decreased with each year of metformin use (adjusted HR 0.88; 95 % CI 0.75–1.04), with a strong association seen with over 2 years of use (adjusted HR 0.47; 95 % CI 0.26–0.82). Sulphonylurea derivative use for less than 2 years was associated with increased breast cancer-specific mortality (adjusted HR 1.70; 95 % CI 1.18–2.46), but longer use was not (adjusted HR 0.94; 95 % CI 0.54–1.66). In 706 patients who developed diabetes after breast cancer, similar patterns were seen for metformin, but sulphonylurea derivative use was strongly associated with cancer-specific mortality (adjusted HR 3.64; 95 % CI 2.16–6.16), with similar estimates for short- and long-term users. This study provides some support for an inverse association between, mainly long-term, metformin use and (breast cancer-specific) mortality. In addition, sulphonylurea derivative use was associated with increased breast cancer-specific mortality, but this should be interpreted cautiously, as it could reflect selective prescribing in advanced cancer patients.

Blind Characterisation of Sensors with Second-Order Dynamic Response

Compensation for the dynamic response of a temperature sensor usually involves the estimation of its input on the basis of the measured output and model parameters. In the case of temperature measurement, the sensor dynamic response is strongly dependent on the measurement environment and fluid velocity. Estimation of time-varying sensor model parameters therefore requires continuous textit{in situ} identification. This can be achieved by employing two sensors with different dynamic properties, and exploiting structural redundancy to deduce the sensor models from the resulting data streams. Most existing approaches to this problem assume first-order sensor dynamics. In practice, however second-order models are more reflective of the dynamics of real temperature sensors, particularly when they are encased in a protective sheath. As such, this paper presents a novel difference equation approach to solving the blind identification problem for sensors with second-order models. The approach is based on estimating an auxiliary ARX model whose parameters are related to the desired sensor model parameters through a set of coupled non-linear algebraic equations. The ARX model can be estimated using conventional system identification techniques and the non-linear equations can be solved analytically to yield estimates of the sensor models. Simulation results are presented to demonstrate the efficiency of the proposed approach under various input and parameter conditions.