Bayesian modeling of joint and conditional distributions

In this paper, we study a Bayesian approach to flexible modeling of conditional distributions. The approach uses a flexible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution. We use a finite mixture of multivariate normals (FMMN) to estimate the joint distribution. The conditional distributions can then be assessed analytically or through simulations. The discrete variables are handled through the use of latent variables. The estimation procedure employs an MCMC algorithm. We provide a characterization of the Kullback–Leibler closure of FMMN and show that the joint and conditional predictive densities implied by the FMMN model are consistent estimators for a large class of data generating processes with continuous and discrete observables. The method can be used as a robust regression model with discrete and continuous dependent and independent variables and as a Bayesian alternative to semi- and non-parametric models such as quantile and kernel regression. In experiments, the method compares favorably with classical nonparametric and alternative Bayesian methods.     

Robust estimation with flexible parametric distributions: estimation of utility stock betas

The distributions of stock returns and capital asset pricing model (CAPM) regression residuals are typically characterized by skewness and kurtosis. We apply four flexible probability density functions (pdfs) to model possible skewness and kurtosis in estimating the parameters of the CAPM and compare the corresponding estimates with ordinary least squares (OLS) and other symmetric distribution estimates. Estimation using the flexible pdfs provides more efficient results than OLS when the errors are non-normal and similar results when the errors are normal. Large estimation differences correspond to clear departures from normality. Our results show that OLS is not the best estimator of betas using this type of data. Our results suggest that the use of OLS CAPM betas may lead to erroneous estimates of the cost of capital for public utility stocks.     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 2

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. We consider case 2, with two observation times for each unobservable event time, in the situation that the observation times cannot become arbitrarily close to each other. It is proved that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

Spillover effects and conditional dependence

A better understanding of cross-market linkages and interactions would help to better manage international financial exposure. So far, no attempt has been made to investigate the degree of price and volatility spillovers in a non-Gaussian conditional framework. We present a new model for these transmission mechanisms that relies on asymmetric-t marginal distributions and a copula function to characterize the conditional dependence. Rendering the dependence parameter time varying, we investigate how the dependence structure is affected by stock return innovations.     

Generalised Rational Bias in Financial Forecasts

Laster et al. (Q J Econ 114(1):293–318, 1999) built an economic model in which forecasters have incentives to generate forecasts that differ form the consensus. It is shown that the dispersion of the equilibrium distribution of forecasters, depends on the relative importance given on the intensive forecast users’ loss versus the publicity gain from occasional users. These results depend heavily on the assumption of symmetry for the loss and density functions. In this paper we examine the effects of generalising loss preferences and probability densities to allow for asymmetries through the LinEx loss and the Skewed Normal density, respectively. We derive the generalised equilibrium distribution of forecasts which contains the results of Laster et al. as a special case. The presence of asymmetric preferences is shown to cause a movement of the distribution away from the conditional mean, towards the optimal forecast under loss asymmetry. Furthermore, forecasts now tend to cluster around this quantity in an asymmetric way. These effects tend to be further strengthened or partially offset by the presence of skewness in the distribution of data, a result consistent with the conclusions of Christodoulakis (Finan Res Lett 2:227–233, 2005).The author is grateful to an anonymous referee for helpful comments that have improved the paper. The views expressed in the paper are those of the author and should in no part be attributed to the Bank of Greece.     

Estimation of the scale matrix of a multivariate t-model under entropy loss

This paper deals with the estimation of the scale matrix of a multivariatet-model with unknown location vector and scale matrix to improve upon the usual estimators based on the sample sum of product matrix. The well-known results of the estimation of the scale matrix of the multivariate normal model under the assumption of entropy loss function have been generalized to that of a multivariatet-model. The paper is based on the first author’s unpublished Ph.D. dissertation ‘Estimation of the Scale Matrix of a Multivariate T-model’, University of Western Ontario, Canada. Present address: School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia.     

Signed Central Moments of Integer Random Variables with Decreasing Density

Signed central α-moments of integer valued rv with decreasing density are considered. These are all positive if α≥3/2. We state sharp universal bounds on α depending only on the expectation of the random variable. For special cases the bounds are also evaluated numerically.     

A bivariate Poisson count data model using conditional probabilities

The applied econometrics of bivariate count data predominantly focus on a bivariate Poisson density with a correlation structure that is very restrictive. The main limitation is that this bivariate distribution excludes zero and negative correlation. This paper introduces a new model which allows for a more flexible correlation structure. To this end the joint density is decomposed by means of the multiplication rule in marginal and conditional densities. Simulation experiments and an application of the model to recreational data are presented.     

Estimating Systematic Risk Using Time Varying Distributions

This article proposes a dynamic vector GARCH model for the estimation of time-varying betas. The model allows the conditional variances and the conditional covariance between individual portfolio returns and market portfolio returns to respond asymmetrically to past innovations depending on their sign. Covariances tend to be higher during market declines. There is substantial time variation in betas but the evidence on beta asymmetry is mixed. Specifically, in 50% of the cases betas are higher during market declines and for the remaining 50% the opposite is true. A time series analysis of estimated time varying betas reveals that they follow stationary mean-reverting processes. The average degree of persistence is approximately four days. It is also found that the static market model overstates non-market or, unsystematic risk by more than 10%. On the basis of an array of diagnostics it is confirmed that the vector GARCH model provides a richer framework for the analysis of the dynamics of systematic risk.     

A Simple Proof of the Equivalence of the Limiting Distributions of the Continuous-Time and the Embedded Process of the Queue Size in the M/G/1 Queue*

This paper presents an extremely simple proof of the known remarkable fact that for the M/G/1 queue the continuous-time process describing the number of customers in the system has the same limiting distribution as the embedded process describing the number of customers in the system just after service completion epochs.