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Time-resolved microscopy is a widely used approach for imaging and quantifying charge and energy transport in functional materials. While it is generally recognized that resolving small diffusion lengths is limited by measurement noise, the impacts of noise have not been systematically assessed or quantified. This article reports modeling efforts to elucidate the impact of noise on optical probes of transport. Excited state population distributions, modeled as Gaussians with additive white noise typical of experimental conditions, are subject to decay and diffusive evolution. Using a conventional composite least-squares fitting algorithm, the resulting diffusion constant estimates are compared with the model input parameter. The results show that heteroscedasticity (i.e., time-varying noise levels), insufficient spatial and/or temporal resolution, and small diffusion lengths relative to the magnitude of noise lead to a surprising degree of imprecision under moderate experimental parameters. Moreover, the compounding influence of low initial contrast and small diffusion length leads to systematic overestimation of diffusion coefficients. Each of these issues is quantitatively analyzed herein, and experimental approaches to mitigate them are proposed. General guidelines for experimentalists to rapidly assess measurement precision are provided, as is an open-source tool for customizable evaluation of noise effects on time-resolved microscopy transport measurements. [ABSTRACT FROM AUTHOR]

AbstractTesting for the autoregressive conditional heteroscedasticity (ARCH) effect is an important problem in economic and financial time series. In this article, we consider the ARCH effect test for high-dimensional time series. Our test statistic is built based on the maximum element of Spearman’s rank correlation at different lags. The bootstrap methods are used to approximate the null distribution of the proposed test statistics. We also consider the goodness-of-fit test for ARCH models by applying the test to the residuals of fitted models. Simulation results show that the proposed test statistics enjoy good properties of size in finite samples. Compared to the existing methods, the new test possesses much better power. Moreover, the test is not sensitive to the underlying distribution of the time series. The proposed method is illustrated via two real data. [ABSTRACT FROM AUTHOR]

Research has substantiated that the presence of outliers in data usually introduces additional errors and biases, which typically leads to a degradation in the precision of volatility forecasts. However, correcting outliers can mitigate these adverse effects. This study corrects the additive outliers through a weighting method and let these corrected values to replace the original outliers. Then, the model parameters are re-estimated based on this new return series. This approach reduces the extent to which outliers distort volatility estimates, allowing the model to better adapt to market conditions and improving the accuracy of volatility forecasts. This study introduces this approach for the first time to generalized autoregressive conditional heteroskedasticity mixed data sampling (GARCH-MIDAS) models, so as to establish an additional outliers corrected GARCH-MIDAS model (AO-GARCH-MIDAS). This pioneering approach marks a unique innovation. The research employs a diverse array of evaluation methods to validate the model's robustness and consistently demonstrates its dependable performance. Findings unequivocally reveal the substantial influence of outliers on the model's predictive capacity, with the AO-GARCH-MIDAS model exhibiting consistent superiority across all evaluation criteria. Additionally, while the GARCH model showcases stronger estimation capabilities compared to the GARCH-MIDAS model, the latter demonstrates heightened predictive prowess. Notably, regarding variable selection, the results underscore the greater predictive informational value inherent in realized volatility over other low-frequency factors. [ABSTRACT FROM AUTHOR]

Spike‐and‐slab and horseshoe regressions are arguably the most popular Bayesian variable selection approaches for linear regression models. However, their performance can deteriorate if outliers and heteroskedasticity are present in the data, which are common features in many real‐world statistics and machine learning applications. This work proposes a Bayesian nonparametric approach to linear regression that performs variable selection while accounting for outliers and heteroskedasticity. Our proposed model is an instance of a Dirichlet process scale mixture model with the advantage that we can derive the full conditional distributions of all parameters in closed‐form, hence producing an efficient Gibbs sampler for posterior inference. Moreover, we present how to extend the model to account for heavy‐tailed response variables. The model's performance is tested against competing algorithms on synthetic and real‐world datasets. [ABSTRACT FROM AUTHOR]

Bootstrap is a widely applicable computational statistical method. The focus of this paper lies in developing a bootstrap method for linear mixed models under homoscedasticity violation (heteroscedasticity) in variance of errors. We assume that the form of heteroscedasticity is unknown. To generate bootstrap response data as close as possible to the actual response data, we transform the marginal residuals to ensure that the variance of the modified marginal residuals in bootstrap samples is an unbiased estimator for the variance of the response variable in the linear mixed models. The consistency is proved, implying that the parameter estimators by the proposed method are asymptotically unbiased. The simulations are conducted with varying error terms and sample sizes to show improvement of the proposed method in parameter estimation. The simulation results are compared to demonstrate that the proposed method outperforms the other considered approaches including the wild method in the heteroscedastic linear mixed models under small samples and performs competitively with the parametric method and both methods outperform the other considered methods in homoscedastic linear mixed models. The proposed bootstrap method is applied to squid data for illustration of its effectiveness. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study serial correlations, allowing for unconditional heteroscedasticity and time‐varying probabilities of zero financial returns. Depending on the set‐up, we investigate how the standard autocorrelations can be accommodated to deliver an accurate representation of the serial correlations of stock price changes. We shed light on the properties of the different serial correlations measures by means of Monte Carlo experiments. Theoretical results are also illustrated on shares from the Chilean stock market and Facebook stock intraday data. [ABSTRACT FROM AUTHOR]

Eutrophication is a main threat to continental aquatic ecosystems. Prevention and amelioration actions have been taken under the assumption of a stable climate, which needs reconsideration. Here, we show that reduced precipitation can bring a lake ecosystem to a more productive regime even with a decline in nutrient external load. By analyzing time series of several decades in the largest lake of the Iberian Peninsula, we found autocorrelated changes in the variance of state variables (i.e., chlorophyll and oxygen) indicative of a transient situation towards a new ecosystem regime. Indeed, exceptional planktonic diatom blooms have occurred during the last few years, and the sediment record shows a shift in phytoplankton composition and an increase in nutrient retention. Reduced precipitation almost doubled the water residence time in the lake, enhancing the relevance of internal processes. This study demonstrates that ecological quality targets for aquatic ecosystems must be tailored to the changing climatic conditions for appropriate stewardship. [ABSTRACT FROM AUTHOR]

Competencies related to the evaluation of own cognitive processes, called metacognitive monitoring, are crucial as they help decide whether to persist in or desist from cognitive efforts. One of the most well-known phenomena in this context—the Dunning–Kruger effect—is that less skilled people tend to overestimate their performance. This effect has been reported for various kinds of performance including creativity. More recently, however, it has been suggested that this phenomenon could be a statistical artifact caused by the better-than-average effect and by regression toward the mean. Therefore, we examined the Dunning–Kruger effect in the context of creative thinking performance (i.e., divergent thinking ability) across two studies (Study 1: N = 425; Study 2: N = 317) and applied the classical quartile-based analysis as well as newly recommended, advanced statistical approaches: the Glejser test of heteroscedasticity and nonlinear quadratic regression. We found that the results indeed depended on the employed statistical method: While classical analyses supported the Dunning–Kruger effect across all conditions, it was not consistently supported by the more advanced statistical methods. These findings are in line with recent work challenging certain assumptions of the Dunning–Kruger effect and we discuss factors that undermine accurate self-assessments, especially in the context of creative performance. [ABSTRACT FROM AUTHOR]

Heteroscedasticity effects are useful for forecasting future stock return volatility. Stock volatility forecasting provides business insight into the stock market, making it valuable information for investors and traders. Predicting stock volatility is a crucial task and challenging. This study proposes a hybrid model that predicts future stock volatility values by considering the heteroscedasticity element of the stock price. The proposed model is a combination of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) and a well-known Recurrent Neural Network (RNN) algorithm Long Short-Term Memory (LSTM). This proposed model is referred to as GARCH-LSTM model. The proposed model is expected to improve prediction accuracy by considering heteroscedasticity elements. First, the GARCH model is employed to estimate the model parameters. After that, the ARCH effect test is used to test the residuals obtained from the model. Any untrained heteroscedasticity element must be found using this step. The hypothesis of the ARCH test yielded a p-value less than 0.05 indicating there is valuable information remaining in the residual, known as heteroscedasticity element. Next, the dataset with heteroscedasticity is then modelled using an LSTM-based RNN algorithm. Experimental results revealed that hybrid GARCH-LSTM had the lowest MAE (7.961), RMSE (10.466), MAPE (0.516) and HMAE (0.005) values compared with a single LSTM. The accuracy of forecasting was also significantly improved by 15% and 13% with hybrid GARCH-LSTM in comparison to single LSTMs. Furthermore, the results reveal that hybrid GARCH-LSTM fully exploits the heteroscedasticity element, which is not captured by the GARCH model estimation, outperforming GARCH models on their own. This finding from this study confirmed that hybrid GARCH-LSTM models are effective forecasting tools for predicting stock price movements. In addition, the proposed model can assist investors in making informed decisions regarding stock prices since it is capable of closely predicting and imitating the observed pattern and trend of KLSE stock prices. [ABSTRACT FROM AUTHOR]

In the field of financial risk management, the accuracy of portfolio Value-at-Risk (VaR) forecasts is of critical importance to both practitioners and academics. This study pioneers a comprehensive evaluation of a univariate model that leverages high-frequency intraday data to improve portfolio VaR forecasts, providing a novel contrast to both univariate and multivariate models based on daily data. Existing research has used such high-frequency-based univariate models for index portfolios, it has not adequately studied their robustness for portfolios with diverse risk profiles, particularly under changing market conditions, such as during crises. Our research fills this gap by proposing a refined univariate long-memory realized volatility model that incorporates realized variance and covariance metrics, eliminating the necessity for a parametric covariance matrix. This model captures the long-run dependencies inherent in the volatility process and provides a flexible alternative that can be paired with appropriate return innovation distributions for VaR estimation. Empirical analyses show that our methodology significantly outperforms traditional univariate and multivariate Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models in terms of forecasting accuracy while maintaining computational simplicity and ease of implementation. In particular, the inclusion of high-frequency data in univariate volatility models not only improves forecasting accuracy but also streamlines the complexity of portfolio risk assessment. This research extends the discourse between academic research and financial practice, highlighting the transformative impact of high-frequency data on risk management strategies within the financial sector. [ABSTRACT FROM AUTHOR]

Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its variations have been widely adopted in the study of financial volatilities, while the extension of GARCH‐type models to high‐dimensional data is always difficult because of over‐parameterization and computational complexity. In this article, we propose a multi‐variate GARCH‐type model that can simplify the parameterization by utilizing the network structure that can be appropriately specified for certain types of high‐dimensional data. The asymmetry in the dynamics of volatilities is also considered as our model adopts a threshold structure. To enable our model to handle data with extremely high dimension, we investigate the near‐epoch dependence (NED) of our model, and the asymptotic properties of our quasi‐maximum‐likelihood‐estimator (QMLE) are derived from the limit theorems for NED random fields. Simulations are conducted to test our theoretical results. At last we fit our model to log‐returns of four groups of stocks and the results indicate that bad news is not necessarily more influential on volatility if the network effects are considered. [ABSTRACT FROM AUTHOR]

One of the key tools to understand and reduce the spread of the SARS-CoV-2 virus is testing. The total number of tests, the number of positive tests, the number of negative tests, and the positivity rate are interconnected indicators and vary with time. To better understand the relationship between these indicators, against the background of an evolving pandemic, the association between the number of positive tests and the number of negative tests is studied using a joint modeling approach. All countries in the European Union, Switzerland, the United Kingdom, and Norway are included in the analysis. We propose a joint penalized spline model in which the penalized spline is reparameterized as a linear mixed model. The model allows for flexible trajectories by smoothing the country-specific deviations from the overall penalized spline and accounts for heteroscedasticity by allowing the autocorrelation parameters and residual variances to vary among countries. The association between the number of positive tests and the number of negative tests is derived from the joint distribution for the random intercepts and slopes. The correlation between the random intercepts and the correlation between the random slopes were both positive. This suggests that, when countries increase their testing capacity, both the number of positive tests and negative tests will increase. A significant correlation was found between the random intercepts, but the correlation between the random slopes was not significant due to a wide credible interval. [ABSTRACT FROM AUTHOR]

The analysis of means (ANOM) is a method that can compare the mean of each treatment with the overall mean. As one-way ANOVA, the conventional ANOM is not robust under unequal variances. We applied two inference procedures, single-stage and modified single-stage sampling, to solve heteroscedastic analysis of means (HANOM) under unbalanced design. Using proposed weighted average across groups, the influence of the unknown mean and variance are both eliminated. To validate the stability of HANOM under several scenarios of unequal variances and sample sizes, simulation studies of empirical type I error rate are conducted to test the quality of procedures. A real application is provided for illustrating these two procedures clearly. In addition, we build an user-friendly interface to show the results of the HANOM by using Shiny package in R software. [ABSTRACT FROM AUTHOR]

Volatility estimation and quantile regression are relevant active research areas in statistics, machine learning and econometrics. In this work, we propose two procedures to estimate the local variances in generic regression problems by using kernel smoothers. The proposed schemes can be applied in multidimensional scenarios (not just for time series analysis) and easily in a multi-output framework as well. Moreover, they enable the possibility of providing uncertainty estimation using a generic kernel smoother technique. Several numerical experiments show the benefits of the proposed methods, even compared with the benchmark techniques. One of these experiments involves a real dataset analysis. [ABSTRACT FROM AUTHOR]

In recent years, there has been increased interest in modeling integer-valued time series. Many methods for time series of counts have been developed in the literature because of their wide applications to epidemiology, finance, disease modeling and environmental science. The negative binomial integer-valued generalized autoregressive conditional heteroscedasticity model is a popular one, which can deal with both over-dispersion and potential extreme observations. The accurate estimation of the parameters in the model is extremely important. We adopt the marginal likelihood to estimate the intercept parameter and maximum likelihood to estimate other parameters of the model. We conduct simulations to assess the performance of this estimation method, and compare it with that of estimating all model parameters by maximum likelihood. The results show the superiority of proposed estimation method. We use two real examples to illustrate the model's ability to fit over-dispersed data and the validity of the estimation method. [ABSTRACT FROM AUTHOR]

Given k (≥2) independent and normally distributed populations with unknown means and unknown (and possibly unequal) variances, we used the single-stage sampling procedure for multiple comparison with a control to the problem of unequal sample sizes. A simulation of the family-wise error type I was conducted to validate the quality of the procedure and a numerical example was provided for illustrating this procedure. We provided a user-friendly interface by R shiny to obtain the critical values for the practitioners. [ABSTRACT FROM AUTHOR]

We propose an adjusted robust heteroscedastic autoregressive spatiotemporal model with a data-driven process to predict the hourly PM 2.5 concentrations in Xi'an and Xianyang, China. To begin with, an adjusted variance function for the heteroscedastic model is proposed to capture the different variances of the PM 2.5 concentrations during the periods of heating and non-heating. Compared to the traditional heteroscedastic method, the proposed adjusted heteroscedastic method has lower standard errors for most of the coefficient estimators. Secondly, to improve the prediction accuracy, the temporal correlations of the PM 2.5 data are incorporated into the adjusted heteroscedastic model by augmenting some additional predictors generated from an autoregressive process. The prediction results of the testing data demonstrate that the adjusted robust heteroscedastic autoregressive model significantly improves the prediction. Finally, utilizing the spatiotemporal simple kriging method, the spatial correlations of PM 2.5 concentrations at different air monitoring stations are incorporated into the prediction by adding the weighted robust residuals to the previous prediction. The prediction performance of the final proposed forecasting method is shown to be further enhanced. [ABSTRACT FROM AUTHOR]

The premise for formulating effective emission control strategies is to accurately and reasonably evaluate the actual emission level of vehicles. Firstly, the active subspace method is applied to set up a low-dimensional model of the relationship between CO2 emission and multivariate vehicle driving data, in which the vehicle specific power (VSP) is identified as the most significant factor on the CO2 emission factor, followed by speed. Additionally, acceleration and exhaust temperature had the least impact. It is inferred that the changes in data sampling transform the establishment of subspace matrices, affecting the calculation of eigenvector components and the fitting of the final quadratic response surface, so that the emission sensitivity and final fitting accuracy are impressionable by the data distribution form. For the VSP, the best fitting result can be obtained when the VSP conforms to a uniform distribution. Moreover, the Bayesian linear regression method accounts for fitting parameters between the VSP and CO2 emission factor with uncertainties derived from heteroscedastic measurement errors, and the values and distributions of the intercept and slope α and β are obtained. In general, the high-resolution inventory of the carbon emission factor of the tested vehicle is set up via systematically analyzing it, which brings a bright view of data processing in further counting the carbon footprint. [ABSTRACT FROM AUTHOR]

This study aims to test for detecting a change point in the conditional quantile of general location-scale time series models. This issue is quite important in risk management because the conditional quantile is utilized to measure the value-at-risk or expected shortfall of financial assets. In this paper, we design two types of cumulative sum tests based on the conditional quantiles. Their limiting null distributions are derived under regularity conditions, together with consistency of the proposed tests under the alternative. Monte Carlo simulations demonstrate the good performance of the proposed tests in terms of both stability and power for various time series settings. A real data analysis using the daily returns of the Brent Oil futures also confirms the validity of the tests in real-world applications. [ABSTRACT FROM AUTHOR]

Summary: We compare predictive performance of a multitude of alternative Bayesian vector autoregression (VAR) models allowing for cointegration and time‐varying conditional covariances, described by different multivariate stochastic volatility (MSV) models, including their hybrids with multivariate GARCH processes (MSV‐MGARCH), as well as t‐GARCH and Markov‐switching structures. The forecast accuracy is evaluated mainly through predictive Bayes factors, but energy scores and the probability integral transform are also used. Two empirical studies, for the US and Polish economies, are based on a small model of monetary policy comprising inflation, unemployment and interest rate. The results indicate that capturing conditional heteroskedasticity by some MSV‐MGARCH specifications contributes the most to the forecasting power of the VAR/VEC model. [ABSTRACT FROM AUTHOR]

Fisher–von Mises–Langevin distributions are widely used for modeling directional data. In this paper, the problem of testing homogeneity of mean directions of several Fisher–von Mises–Langevin populations is considered when the concentration parameters are unknown and heterogeneous. First, an adaptive test based on the likelihood ratio statistic is proposed. Critical points are evaluated using a parametric bootstrap. Second, a heuristic test statistic is considered based on pairwise group differences. A nonparametric bootstrap procedure is adapted for evaluating critical points. Finally, a permutation test is also proposed. An extensive simulation study is performed to compare the size and power values of these tests with those proposed earlier. It is observed that both parametric and nonparametric bootstrap based tests achieve size values quite close to the nominal size. Asymptotic tests and permutation tests have size values higher than the nominal size. Bootstrap tests are seen to have very good power performance. The robustness of tests is also studied by considering contamination in Fisher–von Mises–Langevin distributions. R packages are developed for the actual implementation of all tests. A real data set has been considered for illustrations. [ABSTRACT FROM AUTHOR]

Modeling the number of air passengers correctly is essential for management policy in the global world. Based on seasonality (depending on the season of the year), data about the number of air passengers are heteroscedastic. Heteroscedasticity violates "Homoscedasticity" which is one of the central assumptions of linear regression analysis. In this study, a new weighting approach called "Weighting Absolute Centered External Variable" (WCEV) is applied to the Turkish total monthly air passenger's data to obtain correct statistical inference and forecasting. Besides scatter plot months vs. studentized residuals, the homoscedasticity assumption is checked with the studentized RCEV test as well. Consequently, the WCEV method is shown superior performance against multiple linear regressions and exponential weighted moving average (EWMA) methods. The study also provides insights into the seasonal patterns of air passenger demand in Turkey, with passenger mobility increasing in the last quarter of each year and the lowest demand in January and February. This information can be used to optimize airport and airplane maintenance schedules and increase capacity during peak months. [ABSTRACT FROM AUTHOR]

Many financial time series not only have varying structures at different quantile levels and exhibit the phenomenon of conditional heteroscedasticity at the same time but also arrive in the stream. Quantile double‐autoregression is very useful for time series analysis but faces challenges with model fitting of streaming data sets when estimating other quantiles in subsequent batches. This article proposes a renewable estimation method for quantile double‐autoregression analysis of streaming time series data due to its ability to break with storage barrier and computational barrier. Moreover, the proposed flexible parametric structure of the quantile function enables us to predict any interested quantile value without quantile curve crossing problem or keeping the desirable monotone property of the conditional quantile function. The proposed methods are illustrated using current data and the summary statistics of historical data. Theoretically, the proposed statistic is shown to have the same asymptotic distribution as the standard version computed on an entire data stream with the data batches pooled into one data set, without additional condition. Simulation studies and an empirical example are presented to illustrate the finite sample performance of the proposed methods. [ABSTRACT FROM AUTHOR]

We consider a non-inferiority test conducted in the three-arm trials with coefficient of variations (CV) in sample means. A procedure for this non-inferiority test is proposed based on the generalized p-value (GPV) based method under normality assumption and heteroskedasticity. We demonstrated that first, the GPV-based method outperforms the comparable alternative, the Delta method in terms of empirical sizes and powers. Second, under GPV-based method, when the population mean of groups in the trial is estimated by the sample mean with CV, the empirical sizes control the significance level better than when CV is not included, especially when the ratio of the variance of the reference group to that of the experimental group and the ratio of the variance of the placebo group to that of the experimental group are not too small and that the sample size is small. Third, when the CV is included in the sample mean, the empirical powers are always higher, regardless of the sample size and methods. Additionally, when the data violates the normality assumption, it is found that the proposed GPV-based method in conjunction with CV appear to be highly acceptable through simulation results. Finally, the proposed method is illustrated with two data examples. [ABSTRACT FROM AUTHOR]

A common problem that we encounter in linear regression models is that the error variances are not the same for all the observations, that is, there is an issue of heteroscedasticity. To avoid the adverse effects of this issue on the estimates obtained by the ordinary least squares, it is a usual practice to use the estimated weighted least squares (EWLS) method or to use some adaptive methods, especially when the form of heteroscedasticity is unknown. The current article proposes a novel Bayesian version of the EWLS estimator. The performance of the proposed estimator has been evaluated in terms of its efficiency using the Monte Carlo simulations. An example has also been included for the demonstration. [ABSTRACT FROM AUTHOR]

Although regression is a traditional data processing method, machine and deep learning methods have been widely used in the literature in recent years for both modelling and prediction. However, in order to use these methods efficiently, it is important to perform a preliminary evaluation to understand the data type. Therefore, preevaluation procedures are described in this study. Experimental uncertainty analysis was performed to determine the measurement uncertainties in the measurement devices and sensors used in the drying experimental setup. Significant and insignificant relationships between variables in the data set were determined by Pearson correlation matrix. Autocorrelation and partial autocorrelation functions were used to determine the time series lag in the drying data and an AR(5) series with 5 lags was determined. The data were found to have variable variance due to peaks and troughs in the raw data resulting from the natural behaviour of the drying process. Modelling success was achieved with the normalisation pre-evaluation process performed without distorting the raw data. Thus, it has been shown that better models can be obtained compared to traditional models. In order to avoid unnecessary time and computational costs in the trial and error method used to determine the number of hidden layers and neurons in the machine learning method, various formulas proposed in the literature were compared. It is shown that the correlation coefficient alone is not sufficient to determine the goodness of the model. In modelling the data in this study, the NARX model was found to converge to the desired value faster and with less error than ANFIS and LSTM models. In the simulation of a rotary drum dryer, the optimum number of mesh elements was determined as 1137 by mesh independence analysis. In this way, unnecessary over-calculations were also prevented. Of course, all these methods are already available in statistical science. However, in this study, the methods to be used for modelling and prediction purposes are carefully selected and explained with examples, especially for young researchers who are outside this field to gain speed and easy comprehension. [ABSTRACT FROM AUTHOR]

Standard long memory models are in abundance in the literature today. Selecting the best such a model in terms of capturing key requisite features and trends in data becomes a challenge. This paper addresses the issue through a sequence of Monte Carlo experiments on simulated data and introduces an interval estimate on the asymptotic variance for the long-range dependence parameter of the entire family of standard long memory time series considered within the scope of the study. [ABSTRACT FROM AUTHOR]

The objective is to provide a nonparametric bootstrap method for functional data that consists of independent realizations of a continuous one-dimensional process. The process is assumed to be nonstationary, with a functional mean and a functional variance, and dependent. The resampling method is based on nonparametric estimates of the model components. Numerical studies were conducted to check the performance of the proposed procedure, by approximating the bias and the standard error of two estimators. A practical application of the proposed approach to pollution data has also been included. Specifically, it is employed to make inference about the annual trend of ground-level ozone concentration at Yarner Wood monitoring station in the United Kingdom. Supplementary material to this paper is provided online. [ABSTRACT FROM AUTHOR]

A nonparametric procedure to estimate the conditional probability that a nonstationary geostatistical process exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation techniques with nonparametric estimations of the trend and the variability. The nonparametric local linear estimator, considering a bandwidth matrix selected by a method that takes the spatial dependence into account, is used to estimate the trend. The variability is modeled estimating the conditional variance and the variogram from corrected residuals to avoid the biasses. The proposed method allows to obtain estimates of the conditional exceedance risk in non-observed spatial locations. The performance of the approach is analyzed by simulation and illustrated with the application to a real data set of precipitations in the USA.Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

The paper introduces a semiparametric estimator of the correlations among elliptically distributed random variables invariant to any form of heteroscedasticity, robust to outliers, and asymptotically normal. Our estimator is particularly fit for financial applications as vectors of stock returns are generally well approximated by heteroskedastic processes with elliptical (conditional) distributions and heavy tails. The superiority of our estimator with respect to Pearson's sample correlation in financial applications is illustrated using simulated data and real high-frequency stock returns. Using simple exponentially weighted moving averages, we extend our estimator to the case of time-varying correlations and compare it to the popular GARCH-DCC model. We show that the two approaches have comparable performances through simulations and a simple application. However, our estimator is extremely fast to compute, computationally robust, and straightforward to implement. [ABSTRACT FROM AUTHOR]

Multivariate repeated measures data naturally arise in clinical trials and other fields such as biomedical science, public health, agriculture, social science and so on. For data of this type, the classical approach is to conduct multivariate analysis of variance (MANOVA) based on Wilks' Lambda and other multivariate statistics, which require the assumptions of multivariate normality and homogeneity of within-cell covariance matrices. However, data being analyzed nowadays show marked departure from multivariate normality and homogeneity. This paper proposes a finite-sample test by modifying the sums of squares matrices to make them insensitive to the heterogeneity in MANOVA. The proposed test is invariant to affine transformation and robust against nonnormality. The proposed method can be used in various experimental designs, for example, factorial design and crossover design. Under various simulation settings, the proposed method outperforms the classical Doubly Multivariate Model and Multivariate Mixed Model proposed elsewhere, especially for unbalanced sample sizes with heteroscedasticity. The applications of the proposed method are illustrated with ophthalmology data in factorial and crossover designs. The proposed method successfully identified and validated a significant main effect and demonstrated that univariate analysis could be oversensitive to small but clinically unimportant interactions. [ABSTRACT FROM AUTHOR]

Periodic generalized autoregressive conditionally heteroscedastic (PGARCH) models were introduced by Bollerslev and Ghysels [T. Bollerslev and E. Ghysels, Periodic autoregressive conditional heteroscedasticity, J. Bus. Econom. Statist. 14 1996, 2, 139–151]; these models have gained considerable interest and continued to attract the attention of researchers. This paper is devoted to extensions of the standard absolute value GARCH (AVGARCH) model to the periodically time-varying coefficients (PAVGARCH) one. In this class of models, the parameters are allowed to switch between different regimes. Moreover, these models allow to integrate asymmetric effects in the volatility, Firstly, we give necessary and sufficient conditions ensuring the existence of stationary solutions (in the periodic sense). Secondary, a quasi-maximum likelihood (QML) estimation approach for estimating the PAVGARCH model is developed. The strong consistency and the asymptotic normality of the estimator are studied given mild regularity conditions, requiring strict stationarity and the finiteness of moments of some order for the errors term. Next, we present a set of numerical experiments illustrating the practical relevance of our theoretical results. Finally, we apply our model to two foreign exchange rates: of Algerian Dinar to the European currency Euro (Euro/Dinar) and the American currency Dollar (Dollar/Dinar). This empirical work shows that our approach also outperforms and fits the data well. [ABSTRACT FROM AUTHOR]

This study proposes a control chart that monitors conditionally heteroscedastic time series by integrating the Huber support vector regression (HSVR) and the one-class classification (OCC) method. For this task, we consider the model that incorporates nonlinearity to the generalized autoregressive conditionally heteroscedastic (GARCH) time series, named HSVR-GARCH, to robustly estimate the conditional volatility when the structure of time series is not specified with parameters. Using the squared residuals, we construct the OCC-based control chart that does not require any posterior modifications of residuals unlike previous studies. Monte Carlo simulations reveal that deploying squared residuals from the HSVR-GARCH model to control charts can be immensely beneficial when the underlying model becomes more complicated and contaminated with noises. Moreover, a real data analysis with the Nasdaq composite index and Korea Composite Stock Price Index (KOSPI) datasets further disclose the validity of using the bootstrap method in constructing control charts. [ABSTRACT FROM AUTHOR]

Metaverse (MV) technology introduces new tools for users each day. MV companies have a significant share in the total stock markets today, and their size is increasing. However, MV technologies are questioned as to whether they contribute to environmental pollution with their increasing energy consumption (EC). This study explores complex nonlinear contagion with tail dependence and causality between MV stocks, EC, and environmental pollution proxied with carbon dioxide emissions (CO2) with a decade-long daily dataset covering 18 May 2012–16 March 2023. The Mandelbrot–Wallis and Lo's rescaled range (R/S) tests confirm long-term dependence and fractionality, and the largest Lyapunov exponents, Shannon and Havrda, Charvât, and Tsallis (HCT) entropy tests followed by the Kolmogorov–Sinai (KS) complexity measure confirm chaos, entropy, and complexity. The Brock, Dechert, and Scheinkman (BDS) test of independence test confirms nonlinearity, and White's test of heteroskedasticity of nonlinear forms and Engle's autoregressive conditional heteroskedasticity test confirm heteroskedasticity, in addition to fractionality and chaos. In modeling, the marginal distributions are modeled with Markov-Switching Generalized Autoregressive Conditional Heteroskedasticity Copula (MS-GARCH–Copula) processes with two regimes for low and high volatility and asymmetric tail dependence between MV, EC, and CO2 in all regimes. The findings indicate relatively higher contagion with larger copula parameters in high-volatility regimes. Nonlinear causality is modeled under regime-switching heteroskedasticity, and the results indicate unidirectional causality from MV to EC, from MV to CO2, and from EC to CO2, in addition to bidirectional causality among MV and EC, which amplifies the effects on air pollution. The findings of this paper offer vital insights into the MV, EC, and CO2 nexus under chaos, fractionality, and nonlinearity. Important policy recommendations are generated. [ABSTRACT FROM AUTHOR]

Pork price fluctuations are closely related to the national economy and people's livelihoods in China. Based on the monthly pork price fluctuations in China from January 2011 to August 2022, this study uses ARCH family models to assess the characteristics and laws of these fluctuations in China. The pork price fluctuations show obvious clustering, with external shock information from the previous month affecting the pork price in the following period; the pork market price is characterized by risk compensation, with the high risk of pork supply driving the pork price up. In addition, the pork price fluctuations are characterized by asymmetry, with a greater impact of good than of bad news on the pork price. Due to the pork industry' low entry threshold and the existence of sunk costs, positive information on the pork market has a stronger impact on price fluctuations than negative information. To guide pork supply, we recommend improving monitoring and earlywarning mechanisms in the pork market to identify the pork price volatility threshold and measure the price volatility. In addition, price index insurance products should be constantly strengthened, with different types of insurance products being offered to meeting the insurance demand of various sectors in the pig meat supply chain. [ABSTRACT FROM AUTHOR]

High-dimensional data often display heteroscedasticity. If the heteroscedasticity is neglected in the regression model, it will produce inefficient inference for the regression coefficients. Quantile regression is not only robust to outliers, but also accommodates heteroscedasticity. This paper aims to simultaneously carry out variable selection and heteroscedasticity identification for the linear location-scale model under a unified framework. We develop a regularized multiple quantile regression approach simultaneously identifying the heteroscedasticity, seeking common features of quantile coefficients and eliminating irrelevant variables. We also establish the theoretical properties of the proposed method under some regularity conditions. Simulation studies are conducted to evaluate the finite sample performance of the proposed method, showing that it is able to identify the covariates that affect the variability of the response. We further apply the proposed method to analyse the Wage data. [ABSTRACT FROM AUTHOR]

In recent years, the external shock represented by COVID-19 has caused significant fluctuations in global corn prices. Based on the weekly data on international corn prices from 2020 to 2023, this paper constructs autoregressive conditional heteroskedasticity (ARCH) class and time-varying parameter - vector autoregression (TVP-VAR) models. After analysing the characteristics of corn price fluctuations, it further analyses the influence of external uncertainties such as COVID-19, international finance, the corn futures market, and international exports of corn on corn price fluctuations. The results show that international corn price fluctuations always have significant asymmetry. Nevertheless, the influence of past changes on the future will gradually disappear, and the corn market is not characterised by high risk and high return because of the phenomenon of flat or declining absolute returns during the periods of high volatility. All the selected external shocks also have a time-varying impact on corn price fluctuations, and there are differences in the impact size, impact direction, and impact duration. The external shocks led by COVID-19 had a transmission effect on other factors and then affected corn price fluctuations. [ABSTRACT FROM AUTHOR]

Sparse quantile regression is a useful tool for variable selection, robust estimation and heteroscedasticity treatment in high-dimensional data analysis. Due to the non-smooth of quantile loss, the computation is heavier than the least square models. In the literature, there are various numerical methods for linear quantile regression, such as ADMM developed in Gu et al. [Technometrics. 2017;60(3):319–331]. However, the computation of multivariate quantile regression has not yet been fully resolved, especially when the dimension is high. Motivated by this, we will focus on the design of fast numerical algorithms for row-sparse multivariate quantile regression model. By virtue of proximal operator and Majorize–Minimization, four smoothed algorithms are designed. For all the obtained algorithms, we analyse their convergence and the parameter selection. We conduct plenty of simulations and four real data sets analysis. Finally, we conclude that the smoothed method is faster than the non-smooth method, especially when the number of predictors is large. [ABSTRACT FROM AUTHOR]

For derivative function estimation, conventional research only focuses on the derivative estimation of one-dimensional functions. This paper considers partial derivatives estimation of a multivariate variance function in a heteroscedastic model. A wavelet estimator of partial derivatives of a multivariate variance function is proposed. The convergence rates of a wavelet estimator under different estimation errors are discussed. It turns out that the strong convergence rate of the wavelet estimator is the same as the optimal uniform almost sure convergence rate of nonparametric function problems. [ABSTRACT FROM AUTHOR]

While causes and consequences of uncertainty in the US economy have attracted viable interest, the literature still lacks a consensus on several aspects. To name two matters of debate, it remains unclear whether uncertainty shocks are a source or the result of recessions and whether uncertainty shocks have adverse (or even stimulating) effects on the economy. We find that ambiguous results in these regards can be traced back to the selection of an appropriate identification strategy in structural vector autoregressive models. We find that both macroeconomic and financial uncertainty are exogenous to business cycle fluctuations and cause economic slowdowns. [ABSTRACT FROM AUTHOR]

Cognitive functioning in older age profoundly impacts quality of life and health. While most research on cognition in older age has focused on mean levels, intraindividual variability (IIV) around this may have risk factors and outcomes independent of the mean value. Investigating risk factors associated with IIV has typically involved deriving a summary statistic for each person from residual error around a fitted mean. However, this ignores uncertainty in the estimates, prohibits exploring associations with time-varying factors, and is biased by floor/ceiling effects. To address this, we propose a mixed-effects location scale beta-binomial model for estimating average probability and IIV in a word recall test in the English Longitudinal Study of Ageing. After adjusting for mean performance, an analysis of 9,873 individuals across 7 (mean = 3.4) waves (2002–2015) found IIV to be greater at older ages, with lower education, in females, with more difficulties in activities of daily living, in later birth cohorts, and when interviewers recorded issues potentially affecting test performance. Our study introduces a novel method for identifying groups with greater IIV in bounded discrete outcomes. Our findings have implications for daily functioning and care, and further work is needed to identify the impact for future health outcomes. [ABSTRACT FROM AUTHOR]

We study the Feasible Generalized Least-Squares (FGLS) estimation of the parameters of a linear regression model in the presence of heteroskedasticity of unknown form in the errors. We suggest a Lasso based procedure to estimate the skedastic function of the residuals. The advantage of using Lasso is that it can handle a large number of potential covariates, yet still yields a parsimonious specification. Using extensive simulation experiments, we show that our suggested procedure always provide some improvements in the precision of the parameter of interest (lower Mean-Squared Errors) when heteroskedasticity is present and is equivalent to OLS when there is none. It also performs better than previously suggested procedures. Since the fitted value of the skedastic function falls short of the true specification, we form confidence intervals using a bias-corrected version of the usual heteroskedasticity-robust covariance matrix estimator. These have the correct size and substantially shorter length than when using OLS. Our method is applicable to both cross-section (with a random sample) and time series models, though here we concentrate on the former. [ABSTRACT FROM AUTHOR]

We introduce methods to apply stochastic frontier analysis (SFA) to financial assets as an alternative to data envelopment analysis, because SFA allows us to fit a frontier with noisy data. In contrast to conventional SFA, we wish to deal with estimation risk, heteroscedasticity in noise and inefficiency terms. We investigate measurement error in the risk and return measures using a simulation–extrapolation method and develop residual plots to test model fit. We find that shrinkage estimators for estimation risk makes a striking difference to model fit, dealing with measurement error only improves confidence in the model, and the residual plots are vital for establishing model fit. The methods are important because they allow us to fit a frontier under the assumption that the risks and returns are not known exactly. [ABSTRACT FROM AUTHOR]

Investors generally aim to obtain a high return from their stock portfolio. However, investors must realize that a high value-at-risk (VaR) is essential to calculate for this aim. One of the objects in the VaR calculation is the asymmetric return volatility of stocks, which causes an unbalanced decrease and increase in returns. Therefore, this study proposes a mean-value-at-risk (mean-VaR) stock portfolio optimization model based on stocks' asymmetric return volatility and investors' risk aversion preferences. The first stage is the determination of the mean of all stocks in the portfolio conducted using the autoregressive moving average Glosten–Jagannathan–Runkle generalized autoregressive conditional heteroscedasticity (ARMA-GJR-GARCH) models. Then, the second stage is weighting the capital of each stock based on the mean-VaR model with the investors' risk aversion preferences. This is conducted using the Lagrange multiplier method. Then, the model is applied to stock data in Indonesia's capital market. This application also analyzed the sensitivity between the mean, VaR, both ratios, and risk aversion. This research can be used for investors in the design and weighting of capital in a stock portfolio to ensure its asymmetrical effect is as small as possible. [ABSTRACT FROM AUTHOR]

In this research, we evaluated two difference based variance estimators: one by Gasser, Sroka, and Jennen-Steinmetz, and another by Hall, Kay, and Titterington for use in partially linear models. Under various settings, we compared power of tests for heteroskedasticity, and other finite population properties of the estimators using simulation studies. We also proved that under regularity conditions, the estimator from Hall, Kay, and Titterington provides larger power of the tests for heteroskedasticity. A real example is given to illustrate the usage of the estimators. [ABSTRACT FROM AUTHOR]

In randomized clinical trials, adjustments for baseline covariates at both design and analysis stages are highly encouraged by regulatory agencies. A recent trend is to use a model-assisted approach for covariate adjustment to gain credibility and efficiency while producing asymptotically valid inference even when the model is incorrect. In this article we present three considerations for better practice when model-assisted inference is applied to adjust for covariates under simple or covariate-adaptive randomized trials: (a) guaranteed efficiency gain: a model-assisted method should often gain but never hurt efficiency; (b) wide applicability: a valid procedure should be applicable, and preferably universally applicable, to all commonly used randomization schemes; (c) robust standard error: variance estimation should be robust to model misspecification and heteroscedasticity. To achieve these, we recommend a model-assisted estimator under an analysis of heterogeneous covariance working model that includes all covariates used in randomization. Our conclusions are based on an asymptotic theory that provides a clear picture of how covariate-adaptive randomization and regression adjustment alter statistical efficiency. Our theory is more general than the existing ones in terms of studying arbitrary functions of response means (including linear contrasts, ratios, and odds ratios), multiple arms, guaranteed efficiency gain, optimality, and universal applicability. for this article are available online. [ABSTRACT FROM AUTHOR]