Gaussian process volatility model

The prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the evolution of the variance. Moreover, functional parameters are usually learned by maximum likelihood, which can lead to over-fitting. To address these problems we introduce GP-Vol, a novel non-parametric model for time-changing variances based on Gaussian Processes. This new model can capture highly flexible functional relationships for the variances. Furthermore, we introduce a new online algorithm for fast inference in GP-Vol. This method is much faster than current offline inference procedures and it avoids overfitting problems by following a fully Bayesian approach. Experiments with financial data show that GP-Vol performs significantly better than current standard alternatives.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.

Copula Processes

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility (GCPV), to predict the latent standard deviations of a sequence of random variables. To make predictions we use Bayesian inference, with the Laplace approximation, and with Markov chain Monte Carlo as an alternative. We find both methods comparable. We also find our model can outperform GARCH on simulated and financial data. And unlike GARCH, GCPV can easily handle missing data, incorporate covariates other than time, and model a rich class of covariance structures.

Viewing the future

As many industrial organizations have learned to apply roadmapping successfully, they have also learned that it is "roadmapping" rather than "the roadmap" that generates value. This two-part special report has focused primarily on product and technology roadmapping in industry. The first part (RTM, March-April 2003, pp. 26-59) examined the workings of the process at Lucent Technologies, Rockwell Automation, the pharmaceutical/biotechnology industry, and United Kingdom-based Domino Printing Sciences. This second part examines roadmapping in the UK, Motorola, General Motors, the services sector, and in cases that demand major investment decisions under conditions of volatility.

Gaussian Process Regression Networks

We introduce a new regression framework, Gaussian process regression networks (GPRN), which combines the structural properties of Bayesian neural networks with the non-parametric flexibility of Gaussian processes. This model accommodates input dependent signal and noise correlations between multiple response variables, input dependent length-scales and amplitudes, and heavy-tailed predictive distributions. We derive both efficient Markov chain Monte Carlo and variational Bayes inference procedures for this model. We apply GPRN as a multiple output regression and multivariate volatility model, demonstrating substantially improved performance over eight popular multiple output (multi-task) Gaussian process models and three multivariate volatility models on benchmark datasets, including a 1000 dimensional gene expression dataset.

Autoignition of monodisperse biodiesel and diesel sprays in turbulent flows

A new experimental configuration has been developed to examine the effects of flow on the autoignition of dilute diesel and biodiesel sprays, where the spray is injected in the form of monodisperse individual droplets at right angles to a hot air turbulent flow. The ignition location has been measured by monitoring the OH * chemiluminescence. A qualitative comparison of the flame behaviour between ethanol, acetone, heptane and biodiesel as fuels has also been carried out. With decreasing volatility of the fuel, the flame showed progressively a higher number of individual droplets burning, with the first autoignition spots appearing at random locations but in general earlier than the intense droplet-flame emission. The time-averaged autoignition length increased with increasing air velocity and with increasing intensity of the turbulence, while it decreased with the temperature and the droplet size. The data can be used for validating models for two-phase turbulent combustion. © 2012 Elsevier Inc.

Structure of igniting ethanol and n-heptane spray flames with and without swirl

This paper explores the ignition and subsequent evolution of spray flames in a bluff-body configuration with and without swirl. Ethanol and n-heptane are used to compare the effects of volatility. Ignition is performed by a laser spark. High speed imaging of OH *-chemiluminescence and OH-PLIF collected at 5kHz are used to investigate the behaviour of the flames during the first stages of ignition and the stable flame structure following ignition. Swirl induces a wider and shorter flame, precession, and multiple reaction zones, while the non-swirling flames have a simpler structure. The reaction fronts seem thinner with ethanol than with heptane. The dataset can be used for model validation. © 2012 Elsevier Inc.

Investigation into partially premixed combustion in a light-duty multi-cylinder diesel engine fuelled gasoline and diesel with a mixture of

Partially premixed compression ignition (PPCI) engines operating with a low temperature highly homogeneous charge have been demonstrated previously using conventional diesel fuel. The short ignition delay of conventional diesel fuel requires high fuel injection pressures to achieve adequate premixing along with high levels of EGR (exhaust gas recirculation) to achieve low NOx emissions. Low load operating regions are typified by substantial emissions of CO and HC and there exists an upper operating load limitation due to very high rates of in-cylinder gas pressure rise. In this study mixtures of gasoline and diesel fuel were investigated using a multi-cylinder light duty diesel engine. It was found that an increased proportion of gasoline fuel reduced smoke emissions at higher operating loads through an increase in charge premixing resulting from an increase in ignition delay and higher fuel volatility. The results of this investigation confirm that a combination of fuel properties, exhibiting higher volatility and increased ignition delay, would enable a widening of the low emission operating regime, but that consideration must be given to combustion stability at low operating loads. Copyright © 2007 SAE International.

Liquid fuel visualization using laser-induced fluoresence during cold start

The presence of liquid fuel inside the engine cylinder is believed to be a strong contributor to the high levels of hydrocarbon emissions from spark ignition (SI) engines during the warm-up period. Quantifying and determining the fate of the liquid fuel that enters the cylinder is the first step in understanding the process of emissions formation. This work uses planar laser induced fluorescence (PLIF) to visualize the liquid fuel present in the cylinder. The fluorescing compounds in indolene, and mixtures of iso-octane with dopants of different boiling points (acetone and 3-pentanone) were used to trace the behavior of different volatility components. Images were taken of three different planes through the engine intersecting the intake valve region. A closed valve fuel injection strategy was used, as this is the strategy most commonly used in practice. Background subtraction and masking were both performed to reduce the effect of any spurious fluorescence. The images were analyzed on both a time and crank angle (CA) basis, showing the time of maximum liquid fuel present in the cylinder and the effect of engine events on the inflow of liquid fuel. The results show details of the liquid fuel distribution as it enters the engine as a function of crankangle degree, volatility and location in the cylinder. A. semi-quantitative analysis based on the integration of the image intensities provides additional information on the temporal distribution of the liquid fuel flow. © 1998 Society of Automotive Engineers, Inc.

Discrete multicomponent model for biodiesel spray combustion simulation

An important first step in spray combustion simulation is an accurate determination of the fuel properties which affects the modelling of spray formation and reaction. In a practical combustion simulation, the implementation of a multicomponent model is important in capturing the relative volatility of different fuel components. A Discrete Multicomponent (DM) model is deemed to be an appropriate candidate to model a composite fuel like biodiesel which consists of four components of fatty acid methyl esters (FAME). In this paper, the DM model is compared with the traditional Continuous Thermodynamics (CTM) model for both diesel and biodiesel. The CTM model is formulated based on mixing rules that incorporate the physical and thermophysical properties of pure components into a single continuous surrogate for the composite fuel. The models are implemented within the open-source CFD code OpenFOAM, and a semi-quantitative comparison is made between the predicted spray-combustion characteristics and optical measurements of a swirl-stabilised flame of diesel and biodiesel. The DM model performs better than the CTM model in predicting a higher magnitude of heat release rate in the top flame brush region of the biodiesel flame compared to that of the diesel flame. Using both the DM and CTM models, the simulation successfully reproduces the droplet size, volume flux, and droplet density profiles of diesel and biodiesel. The DM model predicts a longer spray penetration length for biodiesel compared to that of diesel, as seen in the experimental data. Also, the DM model reproduces a segregated biodiesel fuel vapour field and spray in which the most abundant FAME component has the longest vapour penetration. In the biodiesel flame, the relative abundance of each fuel component is found to dominate over the relative volatility in terms of the vapour species distribution and vice versa in the liquid species distribution. © 2014 Elsevier Ltd. All rights reserved.