Tail-weighted measures of dependence

Multivariate copula models are commonly used in place of Gaussian dependence models when plots of the data suggest tail dependence and tail asymmetry. In these cases, it is useful to have simple statistics to summarize the strength of dependence in different joint tails. Measures of monotone association such as Kendall's tau and Spearman's rho are insufficient to distinguish commonly used parametric bivariate families with different tail properties. We propose lower and upper tail-weighted bivariate measures of dependence as additional scalar measures to distinguish bivariate copulas with roughly the same overall monotone dependence. These measures allow the efficient estimation of strength of dependence in the joint tails and can be used as a guide for selection of bivariate linking copulas in vine and factor models as well as for assessing the adequacy of fit of multivariate copula models. We apply the tail-weighted measures of dependence to a financial data set and show that the measures better discriminate models with different tail properties compared to commonly used risk measures – the portfolio value-at-risk and conditional tail expectation.     

TESTING FOR LINEAR DEPENDENCE IN HEAVY-TAILED DATA

ABSTRACT

We use the sample covariation to develop tests for lagged linear dependence in symmetric time series data. We propose tests for both finite and infinite variance processes. The finite sample performance of the tests is investigated using simulated data and compared to tests based on the von Neumann ratio.     

A semi‐Markovian approach to using event history data in multiregional demography

As a first step towards infusing event‐history analysis into multiregional demography, this paper introduces a semi‐Markovian framework and outlines its salient features as differentiated from a pure Markovian framework. Specifically, what differentiates the former from the latter is an explicit consideration of duration‐dependence in migrating from one region to another. This duration‐dependence is one of the complexities involved in using event‐history data in multiregional demography. The use of event‐history data lends itself easily to defining basic probabilities involved in a semi‐Markovian framework directly on sample paths of individuals. The underlying concepts of a semi‐Markov process in the special case of time‐homogeneity or age‐independence of transition probabilities are given in a coherent and concise form. Illustrations of empirical applications to the event‐history data on migration as provided by the Korean National Migration Survey conducted in 1983, and of distinct features of the semi‐Markovian analysis through a parametrization of the basic probabilities are also given in this paper.     

Rank correlation plots for use with correlated input variables

A method for inducing a desired rank correlation matrix on multivariate input vectors for simulation studies has recently been developed by Iman and Conover (1982). The primary intention of this procedure is to produce correlated input variables for use with computer models. Since this procedure is distribution free and allows the exact marginal distributions to remain intact it can be used with any marginal distributions for which it is reasonable to think in terms of correlation. In this paper we present a series of rank correlation plots based on this procedure when the marginal distributions are normal, lognormal, uniform and loguniform. These plots provide a convenient tool both for aiding the modeler in determining the degree of dependence among input variables (rather than guessing) and for communicating with the modeler the effect of different correlation assumptions. In addition this procedure can be used with sample multivariate data by sampling directly from the respective marginal empirical distribution functions.     

Real and Spurious Long-Memory Properties of Stock-Market Data

We test for the presence of long memory in daily stock returns and their squares using a robust semiparametric procedure of Lobato and Robinson. Spurious results can be produced by nonstationarity and aggregation. We address these problems by analyzing subperiods of returns and using individual stocks. The test results show no evidence of long memory in the returns. By contrast, there is strong evidence in the squared returns.     

On Directional Dependence in a Regression Line

Abstract

In this paper, under the assumption of linear relationship between two variables we provide alternative simple method of proving the existing result connecting correlation coefficient with those of skewness of response and explanatory variables. Further we have given a relationship between correlation coefficient and coefficient of kurtosis of response and explanatory variables assuming the linear relationship between the two variables. Simple alternative way of deriving the formula, which helps in finding the direction dependence in linear regression, is discussed.     

On parameter estimation in Bernoulli trials with dependence

A simple estimator is proposed for the dependence parameter for the Klotz model of Bernoulli trials with Markov dependence and it is compared with the ratio estimator given by Price and the approximate maximum likelihood estimator given by Klotz. The proposed estimator is shown to have considerably smaller bias than the other two estimators with comparable mean squared errors, and has all the large sample optimal properties that the other two estimators have.     

Reemployment Probability and Multiple Unemployment Spells: A Partial-Likelihood Approach

An extended version of the mixed-proportional-hazards model is used to study the determinants of the conditional probability of reemployment of long-term unemployed young persons sampled in the first stage of the Australian National Longitudinal Survey. The survey data facilitate an econometric comparison between the effect of different factors on the conditional reemployment probability of those in their first unemployment spell with those who have experienced multiple spells. The article uses Cox's partial-likelihood approach. The empirical results support the hypothesis of lagged-duration dependence in that the length of previous job experience or the duration of previous unemployment is found to be an important determinant of reemployment probability. The results strongly suggest that fitting a common duration model to data from different spells involves a major misspecification.     

Identifying Bull and Bear Markets in Stock Returns

This article uses a Markov-switching model that incorporates duration dependence to capture nonlinear structure in both the conditional mean and the conditional variance of stock returns. The model sorts returns into a high-return stable state and a low-return volatile state. We label these as bull and bear markets, respectively. The filter identifies all major stock-market downturns in over 160 years of monthly data. Bull markets have a declining hazard functions although the best market gains come at the start of a bull market. Volatility increases with duration in bear markets. Allowing volatility to vary with duration captures volatility clustering.     

The ordering of negative quadrant dependence

A partial ordering is developed among negative quadrant dependent distributions with fixed marginals. Basic properties and closure under certain statistical operations are derived. Applications of the results in statistics and probability are given.