Conditional Quantiles Research Articles

Sequential monitoring for conditional quantiles of general conditional heteroscedastic time series models

AbstractIn this study, we introduce an online monitoring procedure designed to sequentially detect change points in the conditional quantiles of location‐scale time series models. This statistical process control issue holds great significance in risk management, particularly in measuring the value‐at‐risk or expected shortfall of financial assets. Our approach employs suitable detectors, including cumulative sum statistics. We then define a stopping rule and determine control limits based on asymptotic theorems to signal an anomaly. To further evaluate the proposed methods, we conduct a comprehensive empirical study analyzing various aspects of our monitoring procedures when applied to location‐scale time series models. Additionally, we perform a real data analysis using the daily returns of the Korea Composite Stock Price Index (KOSPI) and EuroStoxx 50 indices to affirm the adequacy of the proposed monitoring procedures in real‐world applications.

Financial conditions, macroeconomic uncertainty, and macroeconomic tail risks

This paper investigates how financial conditions and macroeconomic uncertainty jointly affect macroeconomic tail risks. We first document that tight financial conditions decrease all conditional quantiles of future output growth in the near term, while high macroeconomic uncertainty only stretches the interquartile range. Because financial conditions and uncertainty comove substantially, the conditional means and variances shift simultaneously in the opposite direction. Consequently, the downside risk varies much more than the upside risk. A quantile impulse response analysis indicates that both financial and uncertainty shocks are responsible for the asymmetric behaviors in the downside and upside risks.

Bayesian analysis of joint quantile regression for multi-response longitudinal data with application to primary biliary cirrhosis sequential cohort study.

This article proposes a Bayesian approach for jointly estimating marginal conditional quantiles of multi-response longitudinal data with multivariate mixed effects model. The multivariate asymmetric Laplace distribution is employed to construct the working likelihood of the considered model. Penalization priors on regression parameters are incorporated into the working likelihood to conduct Bayesian high-dimensional inference. Markov chain Monte Carlo algorithm is used to obtain the fully conditional posterior distributions of all parameters and latent variables. Monte Carlo simulations are conducted to evaluate the sample performance of the proposed joint quantile regression approach. Finally, we analyze a longitudinal medical dataset of the primary biliary cirrhosis sequential cohort study to illustrate the real application of the proposed modeling method.

Association between per- and poly-fluoroalkyl substances and nonalcoholic fatty liver disease: A nested case-control study in northwest China

Per- and poly-fluoroalkyl substances (PFAS) have been reported to have hepatotoxic effects. However, it is unclear whether they are linked to non-alcoholic fatty liver disease (NAFLD). This nested case-control study focused on the epidemiological links between PFAS and the prevalence of NAFLD. We selected 476 new cases of NAFLD and 952 age- and sex-matched controls from the Jinchang cohort population between 2014 and 2019. Serum concentrations of PFAS were measured using high-performance liquid chromatography-tandem mass spectrometry (HPLC-MS/MS). Only PFAS with a detection rate of ≥90 % were included for analysis, which included PFPeA, PFOA, PFNA, PFHxS, PFOS, and 9Cl-PF3ONS. The relationship between single and co-exposure to PFAS and the occurrence of NAFLD was evaluated using conditional logistic regression, Quantile g-computation (QgC), and Bayesian kernel machine regression (BKMR) model. Logistic regression indicated that PFPeA, PFOA, and 9Cl-PF3ONS were positive correlation with the incidence of NAFLD after adjusting for confounders, with odds ratios (OR) and 95 % confidence interval (CI) of 3.13 (95 % CI: 2.53, 3.86), 1.39 (95 % CI: 1.12, 1.73), and 1.41 (95 % CI: 1.20, 1.66), respectively. PFNA, PFHxS, and PFOS were nonlinearly and negatively associated with the incidence of NAFLD, with OR (95 % CI) of 0.53 (0.46, 0.62), 0.83 (0.73, 0.95), and 0.52 (0.44, 0.61), respectively. QgC showed a significant joint effect of PFAS mixture on NAFLD onset (OR: 1.52, 95 % CI: 1.24, 1.88). BKMR showed a weak positive trend between PFAS mixtures and NAFLD incidence. Positive correlations were primarily driven by PFPeA and 9Cl-PF3ONS, while negative correlations were mainly influenced by PFNA and PFOS. The BKMR model also suggested that there was an interaction between PFOS and PFNA and other four PFAS compounds. In conclusion, our findings suggest that individual and co-exposure to PFAS is associated with a risk of NAFLD onset.

Corneal biomechanics are not exclusively compromised in high myopia.

Research assuming linearity has concluded that corneal biomechanics are compromised in high myopia. We investigated whether this assumption was appropriate and re-examined these associations across different levels of myopia. Myopic (spherical equivalent refraction, SER ≤ -0.50 D) eyes of 10,488 adults aged 40-69 years without any history of systemic and ocular conditions were identified in the UK Biobank. Ordinary least squares (OLS) regression was employed to test the linear association between corneal hysteresis (CH) or corneal resistance factor (CRF), separately, and SER while controlling for age, sex, corneal radius and intraocular pressure. Quantile regression (QR) was used to test the same set of associations across 49 equally spaced conditional quantiles of SER. In OLS regression, each standard deviation (SD) decrease in CH and CRF was associated with 0.08 D (95% CI: 0.04-0.12; p < 0.001) and 0.10 D (95% CI: 0.04-0.15; p < 0.001) higher myopia, respectively. However, residual analysis indicated that the linearity assumption was violated. QR revealed no evidence of a significant association between CH/CRF and SER in low myopia, but a significant (p < 0.05) positive association became evident from -2.78 D (0.06 and 0.08 D higher myopia per SD decrease in CH and CRF). The magnitude of association increased exponentially with increasing myopia: in the -5.03 D quantile, every SD decrease in CH and CRF was associated with 0.17 D (95% CI: 0.08-0.25; p < 0.001) and 0.21 D (95% CI: 0.10-0.31; p < 0.001) higher myopia. In the -8.63 D quantile, this further increased to 0.54 D (95% CI: 0.33-0.76; p < 0.001) and 0.67 D (95% CI: 0.41-0.93; p < 0.001) higher myopia per SD decrease in CH and CRF. Corneal biomechanics appeared compromised from around -3.00 D. These changes were observed to be exponential with increasing myopia.

Inference on Conditional Quantile Processes in Partially Linear Models with Applications to the Impact of Unemployment Benefits

Abstract We propose methods to estimate and make inferences on conditional quantile processes for models with both nonparametric and (locally or globally) linear components. We derive their asymptotic properties, optimal bandwidths, and uniform confidence bands over quantiles allowing for robust bias correction. Our framework covers the sharp regression discontinuity design, which is used to study the effects of unemployment insurance benefits extensions, focusing on heterogeneity over quantiles and covariates. We show economically strong effects in the tails of the outcome distribution. They reduce the within-group inequality, but can be viewed as enhancing between-group inequality, although they help to bridge the gender gap.

Forecasting international financial stress: The role of climate risks

We study the predictive value of climate risks for subsequent financial stress in a sample of daily data running from October 2006 to December 2022 of thirteen countries, which include China, ten European Union (EU) countries, the United Kingdom (UK), and the United States (US). The climate risk indicators are the result of a text-based approach which combines the term frequency-inverse document frequency and the cosine-similarity techniques. Given the persistence of financial stress as well as the importance of spillover effects of financial stress from other countries, we use random forests, a machine-learning technique tailored to handle many predictors, to estimate our forecasting models. Our findings show that climate risks tend to have a moderate impact, albeit in several cases statistically significant, on predictive accuracy, which tends to be stronger, in our cross-section of countries, on a daily than at a weekly or monthly forecast horizon of financial stress. Furthermore, the predictive value of climate risks for financial stress is heterogeneous across the countries in our sample, implying that a univariate forecasting model appears to be better suited than a corresponding multivariate one. Finally, the predictive value of climate risks for financial stress appears to be stronger in several countries at the lower conditional quantiles of financial stress.

Multichannel relational communication strategy: does one-sized strategy fit all customers?

PurposeThis study aims to capture how the association between a multichannel relational communication strategy (MRCS) and customer performance is contingent upon such customer performance (low- versus high-performance customers) and to reconcile past contradictory results in this marketing-related topic. To this end, the authors propose and validate the method of quantile regression as an unconventional, yet effective, means to proceed to that reconciliation.Design/methodology/approachThis study collected data from 4,934 customers of a private pension fund firm and accounted for both firm- and customer-initiated relational communication channels (RCCs) and for customer lifetime value (CLV). This study estimated a generalized linear model and then a quantile regression model was used to account for customer performance heterogeneity.FindingsThis study finds that specific RCCs present different levels of association with performance for low- versus high-performance customers, where outcome customer performance is the dependent variable. For example, the relation between firm-initiated communication (FIC) and performance is stronger for low-CLV customers, whereas the relation between customer-initiated communication (CIC) and performance is increasingly stronger for high-CLV customers but not for low-CLV ones. This study also finds that combining different forms of FIC can result in a negative association with customer performance, especially for low-CLV customers.Research limitations/implicationsThe authors tested the conceptual model in one single firm in the specific context of financial services and with cross-sectional data, so there should be caution when extrapolating this study’s findings.Practical implicationsThis study offers nuanced and precise managerial insights on recommended resource allocation along with relational communication efforts, showing how managers can benefit from adopting a differentiated-customer performance approach when designing their MRCS.Originality/valueThis study provides an overview of the state of the art of MRCS, proposes a contingency analysis of the relationship between MRCS and performance based on customer performance heterogeneity and suggests the quantile method to perform such analysis and help reconcile past contradictory findings. This study shows how the association between RCCs and CLV varies across the conditional quantiles of the distribution of customer performance. This study also addresses a recent call for a more holistic perspective on the relationships between independent and dependent variables.

Quantile mortality modelling of multiple populations via neural networks

Quantiles of the mortality rates are relevant in life insurance to control longevity risk properly. Recently, Santolino (2020) adapts the framework of the popular Lee-Carter model to compute the conditional quantiles of the mortality rates. The parameters of the quantile Lee-Carter model are fitted on the mortality data of the population of interest, ignoring the information related to the others. In this paper, we show that more robust parameter estimates can be obtained exploiting the mortality experiences of multiple populations. A neural network is employed to calibrate individual quantile Lee-Carter models jointly using all the available mortality data. In this setting, some common network parameters are used to learn the age and period effects of multiple quantile LC models. Numerical experiments performed on all the countries of the Human Mortality Database validate our approach. The predictions obtained considering the median level appear more accurate than those obtained with the mean models; moreover, those at the tail quantile levels capture the future mortality evolution of the populations well.

Parametric Quantile Beta Regression Model

SummaryIn this paper, we develop a fully parametric quantile regression model based on the generalised three‐parameter beta (GB3) distribution. Beta regression models are primarily used to model rates and proportions. However, these models are usually specified in terms of a conditional mean. Therefore, they may be inadequate if the observed response variable follows an asymmetrical distribution. In addition, beta regression models do not consider the effect of the covariates across the spectrum of the dependent variable, which is possible through the conditional quantile approach. In order to introduce the proposed GB3 regression model, we first reparameterise the GB3 distribution by inserting a quantile parameter, and then we develop the new proposed quantile model. We also propose a simple interpretation of the predictor–response relationship in terms of percentage increases/decreases of the quantile. A Monte Carlo study is carried out for evaluating the performance of the maximum likelihood estimates and the choice of the link functions. Finally, a real COVID‐19 dataset from Chile is analysed and discussed to illustrate the proposed approach.

Probabilistic En Route Sector Traffic Demand Prediction Based on Quantile Regression Neural Network and Kernel Density Estimation

With the development of civil aviation in China, airspace congestion has become more and more serious and has gradually spread from airport terminal areas to en route networks. Traditionally, most prediction methods that obtain traffic flow data are based on the number of aircraft passing through an en route sector and require flight data to meet strict assumptions and conditions. While these methods are normally used in the actual operation of air traffic flow management departments in China, the results are not satisfactory due to the nonlinearity of traffic demand along en route sectors and the change in high-frequency noise. In order to refine aircraft control in airspace, it is necessary to predict traffic flow accurately. Thus, this paper proposes the quantile regression neural network and kernel density estimation method to obtain some quantiles of continuous traffic demand data in the future, which combines the strong nonlinear adaptive ability of neural networks with the ability of quantile regression to describe explanatory variables. By using these continuous conditional quantiles, we obtain the probability density function and probability density curve of the continuous traffic demand in the future using the kernel density estimation method. In this way, we can obtain not only a specific point prediction value and its change interval but also the probability of each value in the prediction change interval of traffic demand in the en route sector as well as a more accurate point prediction value for a specific day.

Fostering green progress: The dual influence of natural resource rent and human capital on emerging economy energy transition

AbstractThe scale and complexity of the energy transition pose formidable challenges. For the fast‐track progress of energy transition, emerging economies must identify the barriers to a successful transition. This study aims to investigate the role of natural resource depletion and human capital in achieving clean energy affordability and climate action through successful energy transition in emerging economies from 1990 to 2021. The study used quantile regression to analyze and estimate the relationship between variables at different conditional quantiles. The outcomes of the analysis suggest that natural resource depilation, human capital, and economic growth significantly facilitate the energy transition in emerging economies at all quantiles (Q0.10 – Q0.90), while the study identifies a paradoxical inverse relationship between financial development and energy transition across all quantiles, which implies that it impedes the transformation from traditional fossil fuels to the green energy resources. The study's outcomes suggest policy implications for advancing the energy transition in the context of natural resources and human capital management for emerging economies.

Asymmetric dynamics between cryptocurrency uncertainty and the oil and gold markets: evidence from Granger causality in quantiles

ABSTRACT This research examines the causal relationships between cryptocurrency uncertainty, the price of crude oil, and the price of gold using weekly data from 30 December 2013, to 21 February 2021, applying Granger-causality analysis on each quantile. Under this approach, we are able to distinguish between median and tail relationships for conditional quantiles. We find a bidirectional causal relationship between cryptocurrency uncertainty and crude oil prices, implying that crude oil price volatility is one source of cryptocurrency uncertainty, whereas a causal relationship from cryptocurrency uncertainty or crude oil prices to gold suggests that gold hedges cryptocurrency uncertainty and crude oil price shocks. Our research calls on governments to maintain cryptocurrency market stability to reduce market volatility in crude oil prices. Investors and fund managers can consider adding gold assets to portfolios that contain cryptocurrencies or crude oil in order to hedge against the risks of cryptocurrency uncertainty and crude oil price volatility.

Dynamic spillovers among global oil shocks, economic policy uncertainty, and inflation expectation uncertainty under extreme shocks

This study explores the quantile connectedness between United States (U.S.) economic policy uncertainty (EPU), global structural oil shocks, and U.S. inflation expectations uncertainty (IEU) under extreme shocks using a connectedness method based on the quantile VAR model. We find that the total connectedness index (TCI) exhibits a U-shaped pattern that varies with the conditional quantiles of variables, demonstrating that the spillover effect under extreme market conditions is much greater than under regular market conditions. Further proven that the spillover effect in the extreme upward state is stronger than in the extreme downward state. Moreover, the dynamic TCI is heterogeneous over time and economic-event dependent, specifically affected by COVID-19 epidemic. IEU is the largest net receiver of spillover effects among variables and hence is more susceptible to EPUs and oil shocks. Finally, although there is significant heterogeneity in the spillover effects of different EPUs and structural oil price shocks, overall, EPUs influence the IEU more than global oil shocks.

Unconditional Quantile Regression for Streaming Datasets

The Unconditional Quantile Regression (UQR) method, initially introduced by Firpo et al. has gained significant traction as a popular approach for modeling and analyzing data. However, much like Conditional Quantile Regression (CQR), UQR encounters computational challenges when it comes to obtaining parameter estimates for streaming datasets. This is attributed to the involvement of unknown parameters in the logistic regression loss function used in UQR, which presents obstacles in both computational execution and theoretical development. To address this, we present a novel approach involving smoothing logistic regression estimation. Subsequently, we propose a renewable estimator tailored for UQR with streaming data, relying exclusively on current data and summary statistics derived from historical data. Theoretically, our proposed estimators exhibit equivalent asymptotic properties to the standard version computed directly on the entire dataset, without any additional constraints. Both simulations and real data analysis are conducted to illustrate the finite sample performance of the proposed methods.

Quantile set-regression with application in precision medicine

Quantile regression is commonly used in statistical analysis. It is more general than the ordinary regression. However in some practical investigations, the interest is the conditional quantile of the response given the covariates belonging to some set. For example in subgroup analysis, the goal is to classify the patients into two subgroups, one with whom benefit the most from the treatment and the other not so beneficial. This is equivalent to finding an optimal set in the covariate space, such that a patient is favored for the treatment if his/her covariates fall in this set, and otherwise not. Motivated by this practical problem we extend our recent work on set-regression to quantile set regression, defined as the conditional quantile of the response given the covariates belonging to a given set. This extends the notion of the classical quantile regression and is particularly suitable for precision medicine and other applications. The method is easy to use and in principle it works for sets of any shapes, but our current codes only work for certain particular shaped sets, the balls and rectangles. Simulation studies are conducted to evaluate the performance of the proposed method, which show superior promising results of the proposed method. Then the method is applied to analyze an AIDS Clinical Trials Group data.

Asymptotic Normality of Single Functional Index Quantile Regression for Functional Data with Missing Data at Random

This work addresses the problem of the nonparametric estimation of the regression function, namely the conditional distribution and the conditional quantile in the single functional index model (SFIM) under the independent and identically distributed condition with randomly missing data. The main result of this study was the establishment of the asymptotic properties of the estimator, such as the almost complete convergence rates. Moreover, the asymptotic normality of the constructs was obtained under certain mild conditions. Lastly, the authors discussed how to apply the result to construct confidence intervals.

Modelling an Improved Swarm Optimizer and Boosted Quantile Estimator For Malicious Flow Monitoring And Prediction In Network

For a long time, malware has posed a significant risk to computer system security. The effectiveness of conventional detection techniques based on static and dynamic analysis is restricted due to the quick advancement of anti-detection technologies. In recent years, AI-based malware detection has increasingly been employed to combat malware due to its improved predictive ability. Unfortunately, because malware may be so diverse, it can be challenging to extract features from it, which makes using AI for malware detection ineffective. A malware classifier based on an Improved Salp Swarm optimization for feature selection and a Boosted tree with Conditional Quantile Estimation (ISSO-BCQE) is developed to adapt different malware properties to solve the problem. Specifically, the malware code is extracted, and the feature sequence is generated into a boosting tree where the feature map of the node is extracted using BCQE, where a boosting network is used to design a classifier and the method's performance is finally analyzed and compared. The results show that our model works better than other approaches regarding FPR and accuracy. It also shows that the method beats current methods with the highest accuracy of 99.6% in most detecting circumstances. It is also stable in handling malware growth and evolution.

Estimation of extreme multivariate expectiles with functional covariates

The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate, belonging to an infinite-dimensional space. By using the first order optimality condition, we interpret these expectiles as solutions of a multidimensional nonlinear optimum problem. Then the inference is based on a minimization algorithm of gradient descent type, coupled with consistent kernel estimations of our key statistical quantities such as conditional quantiles, conditional tail index and conditional tail dependence functions. The method is valid for equivalently heavy-tailed marginals and under a multivariate regular variation condition on the underlying unknown random vector with arbitrary dependence structure. Our main result establishes the consistency in probability of the optimum approximated solution vectors with a speed rate. This allows us to estimate the global computational cost of the whole procedure according to the data sample size. The finite-sample performance of our methodology is provided via a numerical illustration of simulated datasets.

Assessing systemic risk and connectedness among dirty and clean energy markets from the quantile and expectile perspectives

In response to environmental and climate change issues in recent decades, clean energy resources have been promoted as substitutes for fossil fuel-based dirty energy resources. While receiving great attention from environmentally conscious investors and policy-makers, the markets for the former energies could be affected by financial instability in the markets for the latter, which could lead to systemic risk and directional connectedness. In this paper, we aimed to assess potential systemic risk in such markets by employing conditional quantile- and conditional expectile-based Value-at-Risk (henceforth CoVaR and CoEVaR, respectively). Due to their definition through expected conditional asymmetric loss functions, we adopted Kabaila’s efficient method for the computation of conditional expectations and proposed a backtesting technique based on Diebold and Mariano’s test. Using Delta-CoVaR and Delta-CoEVaR, we constructed conditional tail risk networks to describe the directional tail risk connectedness. We revealed that the CoVaR and CoEVaR for almost all pairs of energy markets had the best forecast accuracy when computed using a copula exhibiting symmetric tail dependence with asymmetric and heavy-tailed margins. Compared to CoVaR, CoEVaR possessed a relatively better conditional coverage performance in several cases, complementing its advantage of being more sensitive to (extreme) loss magnitude. In addition, we found crude oil, heating oil, and sectoral clean energy indices to be highly interconnected, but the connectedness weakened following the 2015 Paris Climate Agreement. In particular, crude oil and the renewable energy sector played a consistent role as the most systemically important net receiver and net transmitter, respectively. These results provided important implications for policy-makers and investors aware of systemic risk and connectedness among dirty and clean energy markets.