Parameterizing Unconditional Skewness in Models for Financial Time Series

In this paper we consider the third-moment structure of a class of time series models. It is often argued that the marginal distribution of financial time series such as returns is skewed. Therefore it is of importance to know what properties a model should possess if it is to accommodate unconditional skewness. We consider modeling the unconditional mean and variance using models that respond nonlinearly or asymmetrically to shocks. We investigate the implications of these models on the third-moment structure of the marginal distribution as well as conditions under which the unconditional distribution exhibits skewness and nonzero third-order autocovariance structure. In this respect, an asymmetric or nonlinear specification of the conditional mean is found to be of greater importance than the properties of the conditional variance. Several examples are discussed and, whenever possible, explicit analytical expressions provided for all third-order moments and cross-moments. Finally, we introduce a new tool, the shock impact curve, for investigating the impact of shocks on the conditional mean squared error of return series.

Classification of Airborne LIDAR Intensity Data Using Statistical Analysis and Hough Transform with Application to Power Line Corridors

Light Detection and Ranging (LIDAR) has great potential to assist vegetation management in power line corridors by providing more accurate geometric information of the power line assets and vegetation along the corridors. However, the development of algorithms for the automatic processing of LIDAR point cloud data, in particular for feature extraction and classification of raw point cloud data, is in still in its infancy. In this paper, we take advantage of LIDAR intensity and try to classify ground and non-ground points by statistically analyzing the skewness and kurtosis of the intensity data. Moreover, the Hough transform is employed to detected power lines from the filtered object points. The experimental results show the effectiveness of our methods and indicate that better results were obtained by using LIDAR intensity data than elevation data.

Forecasting time-varying value-at-risk

In this thesis we are interested in financial risk and the instrument we want to use is Value-at-Risk (VaR). VaR is the maximum loss over a given period of time at a given confidence level. Many definitions of VaR exist and some will be introduced throughout this thesis. There two main ways to measure risk and VaR: through volatility and through percentiles. Large volatility in financial returns implies greater probability of large losses, but also larger probability of large profits. Percentiles describe tail behaviour. The estimation of VaR is a complex task. It is important to know the main characteristics of financial data to choose the best model. The existing literature is very wide, maybe controversial, but helpful in drawing a picture of the problem. It is commonly recognised that financial data are characterised by heavy tails, time-varying volatility, asymmetric response to bad and good news, and skewness. Ignoring any of these features can lead to underestimating VaR with a possible ultimate consequence being the default of the protagonist (firm, bank or investor). In recent years, skewness has attracted special attention. An open problem is the detection and modelling of time-varying skewness. Is skewness constant or there is some significant variability which in turn can affect the estimation of VaR? This thesis aims to answer this question and to open the way to a new approach to model simultaneously time-varying volatility (conditional variance) and skewness. The new tools are modifications of the Generalised Lambda Distributions (GLDs). They are four-parameter distributions, which allow the first four moments to be modelled nearly independently: in particular we are interested in what we will call para-moments, i.e., mean, variance, skewness and kurtosis. The GLDs will be used in two different ways. Firstly, semi-parametrically, we consider a moving window to estimate the parameters and calculate the percentiles of the GLDs. Secondly, parametrically, we attempt to extend the GLDs to include time-varying dependence in the parameters. We used the local linear regression to estimate semi-parametrically conditional mean and conditional variance. The method is not efficient enough to capture all the dependence structure in the three indices —ASX 200, S&P 500 and FT 30—, however it provides an idea of the DGP underlying the process and helps choosing a good technique to model the data. We find that GLDs suggest that moments up to the fourth order do not always exist, there existence appears to vary over time. This is a very important finding, considering that past papers (see for example Bali et al., 2008; Hashmi and Tay, 2007; Lanne and Pentti, 2007) modelled time-varying skewness, implicitly assuming the existence of the third moment. However, the GLDs suggest that mean, variance, skewness and in general the conditional distribution vary over time, as already suggested by the existing literature. The GLDs give good results in estimating VaR on three real indices, ASX 200, S&P 500 and FT 30, with results very similar to the results provided by historical simulation.

Modelling Spikes in Electricity Prices

uring periods of market stress, electricity prices can rise dramatically. Electricity retailers cannot pass these extreme prices on to customers because of retail price regulation. Improved prediction of these price spikes therefore is important for risk management. This paper builds a time-varying-probability Markov-switching model of Queensland electricity prices, aimed particularly at forecasting price spikes. Variables capturing demand and weather patterns are used to drive the transition probabilities. Unlike traditional Markov-switching models that assume normality of the prices in each state, the model presented here uses a generalised beta distribution to allow for the skewness in the distribution of electricity prices during high-price episodes.

Conditional coskewness and asset pricing

We explore the empirical usefulness of conditional coskewness to explain the cross-section of equity returns. We find that coskewness is an important determinant of the returns to equity, and that the pricing relationship varies through time. In particular we find that when the conditional market skewness is positive investors are willing to sacrifice 7.87% annually per unit of gamma (a standardized measure of coskewness risk) while they only demand a premium of 1.80% when the market is negatively skewed. A similar picture emerges from the coskewness factor of Harvey and Siddique (Harvey, C., Siddique, A., 2000a. Conditional skewness in asset pricing models tests. Journal of Finance 65, 1263–1295.) (a portfolio that is long stocks with small coskewness with the market and short high coskewness stocks) which earns 5.00% annually when the market is positively skewed but only 2.81% when the market is negatively skewed. The conditional two-moment CAPM and a conditional Fama and French (Fama, E., French, K., 1992. The cross-section of expected returns. Journal of Finance 47,427465.) three-factor model are rejected, but a model which includes coskewness is not rejected by the data. The model also passes a structural break test which many existing asset pricing models fail.

A practical approach for identifying expected solution performance and robustness in operations research applications

A practical approach for identifying solution robustness is proposed for situations where parameters are uncertain. The approach is based upon the interpretation of a probability density function (pdf) and the definition of three parameters that describe how significant changes in the performance of a solution are deemed to be. The pdf is constructed by interpreting the results of simulations. A minimum number of simulations are achieved by updating the mean, variance, skewness and kurtosis of the sample using computationally efficient recursive equations. When these criterions have converged then no further simulations are needed. A case study involving several no-intermediate storage flow shop scheduling problems demonstrates the effectiveness of the approach.

Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

Signal patterns of piston slap of a four-cylinder diesel engine

This paper presents an experimental study on the vibration signal patterns associated with a simulated piston slap test of a four-cylinder diesel engine. It is found that a simulated worn-off piston results in an increase in vibration RMS peak amplitudes associated with the major mechanical events of the corresponding cylinder (i.e., inlet and exhaust valve closing and combustion of Cylinder 1). This then led to an increase of overall vibration amplitude of the time domain statistical features such as RMS, Crest Factor, Skewness and Kurtosis in all loading conditions. The simulated worn-off piston not only increased the impact amplitude of piston slap during the engine combustion, it also produced a distinct impulse response during the air induction stroke of the cylinder attributing to an increase of lateral impact force as a result of piston reciprocating motion and the increased clearance between the worn-off piston and the cylinder. The unique signal patterns of piston slap disclosed in this paper can be utilized to assist in the development of condition monitoring tools for automated diagnosis of similar diesel engine faults in practical applications.

The distribution of construction project bids

This paper describes an analysis of construction project bids to determine (a) the global distribution and (b) factors influencing the distribution of bids. The global distribution of bids was found, by using a battery of ll test statistics, to be approximated by a three-parameter log normal distribution. No global spread parameter was found. A multivariate analysis revealed the year of tender to be the major influencing factor. Consideration of the construction order, tender price and output indices lead to the conclusion that distributional spread reflected the degree of difference in pricing policies between bidders and the skewness of the distributions reflected the degree of competition. The paper concludes with a tentative model of the causal relationships between the factors and distributional characteristics involved.

Applying quantile regression for modeling equivalent property damage only crashes to identify accident blackspots

Hot spot identification (HSID) aims to identify potential sites—roadway segments, intersections, crosswalks, interchanges, ramps, etc.—with disproportionately high crash risk relative to similar sites. An inefficient HSID methodology might result in either identifying a safe site as high risk (false positive) or a high risk site as safe (false negative), and consequently lead to the misuse the available public funds, to poor investment decisions, and to inefficient risk management practice. Current HSID methods suffer from issues like underreporting of minor injury and property damage only (PDO) crashes, challenges of accounting for crash severity into the methodology, and selection of a proper safety performance function to model crash data that is often heavily skewed by a preponderance of zeros. Addressing these challenges, this paper proposes a combination of a PDO equivalency calculation and quantile regression technique to identify hot spots in a transportation network. In particular, issues related to underreporting and crash severity are tackled by incorporating equivalent PDO crashes, whilst the concerns related to the non-count nature of equivalent PDO crashes and the skewness of crash data are addressed by the non-parametric quantile regression technique. The proposed method identifies covariate effects on various quantiles of a population, rather than the population mean like most methods in practice, which more closely corresponds with how black spots are identified in practice. The proposed methodology is illustrated using rural road segment data from Korea and compared against the traditional EB method with negative binomial regression. Application of a quantile regression model on equivalent PDO crashes enables identification of a set of high-risk sites that reflect the true safety costs to the society, simultaneously reduces the influence of under-reported PDO and minor injury crashes, and overcomes the limitation of traditional NB model in dealing with preponderance of zeros problem or right skewed dataset.

Blind steganalysis : a countermeasure for binary image steganography

In this paper, we propose a new blind steganalytic method to detect the presence of secret messages embedded in black and white images using the steganographic techniques. We start by extracting several sets of matrix, such as run length matrix, gap length matrix and pixel difference. We also apply characteristic function on these matrices to enhance their discriminative capabilities. Then we calculate the statistics which include mean, variance, kurtosis and skewness to form our feature sets. The presented empirical works demonstrate our proposed method can effectively detect three different types of steganography. This proves the universality of our proposed method as a blind steganalysis. In addition, the experimental results show our proposed method is capable of detecting small amount of the embedded message.

Decision support system for age-related macular degeneration using discrete wavelet transform

Age-related macular degeneration (AMD) affects the central vision and subsequently may lead to visual loss in people over 60 years of age. There is no permanent cure for AMD, but early detection and successive treatment may improve the visual acuity. AMD is mainly classified into dry and wet type; however, dry AMD is more common in aging population. AMD is characterized by drusen, yellow pigmentation, and neovascularization. These lesions are examined through visual inspection of retinal fundus images by ophthalmologists. It is laborious, time-consuming, and resource-intensive. Hence, in this study, we have proposed an automated AMD detection system using discrete wavelet transform (DWT) and feature ranking strategies. The first four-order statistical moments (mean, variance, skewness, and kurtosis), energy, entropy, and Gini index-based features are extracted from DWT coefficients. We have used five (t test, Kullback–Lieber Divergence (KLD), Chernoff Bound and Bhattacharyya Distance, receiver operating characteristics curve-based, and Wilcoxon) feature ranking strategies to identify optimal feature set. A set of supervised classifiers namely support vector machine (SVM), decision tree, k -nearest neighbor ( k -NN), Naive Bayes, and probabilistic neural network were used to evaluate the highest performance measure using minimum number of features in classifying normal and dry AMD classes. The proposed framework obtained an average accuracy of 93.70 %, sensitivity of 91.11 %, and specificity of 96.30 % using KLD ranking and SVM classifier. We have also formulated an AMD Risk Index using selected features to classify the normal and dry AMD classes using one number. The proposed system can be used to assist the clinicians and also for mass AMD screening programs.

Turbulence and Mixing in the Environment: Multi-Device Study in a Sub-tropical Estuary

In an estuary, mixing and dispersion result from a combination of large-scale advection and smallscale turbulence, which are complex to estimate. The predictions of scalar transport and mixing are often inferred and rarely accurate, due to inadequate understanding of the contributions of these difference scales to estuarine recirculation. A multi-device field study was conducted in a small sub-tropical estuary under neap tide conditions with near-zero fresh water discharge for about 48 hours. During the study, acoustic Doppler velocimeters (ADV) were sampled at high frequency (50 Hz), while an acoustic Doppler current profiler (ADCP) and global positioning system (GPS) tracked drifters were used to obtain some lower frequency spatial distribution of the flow parameters within the estuary. The velocity measurements were complemented with some continuous measurement of water depth, conductivity, temperature and some other physiochemical parameters. Thorough quality control was carried out by implementation of relevant error removal filters on the individual data set to intercept spurious data. A triple decomposition (TD) technique was introduced to access the contributions of tides, resonance and ‘true’ turbulence in the flow field. The time series of mean flow measurements for both the ADCP and drifter were consistent with those of the mean ADV data when sampled within a similar spatial domain. The tidal scale fluctuation of velocity and water level were used to examine the response of the estuary to tidal inertial current. The channel exhibited a mixed type wave with a typical phase-lag between 0.035π– 0.116π. A striking feature of the ADV velocity data was the slow fluctuations, which exhibited large amplitudes of up to 50% of the tidal amplitude, particularly in slack waters. Such slow fluctuations were simultaneously observed in a number of physiochemical properties of the channel. The ensuing turbulence field showed some degree of anisotropy. For all ADV units, the horizontal turbulence ratio ranged between 0.4 and 0.9, and decreased towards the bed, while the vertical turbulence ratio was on average unity at z = 0.32 m and approximately 0.5 for the upper ADV (z = 0.55 m). The result of the statistical analysis suggested that the ebb phase turbulence field was dominated by eddies that evolved from ejection type process, while that of the flood phase contained mixed eddies with significant amount related to sweep type process. Over 65% of the skewness values fell within the range expected of a finite Gaussian distribution and the bulk of the excess kurtosis values (over 70%) fell within the range of -0.5 and +2. The TD technique described herein allowed the characterisation of a broader temporal scale of fluctuations of the high frequency data sampled within the durations of a few tidal cycles. The study provides characterisation of the ranges of fluctuation required for an accurate modelling of shallow water dispersion and mixing in a sub-tropical estuary.

Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering

The family of location and scale mixtures of Gaussians has the ability to generate a number of flexible distributional forms. The family nests as particular cases several important asymmetric distributions like the Generalized Hyperbolic distribution. The Generalized Hyperbolic distribution in turn nests many other well known distributions such as the Normal Inverse Gaussian. In a multivariate setting, an extension of the standard location and scale mixture concept is proposed into a so called multiple scaled framework which has the advantage of allowing different tail and skewness behaviours in each dimension with arbitrary correlation between dimensions. Estimation of the parameters is provided via an EM algorithm and extended to cover the case of mixtures of such multiple scaled distributions for application to clustering. Assessments on simulated and real data confirm the gain in degrees of freedom and flexibility in modelling data of varying tail behaviour and directional shape.