Conditional Mean Research Articles

Extreme time–frequency connectedness between oil shocks and sectoral markets in the United States

This study assessed the connectedness between oil shocks and industry stock indexes in the United States (US). We consider the normal and extreme conditions across different frequency horizons, and the quantile time–frequency connectedness method is used to determine the tail risk contagion under different frequency horizons. Our results reveal that the short-term frequency connectedness significantly exceeds the long-term frequency connectedness. We also indicate that the connectedness in the lower and upper quantiles is greater than at the conditional mean. Importantly, oil risk shock is the biggest net transmitter of shocks to the US sectors in normal and extreme conditions, highlighting that oil risk shocks cause substantial variations in US sector stock returns in the short, medium, and long term. Finally, QAR(3) model demonstrates the significant impact of oil risk shocks on US sector stock returns during extreme and normal conditions. Therefore, our study underscores the role of asymmetry in the reaction of US sector stock returns to oil-related shocks, and we suggest that policies aimed at overcoming the adverse effects of oil shocks on stock markets and promoting financial stability should incorporate asymmetric features.

Transfer Learning-Based Health Monitoring of Robotic Rotate Vector Reducer Under Variable Working Conditions

Due to their precision, compact size, and high torque transfer, Rotate vector (RV) reducers are becoming more popular in industrial robots. However, repetitive operations and varying speed conditions mean that these components are prone to mechanical failure. Therefore, it is important to develop effective health monitoring (HM) strategies. Traditional approaches for HM, including those using vibration and acoustic emission sensors, encounter such challenges as noise interference, data inconsistency, and high computational costs. Deep learning-based techniques, which use current electrical data embedded within industrial robots, address these issues, offering a more efficient solution. This research provides transfer learning (TL) models for the HM of RV reducers, which eliminate the need to train models from scratch. Fine-tuning pre-trained architectures on operational data for the three different reducers of health conditions, which are healthy, faulty, and faulty aged, improves fault classification across different motion profiles and variable speed conditions. Four TL models, EfficientNet, MobileNet, GoogleNet, and ResNET50v2, are considered. The classification accuracy and generalization capabilities of the suggested models were assessed across diverse circumstances, including low speed, high speed, and speed fluctuations. Compared to the other models, the proposed EfficientNet model showed the most promising results, achieving a testing accuracy and an F1-score of 98.33% each, which makes it best suited for the HM of robotic reducers.

Omnibus diagnostic procedures for vector multiplicative errors models

We suggest specification tests for the conditional mean function in vector multiplicative error models. The test statistics are easy to compute given a suitable estimator of the model parameters. Consistency of the test statistic is proved, the asymptotic distribution of the test under the null hypothesis is studied, while a bootstrap resampling is used in order to approximate critical points and actually carry out the test. Finite-sample results are presented as well as applications of the proposed procedures to real data from the financial markets.

Spillovers on the mean and tails: a semiparametric dynamic panel modeling approach

Abstract Recently, there has been a surge in interest in exploring how common macroeconomic factors impact different economic results. We propose a semiparametric dynamic panel model to analyze the impact of common regressors on the conditional distribution of the dependent variable (global output growth distribution in our case). Our model allows conditional mean, variance, and skewness to be influenced by common regressors, whose effects can be nonlinear and time-varying driven by contextual variables. By incorporating dynamic structures and individual unobserved heterogeneity, we propose a consistent two-step estimator and showcase its attractive theoretical and numerical properties. We apply our model to investigate the impact of US financial uncertainty on the global output growth distribution. We find that an increase in US financial uncertainty significantly shifts the output growth distribution leftward during periods of market pessimism. In contrast, during periods of market optimism, the increased uncertainty in the US financial markets expands the spread of the output growth distribution without a significant location change, indicating increased future uncertainty.

The dynamic risk spillover of higher-order moments in the China’s energy market: A time-frequency perspective

ABSTRACT This study employs a risk spillover measurement method based on CEEMDAN-SE, GARCHSK, and TVP-VAR-DY models to assess risk spillover among 11 sub-sectors in China’s energy market, such as coal, oil, thermal power, and new energy vehicles. The energy sector index return is decomposed into intrinsic mode functions (IMFs) and reconstructed into high, medium, and low-frequency sequences. The GARCHSK model calculates conditional mean, variances, skewness, and kurtosis sequences for these sequences, which are then integrated into the TVP-VAR-DY model to evaluate return, volatility, and higher-order moment risk spillovers. Empirical findings highlight significant time-varying spillover effects, with return and volatility spillovers surpassing average total skewness and kurtosis spillovers. The New Energy Vehicle (NEV) and Electric Power Grid (EPG) sectors act as major risk transmitters, while primary risk receivers vary by frequency and order. Regulatory authorities should develop a real-time surveillance mechanism to monitor the transfer of risks between the NEV sector and the EPG sector. It is essential to foster inter-industry cooperation to facilitate better resource allocation and swift response to emerging challenges. Furthermore, policymakers should focus on bolstering the resilience of pivotal sectors by employing dynamic risk management strategies and providing appropriate incentives.

Fault diagnosis of gear based on URP-CVAE-MGAN under imbalanced and small sample conditions

To improve diagnosis accuracy for gear fault diagnosis under imbalanced and small sample conditions, a method combining the Un-threshold Recurrence Plots - Conditional Variational Autoencoder-Mean Generative Adversarial Network (URP-CVAE-MGAN) combined with Dropkey-Vision Transformer (DViT) is proposed. First, gear vibrational signals are transformed into Recurrence Plots (RP) images to extract more fault features without threshold effect. Then, a conditional variable and mean feature difference function are incorporated into VAE-GAN to improve the quality and diversity of generated samples, balancing the imbalanced and small sample sets. Dropkey is applied to the diagnosis model Vision Transformer to capture more fault information, improving diagnosis accuracy across various fault types and severities for gear. Finally, the proposed method is verified based on two datasets, demonstrating a significant accuracy improvement of up to 7.84% under the imbalanced and small samples, and confirming its feasibility and superiority.

Moving beyond population variable importance: concept, theory and applications of individual variable importance

Abstract In a non-parametric regression setting, we introduce a novel concept of ‘individual variable importance’, which assesses the relevance of certain covariates to an outcome variable among individuals with specific characteristics. This concept holds practical importance for both risk assessment and association identification. For example, it can represent (i) the usefulness of expensive biomarkers in risk prediction for individuals at a specified baseline risk, or (ii) age-specific associations between physiological indicators. We quantify individual variable importance using a ratio parameter between two conditional mean squared errors. To estimate and infer this parameter, we develop fully non-parametric estimators and establish their asymptotic properties. Our method performs well in simulation studies. Applying our approach to analyse a real dataset reveals a scientifically interesting result: the association between body shape and systolic blood pressure diminishes with increasing age. Our finding aligns with the medical literature based on standard parametric regression techniques, but our approach is more reliable due to its robustness to model misspecification. More importantly, the fully non-parametric nature of our method allows it to be applied in settings with complex relationships between variables, which cannot be correctly characterized by traditional parametric interaction analyses.

A Zero Serial Cross‐Correlation Test Before Fitting Heteroscedasticity

ABSTRACTMany statistical inferences for a multivariate innovation‐based copula time series model rely on the serial independence of innovation vectors after filtering the conditional means and conditional covariance. Zero (respectively nonzero) serial cross‐correlations for the heteroscedastic noises before filtering the conditional covariance may suggest the use of univariate (respectively multivariate) GARCH models. This paper develops a zero serial cross‐correlation test for the heteroscedastic noises with heavy tails before fitting a multivariate heteroscedasticity model. Applications to exchange rates and mutual fund returns show that this critical assumption could be problematic sometimes and conducting such a test is necessary before building and using a multivariate innovation‐based copula time series model.

A ground motion construction method considering spectrum characteristics as supplement for conditional mean spectrum

A ground motion construction method considering spectrum characteristics as supplement for conditional mean spectrum

Concordance correlation coefficient under multiplicative distortion measurement errors

We study the estimation of the concordance correlation coefficient (CCC) under the multiplicative distortion measurement errors. These unobservable variables are distorted in a multiplicative fashion by an observed confounding variable. A direct estimator and a two-steps estimators of CCC are proposed under the conditional mean, the conditional absolute mean, the conditional variance, the conditional absolute logarithmic mean calibration methods. The asymptotic results of estimators and the asymptotic confidence intervals for CCC are studied under different calibration methods. Simulation studies demonstrate the performance of the proposed procedure in this paper, and a real example is analyzed to illustrate its practical usage.

Short-term forecasting of solar irradiance using decision tree-based models and non-parametric quantile regression.

The renewable energy industry requires accurate forecasts of intermittent solar irradiance (SI) to effectively manage solar power generation and supply. Introducing the random forests (RFs) model and its hybridisation with quantile regression modelling, the quantile regression random forest (QRRF), can help improve the forecasts' accuracy. This paper assesses the RFs and QRRF models against the quantile generalised additive model (QGAM) by evaluating their forecast performances. A simulation study of multivariate data-generating processes was carried out to compare the forecasting accuracy of the models when predicting global horizontal solar irradiance. The QRRF and QGAM are completely new forecasting frameworks for SI studies, to the best of our knowledge. Simulation results suggested that the introduced QRRF compared well with the QGAM when predicting the forecast distribution. However, the evaluations of the pinball loss scores and mean absolute scaled errors demonstrated a clear superiority of the QGAM. Similar results were obtained in an application to real-life data. Therefore, we recommend that the QGAM be preferred ahead of decision tree-based models when predicting solar irradiance. However, the QRRF model can be used alternatively to predict the forecast distribution. Both the QGAM and QRRF modelling frameworks went beyond representing forecast uncertainty of SI as probability distributions around a prediction interval to give complete information through the estimation of quantiles. Most SI studies conducted are residual and/or non-parametric modelling that are limited to represent information about the conditional mean distribution. Extensions of the QRRF and QGAM frameworks can be made to model other renewable sources of energy that have meteorological characteristics similar to solar irradiance.

Necessary and sufficient conditions in theorems

When students and professional mathematicians are asked what the difference between necessary and sufficient conditions is, they often have difficulty answering the question. Even when presented with concrete formulations of state and asked what the difference between necessary and sufficient conditions means, the answer is not always correct. Meanwhile, these two notions are widespread in modern mathematics. This article attempts to consider necessary and sufficient conditions, hoping to increase the mathematical culture of both readers and their authors.

Female and male treatable mortality: socioeconomic and public finance related factors across European countries.

About 36.5% of premature deaths in European Union countries could have been avoided through prompt and effective medical treatment. This treatable mortality is even a priority established in Sustainable Development Goal (SDG) target 3.4. Given the gap in the literature about the socioeconomic drivers of this type of mortality, as well as the increasing importance of public financial management in defining priority policies, this study aims to analyze the socioeconomic and public finance drivers associated with treatable mortality for women and men across European countries. Eurostat data is collected for 31 countries for the period 2011-2019 stratified by sex. Panel data quantile regression with fixed effects and conditional mean panel data model using feasible generalized least squares are estimated to explain treatable mortality in women and men. Key findings point to a positive association between the public finance indicator proxying health priority and the treatable mortality rate for both sexes; a difference between drivers of treatable mortality between men and women; and a different set of drivers across the different quantiles of treatable mortality. Drivers of male and female treatable mortality may differ according to the country's level of mortality rate. Government health priority seems to account for previous treatable mortality rates as a reactive measure. Policymakers aiming to reduce treatable mortality are likely to use instruments such as health expenditure, improved employment, education levels, and perhaps proactive policy-setting priorities concerning health.

Impact of household characteristics on patient outcomes post hip fracture: a Welsh nationwide observational cohort study

BackgroundHip fracture is common in older people and has significant health and care implications. This study aimed to examine the impact of household characteristics (living alone or living with someone who is themselves ill) on adverse outcomes following hip fracture.MethodsA cohort study of hip fracture patients aged ≥ 50 years living alone or with one co-resident using Welsh nationwide data between January 2013 and December 2018. Outcomes were emergency hospital admission within 30 days and care-home admission and mortality within one year of hospital discharge. Analysis used cause-specific Cox proportional hazards models to examine associations with living alone and with co-resident chronic disease status.ResultsOf the 12,089 hip fracture patients discharged, 56.0% lived alone. Compared to hip fracture patients living with a co-resident, those living alone were more commonly women (78.4% versus 65.2%), older (mean 83.1 versus 78.5 years), and had more long-term conditions (mean 5.7 versus 5.3). In unadjusted analyses, compared to living with a co-resident with 0–1 long-term condition and no dementia, living alone (hazard ratio [HR] 1.44, 95%CI 1.23–1.68), living with someone with dementia (HR 1.57, 95%CI 1.07–2.30), and living with someone with 4 + physical long-term conditions (HR 1.24, 95%CI 1.03–1.49) were associated with an increase in mortality, but no significant association was found in adjusted analysis. Adjusted for age, sex, socioeconomic position, and long-term condition count of the hip fracture patient, living alone (adjusted HR [aHR] 2.26, 95%CI 1.81–2.81) and living with a co-resident with dementia (aHR 2.38, 95%CI 1.59–3.57) were both associated with more than double the risk of care home admission. There were no significant associations with 30-day hospital admission.ConclusionsHip fracture patients who live alone have higher one-year mortality, but associations are explained by the demographic and clinical characteristics of those living alone. However, living alone or living with a co-resident with dementia was independently associated with an additional doubling of the risk of care home admission. Household-based approaches to research and health policy may help target risk groups following hip fracture community discharge and further research is needed to understand the mechanisms by which these associations act.

Symmetry measures under additive distortion measurement errors

We examine the symmetry or asymmetry of the density function of a continuous variable under the setting of additive distortion measurement errors. The unobservable variable is distorted in an additive manner by an observed confounding variable. We adopt the covariance ratio-based measure under conditional mean calibration and conditional exponential mean calibration methods. Using the empirical likelihood method, we consider statistical inference of the covariance ratio-based measure under additive distortions to check for symmetry. The calibrated covariance ratio-based measures are shown to be asymptotically efficient as if there were no additive distortion effects. Additionally, Gupta’s skewness with conditional exponential mean calibration is also studied. We conduct Monte Carlo simulation experiments to access the performance of the calibrated measures and test procedures. These methods are applied to analyze a real dataset for illustrative purposes.

A Varying Precision Beta Prime Autoregressive Moving Average Model With Application to Water Flow Data

ABSTRACTWe introduce a dynamic model tailored for positively valued time series. It accommodates both autoregressive and moving average dynamics and allows for explanatory variables. The underlying assumption is that each random variable follows, conditional on the set of previous information, the beta prime distribution. A novel feature of the proposed model is that both the conditional mean and conditional precision evolve over time. The model thus comprises two dynamic submodels, one for each parameter. The proposed model for the conditional precision parameter is parsimonious, incorporating first‐order time dependence. Changes over time in the shape of the density are determined by the time evolution of two parameters, and not just of the conditional mean. We present simple closed‐form expressions for the model's conditional log‐likelihood function, score vector, and Fisher's information matrix. Monte Carlo simulation results are presented. Finally, we use the proposed approach to model and forecast two seasonal water flow time series. Specifically, we model the inflow and outflow rates of the reservoirs of two hydroelectric power plants. Overall, the forecasts obtained using the proposed model are more accurate than those yielded by alternative models.

Estimation and Inference for Extreme Continuous Treatment Effects*

This paper studies estimation and inference for the treatment effect in deep tails of the potential outcome distributions corresponding to a continuously valued treatment, namely the extreme continuous treatment effect. We consider two measures for the tail characteristics: the quantile function and the tail mean function defined as the conditional mean beyond a quantile level. Then, for a quantile level close to 1, we define the extreme quantile treatment effect (EQTE) and extreme average treatment effect (EATE), which are, respectively, the ratios of the quantile and tail mean at different treatment statuses. We propose estimators for the EQTE and EATE based on tail approximations from the extreme value theory. Our limiting theory is for the EQTE and EATE processes indexed by a set of quantile levels and pairs of different treatment statuses. It facilitates uniform inference for the EQTE and EATE over multiple tail levels and multiple treatment effects. Simulations suggest that our method works well in finite samples, and an empirical study illustrates its practical merits.

Parametric Quantile Autoregressive Conditional Duration Models With Application to Intraday Value‐at‐Risk Forecasting

ABSTRACTThe modeling of high‐frequency data that qualify financial asset transactions has been an area of relevant interest among statisticians and econometricians—above all, the analysis of time series of financial durations. Autoregressive conditional duration (ACD) models have been the main tool for modeling financial transaction data, where duration is usually defined as the time interval between two successive events. These models are usually specified in terms of a time‐varying mean (or median) conditional duration. In this paper, a new extension of ACD models is proposed which is built on the basis of log‐symmetric distributions reparametrized by their quantile. The proposed quantile log‐symmetric conditional duration autoregressive model allows us to model different percentiles instead of the traditionally used conditional mean (or median) duration. We carry out an in‐depth study of theoretical properties and practical issues, such as parameter estimation using maximum likelihood method and diagnostic analysis based on residuals. A detailed Monte Carlo simulation study is also carried out to evaluate the performance of the proposed models and estimation method in retrieving the true parameter values as well as to evaluate a form of residuals. Finally, we derive a semiparametric intraday value‐at‐risk (IVaR) model and then the proposed models are applied to two price duration data sets.

Copula-Based Regression with Mixed Covariates

In this paper, we focused on developing copula-based modeling procedures that effectively capture the dependence between response and explanatory variables. Building upon the work of Noh et al. (J. Am. Stat. Assoc. 2013, 108, 676–688) we extended copula-based regression to accommodate both continuous and discrete covariates. Specifically, we explored the construction of copulas to estimate the conditional mean of the response variable given the covariates, elucidating the relationship between copula structures and marginal distributions. We considered various estimation methods for copulas and distribution functions, presenting a diverse array of estimators for the conditional mean function. These estimators range from non-parametric to semi-parametric and fully parametric, offering flexibility in modeling regression relationships. An adapted algorithm is applied to construct copulas and simulations are carried out to replicate datasets, estimate prediction model parameters, and compare with the OLS method. The practicality and efficacy of our proposed methodologies, grounded in the principles of copula-based regression, are substantiated through methodical simulation studies.

On some cognates of Avestan hakat̰

Abstract This article deals with a number of Middle and New Iranian words of doubtful etymology for which a derivation from Ir. *hakat ‘together, at once’ is proposed. Its possible reflexes in Western Iranian witness a development towards a conditional or temporal meaning (Parth. ag ‘if’, NP aknūn ‘now’), but remnants of the old meaning ‘together’ can be identified in MP ag(e)nēn ‘together’ and in the Arm. loanword hakaṙak ‘opposite, against’. In Eastern Iranian it seems to have undergone grammaticalization and developed into a preverb (Khot. gga‑) or a preposition (Sogd. ku ‘towards’, Orm. ku- ‘to, on, etc.’, Ishk. kI ‘to, on, for’, Zeb. ka ‘id.’). Especially in this latter group of languages, Ir. *hakat shows an evolution largely comparable to that of *hačā ‘from’, which, according to most scholars, belongs to the same root.