Conditional Quantile Models Research Articles

An Oracle Inequality for Multivariate Dynamic Quantile Forecasting

I derive an oracle inequality for a family of possibly misspecified multivariate conditional autoregressive quantile models. The family includes standard specifications for (nonlinear) quantile prediction proposed in the literature. This inequality is used to establish that the predictor that minimizes the in-sample average check loss achieves the best out-of-sample performance within its class at a near optimal rate, even when the model is fully misspecified. An empirical application to backtesting global Growth-at-Risk shows that a combination of the generalized autoregressive conditionally heteroscedastic model and the vector autoregression for Value-at-Risk performs best out-of-sample in terms of the check loss.

Reprint of: Out-of-sample tests for conditional quantile coverage: An application to Growth-at-Risk

This paper proposes tests for out-of-sample comparisons of interval forecasts based on parametric conditional quantile models. The tests rank the distance between actual and nominal conditional coverage with respect to the set of conditioning variables from all models, for a given loss function. We propose a pairwise test to compare two models for a single predictive interval. The set-up is then extended to a comparison across multiple models and/or intervals. The limiting distribution varies depending on whether models are strictly non-nested or overlapping. In the latter case, degeneracy may occur. We establish the asymptotic validity of wild bootstrap based critical values across all cases. An empirical application to Growth-at-Risk (GaR) uncovers situations in which a richer set of financial indicators are found to outperform a commonly-used benchmark model when predicting downside risk to economic activity.

Effect of blended teaching on college students' EFL acquisition

The research into the efficacy of blended EFL (English as a Foreign Language) teaching at the collegiate level holds significant importance for comprehending and implementing this novel pedagogical approach on a larger scale within universities. Within this domain, scholars have primarily concentrated on feedback mechanisms and quality assurance, while comparatively neglecting the advancement of college students' foreign language proficiency and the individual variances in the acceptance and rewards of blended teaching across distinct language proficiency groups. In light of this, leveraging micro-data from a provincial normal university's blended college English teaching, this study employs R 3.6.1 and R Studio to implement multiple linear regression and conditional quantile models so as to assess the impact of blended teaching on different language proficiency groups across four dimensions: listening, reading, writing, and overall language proficiency. To mitigate endogenous system risk, students admitted to the same major are selected as samples and their data undergoes additional screening, excluding learners who failed the CET4 exam or did not participate in the CET6 exam. After employing purposive sampling techniques, a valid sample of 676 learners is established, comprising 363 learners in the experimental group for blended teaching intervention and 313 learners in the control group receiving traditional teaching. The study results indicates that the samples had random characteristics. The study findings suggest the following: (1) Blended teaching has a significant positive impact on enhancing the efficiency of English acquisition. (2) The effectiveness of blended teaching in improving learners' reading, listening, and writing skills follows a sequential decrease, exhibiting a downward trend as students' language ability increases. This indicates that blended teaching facilitates the acquisition of foundational language knowledge, however, its impact on more advanced language processing abilities is limited. (3) Blended teaching demonstrates a range effect, primarily benefiting learners at the intermediate level and below in terms of enhancing their language proficiency. Conversely, learners at the medium-high and high proficiency levels derive comparatively lesser benefits from this approach. This study introduces a new methodology by employing multiple linear regression and conditional quantile models to assess the impact of blended teaching. This methodology not only enables us to examine the overall impact of blended teaching, but also allows assessment of its effect on different proficiency groups, helping to identify its effectiveness on individual learners across four dimensions.

CAViaR models for Value-at-Risk and Expected Shortfall with long range dependency features

Abstract We consider alternative specifications of conditional autoregressive quantile models to estimate Value-at-Risk and Expected Shortfall. The proposed specifications include a slow moving component in the quantile process, along with aggregate returns from heterogeneous horizons as regressors. Using data for 10 stock indices, we evaluate the performance of the models and find that the proposed features are useful in capturing tail dynamics better.

Out-of-sample tests for conditional quantile coverage an application to Growth-at-Risk

This paper proposes tests for out-of-sample comparisons of interval forecasts based on parametric conditional quantile models. The tests rank the distance between actual and nominal conditional coverage with respect to the set of conditioning variables from all models, for a given loss function. We propose a pairwise test to compare two models for a single predictive interval. The set-up is then extended to a comparison across multiple models and/or intervals. The limiting distribution varies depending on whether models are strictly non-nested or overlapping. In the latter case, degeneracy may occur. We establish the asymptotic validity of wild bootstrap based critical values across all cases. An empirical application to Growth-at-Risk (GaR) uncovers situations in which a richer set of financial indicators are found to outperform a commonly-used benchmark model when predicting downside risk to economic activity.

Mixed D-vine copula-based conditional quantile model for stochastic monthly streamflow simulation

Copula functions have been widely used in stochastic simulation and prediction of streamflow. However, existing models are usually limited to single two-dimensional or three-dimensional copulas with the same bivariate block for all months. To address this limitation, this study developed a mixed D-vine copula-based conditional quantile model that can capture temporal correlations. This model can generate streamflow by selecting different historical streamflow variables as the conditions for different months and by exploiting the conditional quantile functions of streamflows in different months with mixed D-vine copulas. The up-to-down sequential method, which couples the maximum weight approach with the Akaike information criteria and the maximum likelihood approach, was used to determine the structures of multivariate D-vine copulas. The developed model was used in a case study to synthesize the monthly streamflow at the Tangnaihai hydrological station, the inflow control station of the Longyangxia Reservoir in the Yellow River Basin. The results showed that the developed model outperformed the commonly used bivariate copula model in terms of the performance in simulating the seasonality and interannual variability of streamflow. This model provides useful information for water-related natural hazard risk assessment and integrated water resources management and utilization.

AHP-BP-Based Algorithms for Teaching Quality Evaluation of Flipped English Classrooms in the Context of New Media Communication

Big data analytics constitutes a key component in the pursuit of enhancing educational efficiency. This study defines the concept of the flipped classroom in the context of new media communication, evaluates the state of audiovisual instruction in higher education, and advocates for the use of this methodology to enhance college students' English listening and speaking skills. Utilizing multiple linear regression and a conditional quantile model, this research quantifies the range of impact of flipped instruction on college students' acquisition of a foreign language. To address the deficiencies in the current evaluation process for flipped classroom teaching, it proposes a teaching quality evaluation model based on the AHP and BP neural network. The AHP constructs the teaching quality evaluation index system for the flipped classroom and ascertains the combined weights of the indices. The simulated experiment's results show that utilizing the proposed evaluation model to assess flipped classroom instruction enhances objectivity, efficiency, and precision in the evaluation process.

The role of biomass energy consumption and economic complexity on environmental sustainability in G7 economies

AbstractThis paper empirically examines the effect of biomass energy consumption and economic complexity on environmental sustainability in G7 economies. The current study attempts to report a comprehensive analysis of biomass energy and economic complexity on ecological and carbon footprints and carbon emissions. We employ data from 1990 to 2019 and adopt robust panel econometric techniques that account for the analysis's cross‐sectional dependence. We conduct cointegration analysis, pooled ordinary least squares (OLS), system generalized method of moments (GMM) and conditional quantile model for our empirical analysis. The empirical findings show that both biomass energy consumption and economic complexity are detrimental to the ecological footprint and carbon footprint. Additionally, we find that globalization positively affects the environment, while we find some evidence that bureaucratic quality improves environmental quality. Finally, in line with other research, we find that economic growth has detrimental effects on the environment. Our results suggest that policymakers should be more cautious in promoting biomass as a clean energy source and that the G7 economies should take advantage of their leading position in innovation to invest more in sustainable practices and investment.

A consistent specification test for dynamic quantile models

Correct specification of a conditional quantile model implies that a particular conditional moment is equal to zero. We nonparametrically estimate the conditional moment function via series regression and test whether it is identically zero using uniform functional inference. Our approach is theoretically justified via a strong Gaussian approximation for statistics of growing dimensions in a general time series setting. We propose a novel bootstrap method in this nonstandard context and show that it significantly outperforms the benchmark asymptotic approximation in finite samples, especially for tail quantiles such as Value‐at‐Risk (VaR). We use the proposed new test to study the VaR and CoVaR (Adrian and Brunnermeier (2016)) of a collection of US financial institutions.

Impulse response analysis in conditional quantile models with an application to monetary policy

This paper presents a new method to analyze the effect of shocks on time series using a quantile impulse response function (QIRF). While conventional impulse response analysis is restricted to evaluation using the conditional mean function, here, we propose an alternative impulse response analysis that traces the effect of economic shocks on the conditional quantile function. By changing the quantile index over the unit interval, it is possible to measure the effect of shocks on the entire conditional distribution of a variable of interest in our framework. Therefore we can observe the complete distributional consequences of policy interventions, especially at the upper and lower tails of the distribution as well as at the mean. Using the new approach, it becomes possible to evaluate two distinct features (called “distributional effects”): (i) a change in the dispersion of the conditional distribution of interest after a shock, and (ii) a change in the degree of skewness of the conditional distribution caused by a policy intervention. None of these features can be observed in the conventional impulse response analysis exclusively based on the conditional mean function. In addition to proposing the QIRF, our second contribution is to present a new way to jointly estimate a system of multiple quantile functions. Our proposed system quantile estimator is obtained by extending the result of Jun and Pinkse (2009) to the time series context. We illustrate the QIRF on a VAR model in a manner similar to Romer and Romer (2004) in order to assess the impact of a monetary policy shock on the US economy.

Uniform consistency in number of neighbors of the kNN estimator of the conditional quantile model

Uniform consistency in number of neighbors of the kNN estimator of the conditional quantile model

Risk-predictive probabilities and dynamic nonparametric conditional quantile models for longitudinal analysis

Risk-predictive probabilities and dynamic nonparametric conditional quantile models for longitudinal analysis

Conditional Quantile Coverage: an Application to Growth-at-Risk

This paper proposes tests for out-of-sample comparisons of interval forecasts based on parametric conditional quantile models. The tests rank the distance between actual and nominal conditional coverage with respect to the union of information sets across models, for a given loss function. We propose a pairwise test to compare two models for a single predictive interval. The set-up is then extended to a comparison across multiple models and/or intervals. The limiting distribution varies depending on whether models are strictly non-nested or overlapping. In the latter case, degeneracy may occur. We establish the asymptotic validity of wild bootstrap based critical values across all cases. An empirical application to Growth-at-Risk (GaR) uncovers situations in which a richer set of financial indicators are found to outperform a commonly-used benchmark model when predicting downside risk to economic activity.

A specification test for dynamic conditional distribution models with function-valued parameters

This paper proposes a practical and consistent specification test of conditional distribution models for dependent data in a general setting. Our approach covers conditional distribution models indexed by function-valued parameters, allowing for a wide range of useful models for risk management and forecasting, such as the quantile autoregressive model, the CAViaR model, and the distributional regression model. The new specification test (i) is valid for general linear and nonlinear conditional quantile models under dependent data, (ii) allows for dynamic misspecification of the past information set, (iii) is consistent against fixed alternatives, and (iv) has nontrivial power against Pitman deviations from the null hypothesis. As the test statistic is non-pivotal, we propose and theoretically justify a subsampling approach to obtain valid inference. Finally, we illustrate the applicability of our approach by analyzing models of the returns distribution and Value-at-Risk (VaR) of two major stock indexes.

Capturing deep tail risk via sequential learning of quantile dynamics

This paper develops a conditional quantile model that can learn long term and short term memories of sequential data. It builds on sequential neural networks and yet outputs interpretable dynamics. We apply the model to asset return time series across eleven asset classes using historical data from the 1960s to 2018. Our results reveal that it extracts not only the serial dependence structure in conditional volatility but also the memories buried deep in the tails of historical prices. We further evaluate its Value-at-Risk forecasts against a wide range of prevailing models. Our model outperforms the GARCH family as well as models using filtered historical simulation, conditional extreme value theory, and dynamic quantile regression. These studies indicate that conditional quantiles of asset return have persistent sources of risk that are not coming from those responsible for volatility clustering. These findings could have important implications for risk management in general and tail risk forecasts in particular.

Discrete Choice Data with Unobserved Heterogeneity: A Conditional Binary Quantile Model

In political science, data with heterogeneous units are used in many studies, such as those involving legislative proposals in different policy areas, electoral choices by different types of voters, and government formation in varying party systems. To disentangle decision-making mechanisms by units, traditional discrete choice models focus exclusively on the conditional mean and ignore the heterogeneous effects within a population. This paper proposes a conditional binary quantile model that goes beyond this limitation to analyze discrete response data with varying alternative-specific features. This model offers an in-depth understanding of the relationship between the explanatory and response variables. Compared to conditional mean-based models, the conditional binary quantile model relies on weak distributional assumptions and is more robust to distributional misspecification. The model also relaxes the assumption of the independence of irrelevant alternatives, which is often violated in practice. The method is applied to a range of political studies to show the heterogeneous effects of explanatory variables across the conditional distribution. Substantive interpretations from counterfactual scenarios are used to illustrate how the conditional binary quantile model captures unobserved heterogeneity, which extant models fail to do. The results point to the risk of averaging out the heterogeneous effects across units by conditional mean-based models.

Quantile Forecast via Serial Dependence Learning

This paper develops a conditional quantile model that can learn long term and short term memories of sequential data. It builds on sequential neural networks and yet outputs interpretable dynamics. We apply the model to asset return time series across eleven asset classes using historical data from the 1960s to 2018. Our results reveal that it extracts not only the serial dependence structure in conditional volatility but also the memories buried deep in the tails of historical prices. We further evaluate its Value-at-Risk forecasts against a wide range of prevailing models. Our model outperforms the GARCH family as well as models using filtered historical simulation, conditional extreme value theory, and dynamic quantile regression. These studies indicate that conditional quantiles of asset return have persistent sources of risk that are not coming from those responsible for volatility clustering. These findings could have important implications for risk management in general and tail risk forecasts in particular.

Quantile Regression Model for Measurement of Equity Portfolio Risk a Case Study of Nairobi Securities Exchange

Quantile regression provides a method of estimating quantiles from a conditional distribution density. It is achieves this by minimizing asymmetrically weighted sum of absolute errors thus partitioning the conditional distribution into quantiles. Lower conditional quantiles are of interest in estimation of Value-at-Risk because they indicate downward movement of financial returns. Current risk measurement methods do not effectively estimate the VaR since they make assumptions in the distribution tails. Financial data is sampled frequently leading to a heavier tailed distribution compared to a normal and student t distribution. A remedy to this is to use a method that does not make assumptions in the tail distribution of financial returns. Little research has been done on the usage of quantile regression in the estimation of portfolio risk in the Nairobi Securities Exchange. The main aim of this study was to model the portfolio risk as a lower conditional quantile, compare the performance of this model to the existing risk measurement methods and to predict the Value-at-Risk. This study presents summary of key findings and conclusion drawn from the study. From the fitted conditional quantile GARCH model 62.4% of VaR can be explained by past standard deviation and absolute residual of NSE 20 share index optimal portfolio returns. The fitted model had less proportion of failure of 7.65% compared to commonly used VaR models.

Semiparametric Conditional Quantile Models for Financial Returns and Realized Volatility

This paper investigates how the conditional quantiles of future returns and volatility of financial assets vary with various measures of ex-post variation in asset prices as well as option-implied volatility. We work in the flexible quantile regression framework and rely on recently developed model-free measures of integrated variance, upside and downside semivariance, and jump variation. Our results for the S&P 500 and WTI Crude Oil futures contracts show that simple linear quantile regressions for returns and heterogenous quantile autoregressions for realized volatility perform very well in capturing the dynamics of the respective conditional distributions, both in absolute terms as well as relative to a couple of well-established benchmark models. The models can therefore serve as useful risk management tools for investors trading the futures contracts themselves or various derivative contracts written on realized volatility.

Contour regression: A distribution‐regularized regression framework for climate modeling

AbstractRegression methods are commonly used to learn the mapping from a set of predictor variables to a continuous‐valued target variable such that their prediction errors are minimized. However, minimizing the errors alone may not be sufficient for some applications, such as climate modeling, which require the overall predicted distribution to resemble the actual observed distribution. On the other hand, histogram equalization methods, such as quantile mapping, are often used in climate modeling to alter the distribution of input data to fit the distribution of observed data, but they provide no guarantee of accurate predictions. This paper presents a flexible regression framework known as contour regression that simultaneously minimizes the prediction error and removes biases in the predicted distribution. The framework is applicable to linear, nonlinear, and conditional quantile models and can utilize data from heterogenous sources. We demonstrate the effectiveness of the framework in fitting the daily minimum and maximum temperatures as well as precipitation for 14 climate stations in Michigan. The framework showed marked improvement over standard regression methods in terms of minimizing their distribution bias.