Tail Quantiles Research Articles

The tail behavior of extreme stock returns in the Gulf emerging markets

PurposeIn this paper, the aim is to investigate the tail behavior of daily stock returns for three emerging stock in the Gulf region (Bahrain, Oman, and Saudi Arabia) over the period 1998‐2005. In addition, the aim is also to test whether the distributions are similar across these markets.Design/methodology/approachFollowing McNeil and Frey, Wanger and Marsh, and Bystrom, extreme value theory (EVT) methods are utilized to examine the asymptotic distribution of the tail for daily returns in the Gulf region. As a first step and to obtain independent and identically distributed residuals series, the returns are prefiltered with an ordinary time‐series model, taking into account the observed Gulf return dynamics. Then, the “Peaks‐Over‐Threshold” (POT) model is applied to estimate the tails of the innovational distribution.FindingsNot only is the heavy tail found to be a facial appearance in these markets, but also POT method of modelling extreme tail quantiles is more accurate than conventional methodologies (historical simulation and normal distribution models) in estimating the tail behavior of the Gulf markets returns. Across all return series, it is found that left and right tails behave very different across countries.Research limitations/implicationsThe results show that risk models that are able to exploit tail behavior could lead to more accurate risk estimates. Thus, participants in the Gulf equity markets can rely on EVT‐based risk model when assessing their risks.Originality/valueThe paper extends previous studies in two aspects. First, it extends the classical unconditional extreme value approach by first filtering the data by using AR‐FIAPARCH model to capture some of the dependencies in the stock returns, and thereafter applying ordinary extreme value techniques. Second, it provides a broad analysis of return dynamics of the Gulf markets.

The tail risks of FX return distributions: A comparison of the returns associated with limit orders and market orders

This paper measures and compares the tail risks of limit and market orders using Extreme Value Theory. The analysis examines realised tail outcomes using the Dealing 2000-2 electronic broking system based on completed transactions rather than the more common analysis of indicative quotes. In general, limit and market orders exhibit broadly similar tail behaviour, but limit orders have significantly heavier tails and larger tail quantiles than market orders.

The Tail Risks of FX Return Distributions: A Comparison of the Returns Associated with Limit Orders and Market Orders

This paper measures and compares the tail risks of limit and market orders using Extreme Value Theory. The analysis examines realised tail outcomes using the Dealing 2000-2 electronic broking system based on completed transactions rather than the more common analysis of indicative quotes. In general, limit and market orders exhibit broadly similar tail behaviour, but limit orders have significantly heavier tails and larger tail quantiles than market orders.

Monitoring Networked Applications With Incremental Quantile Estimation

Networked applications have software components that reside on different computers. Email, for example, has database, processing, and user interface components that can be distributed across a network and shared by users in different locations or work groups. End-to-end performance and reliability metrics describe the software quality experienced by these groups of users, taking into account all the software components in the pipeline. Each user produces only some of the data needed to understand the quality of the application for the group, so group performance metrics are obtained by combining summary statistics that each end computer periodically (and automatically) sends to a central server. The group quality metrics usually focus on medians and tail quantiles rather than on averages. Distributed quantile estimation is challenging, though, especially when passing large amounts of data around the network solely to compute quality metrics is undesirable. This paper describes an Incremental Quantile (IQ) estimation method that is designed for performance monitoring at arbitrary levels of network aggregation and time resolution when only a limited amount of data can be transferred. Applications to both real and simulated data are provided.

Finite Sample Inference for Quantile Regression Models

Under minimal assumptions finite sample confidence bands for quantile regression models can be constructed. These confidence bands are based on the conditional pivotal property of estimating equations that quantile regression methods aim to solve and will provide valid finite sample inference for both linear and nonlinear quantile models regardless of whether the covariates are endogenous or exogenous. The confidence regions can be computed using MCMC, and confidence bounds for single parameters of interest can be computed through a simple combination of optimization and search algorithms. We illustrate the finite sample procedure through a brief simulation study and two empirical examples: estimating a heterogeneous demand elasticity and estimating heterogeneous returns to schooling. In all cases, we find pronounced differences between confidence regions formed using the usual asymptotics and confidence regions formed using the finite sample procedure in cases where the usual asymptotics are suspect, such as inference about tail quantiles or inference when identification is partial or weak. The evidence strongly suggests that the finite sample methods may usefully complement existing inference methods for quantile regression when the standard assumptions fail or are suspect.

Optimal asymmetric kernels

Kernels are typically justified as a smoothing device in nonparametric analysis. We provide alternative interpretations, which could lead to the use of asymmetric kernels. We thus derive the class of optimal asymmetric kernels, and analyse its main properties. We illustrate numerically its optimality by showing how well it fares in locating the mode and tail quantiles of some common asymmetric densities.

Scale invariance of regional wet and dry durations of rain fields: A diagnostic study

Most of the recent work on rainfall data analyses and modeling has focused on either spatial or temporal variability. In this paper the structure of rainfall intermittence in space and time is investigated. Using a series of TOGA‐COARE radar scans converted to maps of pixel rain rate over a tropical oceanic region of size 240 × 240 km2, regionally scale‐invariant behavior of the probability distributions of wet and dry epoch durations is explored. Durations of wet and dry epochs are estimated by lengths of wet and dry spells, respectively, in time series of spatially averaged rain rate over sampled square subregions of spatial scales ranging from 120 km to 2 km. The investigation is based on sample quantiles and sample moments of the underlying marginal probability distributions, focusing on the behavior of their tails and their variation with respect to spatial scale. We find that sample tail quantiles and sample moments of wet durations exhibit power law multiscaling, while sample tail quantiles and sample moments of dry durations exhibit exponential multiscaling across the above range of scales. These findings provide new statistical diagnostic tools for validation of spatiotemporal models for rain fields.

The Variance Ratio Test with Stable Paretian Errors

This paper examines the distribution of the overlapping variance ratio (OVR) statistic when the errors are distributed with thick tails as described by the family of stable Paretian distributions. The asymptotic distribution of the OVR statistic, which depends on the characteristic exponent, can be estimated using simulation. It is found that the convergence of the distribution of the OVR statistic to its asymptotic limit is extremely slow. Thus, the asymptotic results will not be able to provide any useful approximation in finite samples. To facilitate the OVR statistic as a test for the random walk hypothesis, the tail quantiles are estimated for several finite sample sizes.

Control variates and importance sampling for efficient bootstrap simulations

Importance sampling and control variates have been used as variance reduction techniques for estimating bootstrap tail quantiles and moments, respectively. We adapt each method to apply to both quantiles and moments, and combine the methods to obtain variance reductions by factors from 4 to 30 in simulation examples.

A Comparison of Unbiased and Plotting‐Position Estimators of L Moments

Plotting‐position estimators of L moments and L moment ratios have several disadvantages compared with the “unbiased” estimators. For general use, the “unbiased” estimators should be preferred. Plotting‐position estimators may still be useful for estimating extreme upper tail quantiles in regional frequency analysis.

Kernel quantite function estimator for flood frequency analysis

A kernel estimator (KQ) of the quantile function is presented here. Boundary kernels are used for extrapolation of tail quantiles. The bandwidth of the estimator is chosen using an automatic, “plug‐in” method. Confidence intervals for the estimated quantile are estimated by bootstrapping. Comparisons of the estimator with selected tail probability estimators are offered. The KQ estimator presented here is shown to be competitive with other estimators.