Power laws, discontinuities and regional city size distributions

Urban systems are manifestations of human adaptation to the natural environment. City size distributions are the expression of hierarchical processes acting upon urban systems. In this paper, we test the entire city size distributions for the southeastern and southwestern United States (1990), as well as the size classes in these regions for power law behavior. We interpret the differences in the size of the regional city size distributions as the manifestation of variable growth dynamics dependent upon city size. Size classes in the city size distributions are snapshots of stable states within urban systems in flux.     

Explanations of the inconsistencies in survey respondents’ forecasts

A comparison of the point forecasts and the probability distributions of inflation and output growth made by individual respondents to the US Survey of Professional Forecasters indicates that the two sets of forecasts are sometimes inconsistent. We evaluate a number of possible explanations, and find that not all forecasters update their histogram forecasts as new information arrives. This is supported by the finding that the point forecasts are more accurate than the histograms in terms of first-moment prediction.     

Volatility and VaR forecasting in the Madrid Stock Exchange

This paper provides an empirical study to assess the forecasting performance of a wide range of models for predicting volatility and VaR in the Madrid Stock Exchange. The models performance was measured by using different loss functions and criteria. The results show that FIAPARCH processes capture and forecast more accurately the dynamics of IBEX-35 returns volatility. It is also observed that assuming a heavy-tailed distribution does not improve models ability for predicting volatility. However, when the aim is forecasting VaR, we find evidence of that the Student’s t FIAPARCH outperforms the models it nests the lower the target quantile.      

Multivariate t and beta distributions associated with the multivariate F distribution

Relationships between F, skew t and beta distributions in the univariate case are in this paper extended in a natural way to the multivariate case. The result is two new distributions: a multivariate t/skew t distribution (on ℜ^m) and a multivariate beta distribution (on (0,1)^m). A special case of the former distribution is a new multivariate symmetric t distribution. The new distributions have a natural relationship to the standard multivariate F distribution (on (ℜ⁺)^m) and many of their properties run in parallel. We look at: joint distributions, mathematically and graphically; marginal and conditional distributions; moments; correlations; local dependence; and some limiting cases. Received: March 2001     

Bivariate asymmetric GARCH models with heavy tails and dynamic conditional correlations

A bivariate generalized autoregressive conditional heteroskedastic model with dynamic conditional correlation and leverage effect (DCC-GJR-GARCH) for modelling financial time series data is considered. For robustness it is helpful to assume a multivariate Student-t distribution for the innovation terms. This paper proposes a new modified multivariate t-distribution which is a robustifying distribution and offers independent marginal Student-t distributions with different degrees of freedom, thereby highlighting the relationship among different assets. A Bayesian approach with adaptive Markov chain Monte Carlo methods is used for statistical inference. A simulation experiment illustrates good performance in estimation over reasonable sample sizes. In the empirical studies, the pairwise relationship between the Australian stock market and foreign exchange market, and between the US stock market and crude oil market are investigated, including out-of-sample volatility forecasts.     

Spread component costs and stock trading characteristics in the Spanish Stock Exchange. Two flexible fractional response models

This paper investigates relationships between the spread component costs (adverse selection, order processing and inventory costs) and stock trading characteristics in the Spanish Stock Exchange (SSE), taking into account the random nature of these costs. First, we analyse the statistical properties of estimated spread components in the market, which are obtained by using two statistical models to decompose the bid–ask spread. We then propose a fractional response regression model based on two flexible cross-sectional probability density functions with covariates which accommodate certain aspects of the empirical estimates, such as skewness and bounded distribution. Our model has two main advantages: (i) it can be implemented easily in a maximum likelihood framework; (ii) in contrast to linear regression models, it provides a useful estimate of the statistical significance of the parameters, and predicts costs not only at the conditional mean but also by using quantiles of the estimated conditional distribution. The empirical results corroborate the presence of statistically significant large order processing costs and smaller adverse selection and inventory costs in the SSE. These spread components have a skewed empirical distribution and the proposed fractional regression models represent the behaviour of these costs reasonably well, surpassing the linear regression model in various specification tests.     

Estimating Portfolio Credit Losses in Downturns

This paper suggests formulas able to capture potential strong connection among credit losses in downturns without assuming any specific distribution for the variables involved. We first show that the current model adopted by regulators (Basel) is equivalent to a conditional distribution derived from the Gaussian Copula (which does not identify tail dependence). We then use conditional distributions derived from copulas that express tail dependence (stronger dependence across higher losses) to estimate the probability of credit losses in extreme scenarios (crises). Next, we use data on historical credit losses incurred in American banks to compare the suggested approach to the Basel formula with respect to their performance when predicting the extreme losses observed in 2009 and 2010. Our results indicate that, in general, the copula approach outperforms the Basel method in two of the three credit segments investigated. The proposed method is extendable to other differentiable copula families and this gives flexibility to future practical applications of the model.     

Basic Process Capability Indices: An Expository Review

A review of the four basic process capability indices has been made. The interrelationship among these indices has been highlighted. Attention has been drawn to their drawbacks. The relation of these indices to the proportion nonconforming has been dwelt upon and the requirement of the adequate sample size has been emphasized. Cautionary remarks on the use of these indices in the case of nonnormal distributions, skewed distributions, and autocorrelated data are also presented. The effect of measurement error on process capability indices has been dealt with in great detail.     

A new family of bivariate max-infinitely divisible distributions

In this article we discuss the asymptotic behaviour of the componentwise maxima for a specific bivariate triangular array. Its components are given in terms of linear transformations of bivariate generalised symmetrised Dirichlet random vectors introduced in Fang and Fang (Statistical inference in elliptically contoured and related distributions. Allerton Press, New York, 1990). We show that the componentwise maxima of such triangular arrays is attracted by a bivariate max-infinitely divisible distribution function, provided that the associated random radius is in the Weibull max-domain of attraction.     

Efficient hybrid methods for portfolio credit derivatives

In this paper we discuss the computation of basket credit default swaps and collateralized debt obligation squared transactions. We suggest two hybrid algorithms for these two portfolio credit derivatives. The method combines the analytic approximation to the loss distribution of conditionally independent heterogeneous portfolios with the Monte Carlo simulation. The efficiency and accuracy of the algorithms are illustrated with examples.