A quantile approach to US GNP

In this paper we fitted a quantile self-exciting threshold autoregressive (QSETAR) time series model to the growth rate of real US GNP. We also presented a forecasting method for QSETAR models. This forecasting method makes it possible to obtain the predictive quantiles and predictive distribution function of x_t+m given x_t for m > 0, and hence any quantities of interest can be derived. Therefore, this new approach allows us to study the US GNP from a distribution point view, rather than from a mean point of view. The results obtained in this paper show that the method works very well in practice.     

Cyclicality of commodity markets with respect to the U.S. economic policy uncertainty based on granger causality in quantiles

Given the importance of the U.S. in global commodity markets, the goal is to explore whether U.S. economic policy uncertainty impacts the price performance of certain commodities. The analysis uses the Granger causality in quantiles method that allows us to test whether there are different effects under different market conditions. The results document that economic uncertainty impacts the returns on the commodities considered, with the effects clustering around the tail of their conditional distribution. Robust evidence was obtained under alternative definitions of uncertainty.     

Goodness-of-fit test with nuisance regression and scale

In the linear model Y _i = x _i + e _i, i=1,,n, with unknown (, ), {\open R}^p, >0, and with i.i.d. errors e ₁,,e _n having a continuous distribution F, we test for the goodness-of-fit hypothesis H ₀:F(e)F ₀(e/), for a specified symmetric distribution F ₀, not necessarily normal. Even the finite sample null distribution of the proposed test criterion is independent of unknown (,), and the asymptotic null distribution is normal, as well as the distribution under local (contiguous) alternatives. The proposed tests are consistent against a general class of (nonparametric) alternatives, including the case of F having heavier (or lighter) tails than F ₀. A simulation study illustrates a good performance of the tests. Received July 2001     

Characterizing systems of distributions by quantile measures

Modelling an empirical distribution by means of a simple theoretical distribution is an interesting issue in applied statistics. A reasonable first step in this modelling process is to demand that measures for location, dispersion, skewness and kurtosis for the two distributions coincide. Up to now, the four measures used hereby were based on moments.
In this paper measures are considered which are based on quantiles. Of course, the four values of these quantile measures do not uniquely determine the modelling distribution. They do, however, within specific systems of distributions, like Pearson's or Johnson's; they share this property with the four moment-based measures.
This opens the possibility of modelling an empirical distribution—within a specific system—by means of quantile measures. Since moment-based measures are sensitive to outliers, this approach may lead to a better fit. Further, tests of fit—e.g. a test for normality—may be constructed based on quantile measures. In view of the robustness property, these tests may achieve higher power than the classical moment-based tests.
For both applications the limiting joint distribution of quantile measures will be needed; they are derived here as well.     

RISK MEASURES ON AND VALUE AT RISK WITH PROBABILITY/LOSS FUNCTION

We propose a generalization of the classical notion of the V@R_λ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of law invariant risk measures based on an appropriate family of acceptance sets. The V@R_λ and other known law invariant risk measures turn out to be special cases of our proposal. We further prove the dual representation of Risk Measures on .     

On Quantile‐based Asymmetric Family of Distributions: Properties and Inference

In this paper, we provide a detailed study of a general family of asymmetric densities. In the general framework, we establish expressions for important characteristics of the distributions and discuss estimation of the parameters via method‐of‐moments as well as maximum likelihood estimation. Asymptotic normality results for the estimators are provided. The results under the general framework are then applied to some specific examples of asymmetric densities. The use of the asymmetric densities is illustrated in a real‐data analysis.     

Successive Sampling to Estimate Quantiles with P-Auxiliary Variables

The successive sampling is a known technique that can be used in longitudinal surveys to estimate population parameters and measurements of difference or change of a study variable. The paper discusses the estimation of quantiles for the current occasion based on sampling in two successive occasions and using p-auxiliary variables obtained of the previous occasion. A multivariate ratio estimator from the matched portion is used to provide the optimum estimate of a quantile by weighting the estimates inversely to derived optimum weights. Its properties are studied under large–sample approximation and the expressions of the variances are established. The behavior of these asymptotic variances is analyzed on the basis of data from natural populations. A simulation study is also used to measure the precision of the proposed estimator.     

PREDICTING STOCK RETURNS AND VOLATILITY WITH INVESTOR SENTIMENT INDICES: A RECONSIDERATION USING A NONPARAMETRIC CAUSALITY‐IN‐QUANTILES TEST

Evidence of monthly stock returns predictability based on popular investor sentiment indices, namely S^BW and S^PLS as introduced by Baker and Wurgler (2006, 2007) and Huang et al. (2015) respectively are mixed. While, linear predictive models show that only S^PLS can predict excess stock returns, nonparametric models (which accounts for misspecification of the linear frameworks due to nonlinearity and regime changes) finds no evidence of predictability based on either of these two indices for not only stock returns, but also its volatility. However, in this paper, we show that when we use a more general nonparametric causality‐in‐quantiles model of Balcilar et al., (forthcoming), in fact, both S^BW and S^PLS can predict stock returns and its volatility, with S^PLS being a relatively stronger predictor of excess returns during bear and bull regimes, and S^BW being a relatively powerful predictor of volatility of excess stock returns, barring the median of the conditional distribution.     

Kernel density estimation for time series data

A time-varying probability density function, or the corresponding cumulative distribution function, may be estimated nonparametrically by using a kernel and weighting the observations using schemes derived from time series modelling. The parameters, including the bandwidth, may be estimated by maximum likelihood or cross-validation. Diagnostic checks may be carried out directly on residuals given by the predictive cumulative distribution function. Since tracking the distribution is only viable if it changes relatively slowly, the technique may need to be combined with a filter for scale and/or location. The methods are applied to data on the NASDAQ index and the Hong Kong and Korean stock market indices.     

Quantile-locating functions and the distance between the mean and quantiles

Given a random variable X with finite mean, for each 0 < p < 1, a new sharp bound is found on the distance between a p -quantile of X and its mean in terms of the central absolute first moment of X . The new bounds strengthen the fact that the mean of X is within one standard deviation of any of its medians, as well as a recent quantile-generalization of this fact by O'Cinneide.