Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR

Engle and Manganelli (2004) propose CAViaR, a class of models suitable for estimating conditional quantiles in dynamic settings. Engle and Manganelli apply their approach to the estimation of Value at Risk, but this is only one of many possible applications. Here we extend CAViaR models to permit joint modeling of multiple quantiles, Multi-Quantile (MQ) CAViaR. We apply our new methods to estimate measures of conditional skewness and kurtosis defined in terms of conditional quantiles, analogous to the unconditional quantile-based measures of skewness and kurtosis studied by Kim and White (2004). We investigate the performance of our methods by simulation, and we apply MQ-CAViaR to study conditional skewness and kurtosis of S&P 500 daily returns. JEL Classification: C13, C32Asset returns, CAViaR, conditional quantiles, Dynamic quantiles, Kurtosis, Skewness

Directional Prediction of Returns under Asymmetric Loss: Direct and Indirect Approaches

To predict a return characteristic, one may construct models of different complexity describing the dynamics of different objects. The most complex object is the entire predictive density, while the least complex is the characteristic whose forecast is of interest. This paper investigates, using experiments with real data, the relation between the complexity of the modeled object and the predictive quality of the return characteristic of interest, in the case when this characteristic is a return sign, or, equivalently, the direction-of-change. Importantly, we carry out the comparisons assuming that the underlying loss function is asymmetric, which is more plausible than the quadratic loss still prevailing in the analysis of returns. Our experiments are performed with returns of various frequencies on a stock market index and exchange rate. By and large, modeling the dynamics of returns by autoregressive conditional quantiles tends to produce forecasts of higher quality than modeling the whole predictive density or modeling the return indicators themselves.Directional prediction, sign prediction, model complexity, prediction quality, asymmetric loss, predictive density, conditional quantiles, binary autoregression

Robust quantile estimation and prediction for spatial processes

In this paper, we present a statistical framework for modeling conditional quantiles of spatial processes assumed to be strongly mixing in space. We establish the $L_1$ consistency and the asymptotic normality of the kernel conditional quantile estimator in the case of random fields. We also define a nonparametric spatial predictor and illustrate the methodology used with some simulations.Comment: 13 page

Detection of risk factors for obesity in early childhood with quantile regression methods for longitudinal data

This article compares and discusses three different statistical methods for investigating risk factors for overweight and obesity in early childhood by means of the LISA study, a recent German birth cohort study with 3097 children. Since the definition of overweight and obesity is typically based on upper quantiles (90% and 97%) of the age specific body mass index (BMI) distribution, our aim was to model the influence of risk factors and age on these quantiles while as far as possible taking the longitudinal data structure into account. The following statistical regression models were chosen: additive mixed models, generalized additive models for location, scale and shape (GAMLSS), and distribution free quantile regression models. The methods were compared empirically by cross-validation and for the data at hand no model could be rated superior. Motivated by previous studies we explored whether there is an age-specific skewness of the BMI distribution. The investigated data does not suggest such an effect, even after adjusting for risk factors. Concerning risk factors, our results mainly confirm results obtained in previous studies. From a methodological point of view, we conclude that GAMLSS and distribution free quantile regression are promising approaches for longitudinal quantile regression, requiring, however, further extensions to fully account for longitudinal data structures