Conditional Quantiles Research Articles

Probing environmental sustainability aspects of resource efficiency, renewable energy usage and globalization

Given the pace of economic expansion arising from energy usage among other social and economic factors, emerging economies such as Turkey are increasingly becoming the focus for a net zero future. Therefore, the current attempt considers the drivers of environmental sustainability via load capacity factor (LCF) in the context of resource efficiency, renewable energy utilization, and globalization for Turkey over the period 1982 to 2019. By employing series of empirical tools that include cross-quantilogram method, quantile-on-quantile regression, quantile regression approaches, and the nonparametric quantile Granger causality approach, the result shows there is statistically significant evidence of quantile-to-quantile dependence among the trio of (resource efficiency, renewable energy utilization, and globalization) and LCF such that the dependence it reflects some levels of positive directional predictability, thus showing that these indicators are important drivers of environmental sustainability in Turkey. Furthermore, for the quantile-on-quantile regression results, there are statistically significant and positive effects of (i) resource efficiency on LCF across its conditional quantiles of distribution, (ii) renewable energy utilization on LCF and is mostly visible at the lower quantile up to the upper middle quantiles of renewable energy utilization (0.05–0.65), and (iii) globalization on LCF across the lower to upper middle quantiles. With the other empirical approaches providing similar results, the outcome of this investigation offers specific policy insight into resource circularity and energy efficiency.

A new parametric quantile regression model based on an Owen distribution

Quantile regression is a versatile statistical tool for modeling conditional quantiles, offering a comprehensive view of the relationship between explanatory and response variables. This technique is widely used in fields like economics, finance, environmental science, and psychology. This paper introduces a new quantile regression model based on the Owen distribution, which provides flexibility in capturing quantile-specific relationships. The model parameters are estimated using maximum likelihood estimation, with a detailed discussion on the estimation process. Diagnostic measures, including a pseudo- R 2 statistic, quantile residuals, and generalized Cook’s distance, are proposed to assess model adequacy and identify influential data points. Monte Carlo simulations are employed to evaluate the estimators' performance. The model’s effectiveness is illustrated through an application to Chilean household income data, highlighting its advantages over conventional quantile regression models. Implemented in the R programming language, this model is accessible for practical use, offering a valuable addition to the quantile regression field and suggesting promising directions for further research and application across disciplines.

Does climate risk as barometers for specific clean energy indices? Insights from quartiles and time-frequency perspective

This study presents the first analysis of the nexus between the Southern Oscillation Index (SOI), a measure of climate risk, and segmented clean energy indices (such as solar, renewable, and bioenergy). Our research findings indicate that (i) the Granger quantile causality significance of SOI on segmented clean energy indices is asymmetric across different conditional quantiles. Significant predictability of SOI is observed only at the 0.25 and 0.75 quantile levels for all segmented clean energy indices, except for the WilderHill Clean Energy Index and NASDAQ OMX Fuel Cell Index. (ii) The clean energy market is significantly influenced by SOI under bullish market conditions. Impacts of SOI on all clean energy markets are nearly negligible when clean energy indices are at the median and lower quantile levels. (iii) The influence of strong La Niña episodes on segmented clean energy indices is more pronounced than during periods of intense El Niño phenomena. (iv) SOI exhibited a positive correlation at mid-term and long-term frequencies with segmented Clean Energy sectors, excluding bioenergy, for the majority of the sample period. Our conclusions provide deeper insights for investors managing clean energy investments in extreme climate conditions. Additionally, they offer useful information for policymakers to formulate viable economic policies addressing climate change, ensuring energy security, and facilitating a safer transition to clean energy.

Energy transition, institutional quality, and financial development in Africa

This study examines the influence of institutional quality and financial sector size on driving renewable energy (RE) development using a sample of 31 African countries. We first employ a nonparametric trending panel data model that allows us to capture the gradual process of RE transition. The estimated common trend function reveals a steady increase in the share of RE from 2002 to 2019. Although fossil fuels dominate the energy structure in some African countries, a shift toward low-carbon sources is emerging, becoming increasingly significant in the energy mix. In the next step, we apply recent panel quantile regression techniques to model the heterogeneous and asymmetric relationships between RE and its main determinants. We find that institutional quality has a prominent influence on advancing the low-carbon transition, with significant positive effects across almost all conditional quantiles of the RE distribution. However, financial sector size seems to be important only for countries with a lower share of RE. Our results also confirm the asymmetric impact of income growth, which is negative in the lower quantiles but positive in the upper tail of the conditional distribution. From a policy perspective, governance factors, including the quality of policy formulation and implementation, have a critical role in promoting clean energy initiatives in Africa.

A short-term load forecasting method based on QRLSTM considering multiple factors analysis

Abstract Complex characteristics of power loads terribly affect the safety of the power grid. Thus, accurate short-term load forecasting is regarded as a solution to mitigate the effect of load complications. In this regard, this work is putting forward a Long Short-Term Memory Network Quantile Regression (LSTMQR) for power load, obtaining the probability density function (PDF). Firstly, the quantile of future power load was obtained using the LSTMQR model. The conditional quantile obtained by the LSTMQR model is used as the input of the Kernel Density Estimation model (KDE) to predict the future probability density distribution of short-term power load at different prediction times. Furthermore, an assessment method is proposed to quantify the effect of different factors on power load to improve prediction accuracy. Finally, a numerical simulation based on actual data in China is established to validate the effectiveness of the proposed forecasting algorithm, indicating the proposed forecasting algorithm can effectively evaluate the relationship between different factors and power load, and probability density prediction can accurately quantify the uncertainty of load information. The proposed algorithm results in a reduction of 37.6% in forecast error compared to the traditional forecasting algorithm.

Fiber Microstructure Quantile (FMQ) Regression: A Novel Statistical Approach for Analyzing White Matter Bundles from Periphery to Core.

The structural connections of the brain's white matter are critical for brain function. Diffusion MRI tractography enables the in-vivo reconstruction of white matter fiber bundles and the study of their relationship to covariates of interest, such as neurobehavioral or clinical factors. In this work, we introduce Fiber Microstructure Quantile (FMQ) Regression, a new statistical approach for studying the association between white matter fiber bundles and scalar factors (e.g., cognitive scores). Our approach analyzes tissue microstructure measures based on quantile-specific bundle regions. These regions are defined according to the quantiles of fractional anisotropy (FA) from the periphery to the core of a population fiber bundle, which pools all individuals' bundles. To investigate how fiber bundle tissue microstructure relates to covariates of interest, we employ the statistical technique of quantile regression. Unlike ordinary regression, which only models a conditional mean, quantile regression models the conditional quantiles of a response variable. This enables the proposed analysis, where a quantile regression is fitted for each quantile-specific bundle region. To demonstrate FMQ Regression, we perform an illustrative study in a large healthy young adult tractography dataset derived from the Human Connectome Project-Young Adult (HCP-YA), focusing on particular bundles expected to relate to particular aspects of cognition and motor function. Importantly, our analysis considers sex-specific effects in brain-behavior associations. In comparison with a traditional method, Automated Fiber Quantification (AFQ), which enables FA analysis in regions defined along the trajectory of a bundle, our results suggest that FMQ Regression is much more powerful for detecting brain-behavior associations. Importantly, FMQ Regression finds significant brain-behavior associations in multiple bundles, including findings unique to males or to females. In both males and females, language performance is significantly associated with FA in the left arcuate fasciculus, with stronger associations in the bundle's periphery. In males only, memory performance is significantly associated with FA in the left uncinate fasciculus, particularly in intermediate regions of the bundle. In females only, motor performance is significantly associated with FA in the left and right corticospinal tracts, with a slightly lower relationship at the bundle periphery and a slightly higher relationship toward the bundle core. No significant relationships are found between executive function and cingulum bundle FA. Our study demonstrates that FMQ Regression is a powerful statistical approach that can provide insight into associations from bundle periphery to bundle core. Our results also identify several brain-behavior relationships unique to males or to females, highlighting the importance of considering sex differences in future research.

Modeling extreme events: Univariate and multivariate data-driven approaches

AbstractThis article summarizes the contribution of team genEVA to the EVA (2023) Conference Data Challenge. The challenge comprises four individual tasks, with two focused on univariate extremes and two related to multivariate extremes. In the first univariate assignment, we estimate a conditional extremal quantile using a quantile regression approach with neural networks. For the second, we develop a fine-tuning procedure for improved extremal quantile estimation with a given conservative loss function. In the first multivariate sub-challenge, we approximate the data-generating process with a copula model. In the remaining task, we use clustering to separate a high-dimensional problem into approximately independent components. Overall, competitive results were achieved for all challenges, and our approaches for the univariate tasks yielded the most accurate quantile estimates in the competition.

Multivariate copula-based conditional quantiles: analytic higher-order moments and ratio estimation approaches

ABSTRACT In this paper, we aim to modify multivariate copula-based conditional quantiles for a targeted random variable, given multiple random variables attaining their respective quantiles. Specifically, we propose two modifications through the Cornish–Fisher expansion, one of which involves its analytic higher-order unconditional moments. The second one accounts for its higher-order conditional moments estimated using a ratio estimation method. By considering multivariate elliptical and Archimedean copulas with Johnson's SU margins, our simulation study shows that this method provides more accurate conditional moment estimators compared to the naive method. They result in expanded conditional quantile estimators, whose efficiency is relatively better than their unexpanded versions, particularly at lower and higher quantile levels under a stronger (tail) dependence assumption. A much higher efficiency is gained when the first modification is performed. These findings are validated using an empirical study based on cryptocurrency return data and a comparative analysis against the existing estimation approaches.

Is climate change hindering the economic progress of Nigerian economy? Insights from dynamic models

This study investigates the link between climate change and economic growth in Nigeria from 1961 to 2022. To provide a robust analysis that facilitates a nuanced examination of this dynamic relationship, this study employs state-of-the-art econometric approaches, including autoregressive distributed lag (ARDL), fully modified least squares (FMOLS), novel quantile autoregressive distributed lag (QARDL), and time-varying causality. The empirical results of this study are as follows: (1) the impact of climate change on economic growth is not felt in the short run. However, climate change negatively influences economic growth in Nigeria in the long run, (2) the elasticity of climate change increases across the conditional quantile economic growth, (3) unidirectional causality from climate change to economic growth across different time dimensions. These empirical outcomes advocate for a proactive and adaptive policy framework, emphasising the need for the Nigerian government to adopt climate-smart policies.

Exploring asymmetries in cryptocurrency intraday returns and implied volatility: New evidence for high-frequency traders

This paper aims to analyze the return-volatility relationship of Bitcoin and Ethereum across different return frequencies and all conditional quantiles of implied volatility, based on a unique 6.5 million observations. We employ the newly constructed Model-Free Implied Volatility (MFIV) of Bitcoin (BitVol) and Ethereum (EthVol) and use an asymmetric Quantile Regression Model (QRM) to capture the intraday asymmetric return-volatility relationship at different quantiles of the distribution of the dependent variable. Our findings show that the estimated coefficient using daily data is significant only at medium- to high-volatility regimes, while the estimated coefficients using high-frequency data are highly significant across all volatility regimes. Moreover, our results indicate that the asymmetry varies across frequencies and quantiles, with weak asymmetric effects at low quantiles and high frequencies, and strong asymmetric effects at high quantiles and low frequencies. This study provides new insight, especially for high-frequency traders.

Systematically missing data in distributed data networks: multiple imputation when data cannot be pooled

Systematically missing data in distributed data networks presents practical and methodological challenges. Failure to handle it appropriately can bias statistical inference. Multiple imputations can be used to address systematic missingness. However, when data from different study sites cannot be pooled into a unified file, conventional imputation approaches become unavailable due to the absence of a basis for imputation. To address such challenges, we introduce an imputation method based on conditional quantiles – conditional quantile imputation (CQI) – which involves four steps: (i) estimating 99 quantiles for the systematically missing variable in studies with observed data; (ii) deriving a weighted average of regression coefficients across studies and transmitting it to sites with systematically missing data; (iii) imputing the systematically missing values based on observed data and the set of regression coefficients from step ii; and (iv) combining estimates of the substantive outcome model across imputations using Rubin's rules. We evaluate CQI in different simulation scenarios and illustrate it with an applied data example. We conclude that CQI can be a suitable approach for the imputation of systematically missing data when data from multiple studies cannot be pooled.

A Deep Learning Quantile Regression Photovoltaic Power-Forecasting Method under a Priori Knowledge Injection

Accurate and reliable PV power probabilistic-forecasting results can help grid operators and market participants better understand and cope with PV energy volatility and uncertainty and improve the efficiency of energy dispatch and operation, which plays an important role in application scenarios such as power market trading, risk management, and grid scheduling. In this paper, an innovative deep learning quantile regression ultra-short-term PV power-forecasting method is proposed. This method employs a two-branch deep learning architecture to forecast the conditional quantile of PV power; one branch is a QR-based stacked conventional convolutional neural network (QR_CNN), and the other is a QR-based temporal convolutional network (QR_TCN). The stacked CNN is used to focus on learning short-term local dependencies in PV power sequences, and the TCN is used to learn long-term temporal constraints between multi-feature data. These two branches extract different features from input data with different prior knowledge. By jointly training the two branches, the model is able to learn the probability distribution of PV power and obtain discrete conditional quantile forecasts of PV power in the ultra-short term. Then, based on these conditional quantile forecasts, a kernel density estimation method is used to estimate the PV power probability density function. The proposed method innovatively employs two ways of a priori knowledge injection: constructing a differential sequence of historical power as an input feature to provide more information about the ultrashort-term dynamics of the PV power and, at the same time, dividing it, together with all the other features, into two sets of inputs that contain different a priori features according to the demand of the forecasting task; and the dual-branching model architecture is designed to deeply match the data of the two sets of input features to the corresponding branching model computational mechanisms. The two a priori knowledge injection methods provide more effective features for the model and improve the forecasting performance and understandability of the model. The performance of the proposed model in point forecasting, interval forecasting, and probabilistic forecasting is comprehensively evaluated through the case of a real PV plant. The experimental results show that the proposed model performs well on the task of ultra-short-term PV power probabilistic forecasting and outperforms other state-of-the-art deep learning models in the field combined with QR. The proposed method in this paper can provide technical support for application scenarios such as energy scheduling, market trading, and risk management on the ultra-short-term time scale of the power system.

Big portfolio selection by graph-based conditional moments method

This paper proposes a new graph-based conditional moments (GRACE) method to do portfolio selection based on thousands of stocks or even more. The GRACE method first learns the conditional quantiles and mean of stock returns via a factor-augmented temporal graph convolutional network, which is guided by the set of stock-to-stock relations as well as the set of factor-to-stock relations. Next, the GRACE method learns the conditional variance, skewness, and kurtosis of stock returns from the learned conditional quantiles via the quantiled conditional moment method. Finally, the GRACE method uses the learned conditional mean, variance, skewness, and kurtosis to construct several performance measures, which are criteria to sort the stocks to proceed the portfolio selection in the well-known 10-decile framework. An application to NASDAQ and NYSE stock markets shows that the GRACE method performs much better than its competitors, particularly when the performance measures are comprised of conditional variance, skewness, and kurtosis.

The Impact of Financial Efficiency and Renewable Energy Consumption on CO2 Emission Reduction in GCC Economies: A Panel Data Quantile Regression Approach

As prominent oil producers, Gulf Cooperation Council (GCC) countries have played a significant role in the global energy market. However, as the world’s attention increasingly shifts towards environmental sustainability, understanding the implications of the GCC’s economic activities on CO2 emissions becomes indispensable. This research paper investigates the relationship between specific economic indicators and their impact on CO2 emissions in the GCC from 2001 to 2021. This study employs quantile regression, a robust statistical method that estimates the conditional quantiles of a response variable given a set of predictor variables. The findings reveal several essential insights: Financial institution efficiency is significant and negative at a 1% level at the lower (10th, −83,537.3) and higher quantiles (90th, −549,002.3). The relationship between the GDP per capita and CO2 emissions varies across quantiles, highlighting the complexity of the growth–environment nexus. Total patents exhibit a positive and significant relationship with emissions, underscoring the importance of directing innovation towards environmentally sustainable solutions. Renewable energy consumption displays a nuanced relationship with CO2 emissions, with a more substantial negative impact observed at higher consumption levels. This underscores the potential of renewable energy to mitigate emissions when integrated at scale. This study’s outcomes hold crucial policy implications for GCC countries as they seek to align economic growth with environmental sustainability. The findings emphasize the importance of fostering financial institution efficiency, promoting green innovation, and expanding renewable energy sources to reduce emissions.

Examining time–frequency quantile dependence between green bond and green equity markets

In the context of the rapidly growing demand for green investments and the need to combat climate change, this study contributes to the emerging literature on green investments by exploring the time–frequency connectedness between green bonds (GBs) and green equities. Specifically, we examine the degree of connection between GBs and green equities, the extent to which these markets influence each other, and which one is the primary net transmitter versus the net receiver of shocks under diverse market conditions. To accomplish these objectives, we use the wavelet-based Quantile-on-Quantile (QQ), dynamic conditional correlation (DCC), portfolio implications, and Quantile VAR approaches. The results show that GBs and green equities have a strong positive connection, depending on time and frequency domains. However, a negative association between GBs and green equities is observed during periods of crisis, highlighting GBs’ ability to hedge green equity portfolios. The portfolio strategies demonstrate that investors require to invest in the Green Economy equity and S&P GB portfolio to reach the highest level of hedging effectiveness. The findings further imply that the Global Water Equity Index transmits the highest spillover to other green assets, while the Green Economy Equity Index receives the most spillover from other assets. The pairwise volatility connectivity reveals that most pairs have minimal quantile dependence, indicating the potential for diversification across the GB and green equity pairs. These findings have significant implications for investors and policymakers concerned with green investments and climate change mitigation.

Economic policy uncertainty and Indian equity sectors: a quantile regression approach

PurposeThis paper aims to investigate the effect of economic policy uncertainty (EPU) shocks on Indian equity market sectors. The effect of domestic (Indian) and foreign (USA) EPU shocks is examined on ten major Bombay Stock Exchange sectors.Design/methodology/approachThe study uses data covering the period from September 2005 to July 2023 and uses the methodology of quantile regression to investigate the heterogenous response of stock market sectors under diverse market conditions explained through the analysis of conditional quantiles distribution.FindingsThe results demonstrate that domestic and foreign EPU shocks negatively affect most of the sectors in bearish market conditions. Industrials, commodities, utilities, consumer discretionary and financial services are the most affected sectors by domestic EPU. However, the information technology sector is found to be immune to domestic EPU shocks but negatively affected by foreign EPU shocks. On the other hand, energy, financial services and fast-moving consumer goods sectors are found to be immune to foreign EPU shocks but are negatively affected by domestic EPU shocks.Practical implicationsUnderstanding the heterogeneous response of different sectors to EPU shocks could help investors and portfolio managers identify portfolio diversification opportunities.Originality/valueThis study makes an inaugural attempt to examine the responses of Indian stock market sectors to domestic and foreign EPU shocks using the approach of quantile regression and unveils the previously unexamined diverse reactions of Indian stock market sectors to EPU shocks originating from both India and USA.

Metallurgical Copper Recovery Prediction Using Conditional Quantile Regression Based on a Copula Model

This article proposes a novel methodology for estimating metallurgical copper recovery, a critical feature in mining project evaluations. The complexity of modeling this nonadditive variable using geostatistical methods due to low sampling density, strong heterotopic relationships with other measurements, and nonlinearity is highlighted. As an alternative, a copula-based conditional quantile regression method is proposed, which does not rely on linearity or additivity assumptions and can fit any statistical distribution. The proposed methodology was evaluated using geochemical log data and metallurgical testing from a simulated block model of a porphyry copper deposit. A highly heterotopic sample was prepared for copper recovery, sampled at 10% with respect to other variables. A copula-based nonparametric dependence model was constructed from the sample data using a kernel smoothing method, followed by the application of a conditional quantile regression for the estimation of copper recovery with chalcocite content as secondary variable, which turned out to be the most related. The accuracy of the method was evaluated using the remaining 90% of the data not included in the model. The new methodology was compared to cokriging placed under the same conditions, using performance metrics RMSE, MAE, MAPE, and R2. The results show that the proposed methodology reproduces the spatial variability of the secondary variable without the need for a variogram model and improves all evaluation metrics compared to the geostatistical method.

Tail risk spillovers between Islamic sectoral equities and bond markets: a time-frequency domain approach

ABSTRACT This study examines the tail risk spillover between Islamic sectoral stock indices and country specific investable Islamic bonds in time and frequency domain and provides useful implications for portfolio management. For the analyses, Conditional Autoregressive ValueatRisk (CAViaR), Quantile Connectedness, and DCCGARCH t-Copula models are estimated utilizing daily data from 15 countries. The findings show that the connectedness and spillover of risks are much stronger at tails than at median, and in the short-term than in long-term. Whereas median risk connectedness surges during COVID-19 pandemic, the connectedness between tail risks is usually elevated even before the COVID-19 pandemic with industrial sector being consistently a significant net transmitter of shocks. Moreover, all the sectoral stock market indices are significant and consistent transmitter of left tail shocks indicating a much stronger role of sectoral stock markets in transmitting large negative shocks. A heightened connectedness is also observed during Russia-Ukraine war mainly in the short-term frequency. The portfolio analysis shows that long positions in sectoral stocks can usually be hedged by taking short positions in Islamic bonds. Hedging effectiveness and optimal portfolio weights are also calculated to provide market participants with further information.

Atmospheric motion vector (AMV) error characterization and bias correction by leveraging independent lidar data: a simulation using an observing system simulation experiment (OSSE) and optical flow AMVs

Abstract. Accurate estimation of global winds is crucial for various scientific and practical applications, such as global chemical transport modeling and numerical weather prediction. One valuable source of wind measurements is atmospheric motion vectors (AMVs), which play a vital role in the global observing system and numerical weather prediction models. However, errors in AMV retrievals need to be addressed before their assimilation into data assimilation systems, as they can affect the accuracy of outputs. An assessment of the bias and uncertainty in passive-sensor AMVs can be done by comparing them with information from independent sources such as active-sensor winds. In this paper, we examine the benefit and performance of a colocation scheme using independent and sparse lidar wind observations as a dependent variable in a supervised machine learning model. We demonstrate the feasibility and performance of this approach in an observing system simulation experiment (OSSE) framework, with reference geophysical state data obtained from high-resolution Weather Research and Forecasting (WRF) model simulations of three different weather events. Lidar wind data are typically available in only one direction, and our study demonstrates that this single component of wind in high-precision active-sensor data can be leveraged (via a machine learning algorithm to model the conditional mean) to reduce the bias in the passive-sensor winds. Further, this active-sensor wind information can be leveraged through an algorithm that models the conditional quantiles to produce stable estimates of the prediction intervals, which are helpful in the design and application of error analysis, such as quality filters.

Tail connectedness between category-specific policy uncertainty, sovereign debt risk, and stock volatility during a high inflation period

Greece has experienced high inflation, increased fiscal deficit and debt in recent years, and whether the Greek sovereign debt crisis will resurrect has triggered widespread discussion. This study explores the tail connectedness between category-specific economic policy uncertainty (EPUs), sovereign debt risk (SR), and stock volatility in Greece using a connectedness method based on the quantile VAR model. The findings show that (i) The total connectedness index (TCI) features a U-shaped structure that varies with the conditional quantiles of variables, demonstrating that the spillover effect under extreme conditions for variables is greater than under normal conditions; (ii) Under different market conditions, we observe an apparent heterogeneity in the magnitude of category-specific EPUs' effects on the SR; (iii) The Russia-Ukraine war and the COVID-19 pandemic both have a bigger effect on the TCI than other periods; (iv) SR has shifted from being a net spillover receiver in the median and left tail to a net spillover transmitter in the right tail.