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Anomaly detection is a frequently discussed topic in manufacturing. However, the issues of anomaly detection are typically attributed to the manufacturing process or equipment itself. In practice, the sensor responsible for collecting data and monitoring values may fail, leading to a biased detection result – false alarm. In such cases, replacing the sensor is necessary instead of performing equipment maintenance. This study proposes an effective framework embedded with autoencoder-based control limits that can dynamically distinguish sensor anomaly from process anomaly in real-time. We conduct a simulation numerical study and an empirical study of semiconductor assembling manufacturers to validate the proposed framework. The results show that the proposed model outperforms other benchmark methods and can successfully identify sensor failures, even under conditions of (1) large variations in process values or sensor values and (2) heteroscedasticity effect. This is particularly beneficial in various practical applications where sensors are used for numerical measurements and support equipment maintenance. [ABSTRACT FROM AUTHOR]

Scaling is common in empirical accounting research. It is often done to mitigate heteroscedasticity or the influence of firm size on parameter estimates. However, Barth and Clinch conclude that common diagnostic tools are ineffective in detecting various scale effects. Using analytic results and Monte Carlo simulations, we show that common forms of scaling, when misapplied, induce substantial spurious correlation via biased parameter estimates. Researchers, when uncertain about the exact functional form of scale effect, are typically better off dealing with both heteroscedasticity and the influence of larger firms using techniques other than scaling. [ABSTRACT FROM AUTHOR]

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]

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]

Estimating the long-run variance (LRV) is crucial for several econometric issues. Constructing reliable heteroskedasticity autocorrelation consistent (HAC) variance-covariance matrices and implementing efficient generalized method of moments (GMM) estimation procedures require a consistent LRV estimate. A good VARHAC estimator (HAC matrix with the spectral density at frequency zero constructed using a VAR spectral estimation) requires accurately estimating the sum of autoregressive (AR) coefficients; however, a criterion that minimizes the innovation variance does not necessarily yield the best spectral estimate. This article implements an optimal VARHAC estimator using an alternative information criterion, considering the bias in the sum of the parameters for the AR estimator of the spectral density at frequency zero. [ABSTRACT FROM AUTHOR]

In this article, we present a new one-stage multiple comparison procedure for exponential mean lifetimes with the control under heteroscedasticity including one-sided and two-sided confidence intervals by improving the coverage probability and average confidence length compared with the old one. Users can use these simultaneous confidence intervals to identify better-than-the-control, worse-than-the-control and not-much-different-from-the-control products in agriculture, stock market, pharmaceutical industries in terms of the mean lifetimes. In the end, one example is used to demonstrate the proposed procedure. [ABSTRACT FROM AUTHOR]

This study examines whether the disposition effect can explain time‐varying risk preference and predict the equity risk premium. To do so, we propose an augmented general autoregressive conditional heteroskedasticity (GARCH)‐in‐Mean model unraveling the complex relationship between unrealized gains/losses, realized returns, and the equity risk premium. In our model, the risk aversion coefficient varies with the market state of unrealized gains/losses. Using data from the US stock markets, we show strong evidence that the disposition effect drives time‐varying risk preference: The risk aversion coefficient is significantly positive during periods of unrealized gains, but insignificant during periods of unrealized losses. These findings reconcile the conflicting results of the risk‐return trade‐off in existing literature. Moreover, our model shows significant predictability of the equity risk premium, both in‐sample and out‐of‐sample. Incorporating our model's predictions can yield substantial utility gains for a mean‐variance investor. Our results indicate that the disposition effect leads to time‐varying risk preference and thus induces equity risk premium predictability. [ABSTRACT FROM AUTHOR]

We propose a new class of modified regression‐based tests for detecting asset price bubbles designed to be robust to the presence of general forms of both conditional and unconditional heteroskedasticity in the price series. This modification, based on the approach developed in Beare (2018) in the context of conventional unit root testing, is achieved by purging the impact of unconditional heteroskedasticity from the data using a kernel estimate of volatility before the application of the bubble detection methods proposed in Phillips, Shi and Yu (2015) (PSY). The modified statistic is shown to achieve the same limiting null distribution as the corresponding (heteroskedasticity‐uncorrected) statistic from PSY would obtain under homoskedasticity, such that the usual critical values provided in PSY may still be used. Versions of the test based on regressions including either no intercept or a (redundant) intercept are considered. Representations for asymptotic local power against a single bubble model are also derived. Monte Carlo simulation results highlight that neither one of these tests dominates the other across different bubble locations and magnitudes, and across different models of time‐varying volatility. Accordingly, we also propose a test based on a union of rejections between the with‐ and without‐intercept variants of the modified PSY test. The union procedure is shown to perform almost as well as the better of the constituent tests for a given DGP, and also performs very well compared to existing heteroskedasticity‐robust tests across a large range of simulation DGPs. [ABSTRACT FROM AUTHOR]

AbstractThis paper develops permutation versions of identification-robust tests in linear instrumental variables regression. Unlike the existing randomization and rank-based tests in which independence between the instruments and the error terms is assumed, the permutation Anderson-Rubin (AR), Lagrange Multiplier (LM) and Conditional Likelihood Ratio (CLR) tests are asymptotically similar and robust to conditional heteroskedasticity under standard exclusion restriction i.e. the orthogonality between the instruments and the error terms. Moreover, when the instruments are independent of the structural error term, the permutation AR tests are exact, hence robust to heavy tails. As such, these tests share the strengths of the rank-based tests and the wild bootstrap AR tests. Numerical illustrations corroborate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract.In the realm of mixed models, this article explores the estimation method for incorporating a mixture of distributions and addressing controlled heteroscedasticity. By relaxing the assumptions of normality and homoscedasticity, we introduce a more flexible approach to analyzing data. The article presents estimation techniques for variance components, estimable vectors, and cumulants, while also developing prediction intervals and prediction ellipsoids for future observations. A numerical example is employed to illustrate the method and compare it with traditional ANOVA and Bayesian estimation methods. The results demonstrate the superior flexibility and broader applicability of the proposed methods in diverse contexts. By extending the analysis beyond conventional assumptions, these approaches enhance the accuracy and robustness of statistical inference in mixed models. [ABSTRACT FROM AUTHOR]

Spatial homoscedasticity of the error term is commonly assumed in mixed geographically weighted regression analysis. In many practical situations, however, rarely can we know a priori whether the error term is homoscedastic or not. Therefore, it is necessary to first detect the spatial heteroscedasticity of the error term before the mixed geographically weighted regression model is used. In this paper, a statistic is constructed based on the square root of the absolute value of the residuals obtained by the two step estimation. The three moment $ \chi ^2 $ χ 2 approximation is applied to compute the p value of the test. Furthermore, simulation results show that the proposed test method has high accuracy and satisfactory power in detecting spatial heteroscedasticity, even when the model errors follow non-normal distributions. A real-world data set is analysed to demonstrate the application of the proposed test method and the paper is ended with a conclusion. [ABSTRACT FROM AUTHOR]

In ridge regression, we are often concerned with acquiring ridge estimators that lead to the smallest mean square error (MSE). In this article, we have considered the problem of ridge estimation in the presence of multicollinearity and heteroscedasticity. We have introduced a scaling factor which leads to significantly improved performance of the ridge estimators as compared to their classical counterparts. For illustration purposes, we have applied our proposed methodology to some of the popular existing ridge estimators but it can be extended to other estimators as well. We have also compared our proposed estimator with popular existing estimators dealing estimation problem in the same scenario. Extensive simulations reveal the suitability of the proposed strategy, particularly in the presence of severe multicollinearity and heteroscedasticity. A real-life application highlights that the proposed strategy has the potential to be a useful tool for data analysis in the case of collinear predictors and heteroscedastic errors. [ABSTRACT FROM AUTHOR]

When investigating unobservable, complex traits, data collection and aggregation processes can introduce distinctive features to the data such as boundedness, measurement error, clustering, outliers, and heteroscedasticity. Failure to collectively address these features can result in statistical challenges that prevent the investigation of hypotheses regarding these traits. This study aimed to demonstrate the efficacy of the Bayesian beta-proportion generalized linear latent and mixed model (beta-proportion GLLAMM) (Rabe-Hesketh et al., Psychometrika, 69(2), 167–90, 2004a, Journal of Econometrics, 128(2), 301–23, 2004c, 2004b; Skrondal and Rabe-Hesketh 2004) in handling data features when exploring research hypotheses concerning speech intelligibility. To achieve this objective, the study reexamined data from transcriptions of spontaneous speech samples initially collected by Boonen et al. (Journal of Child Language, 50(1), 78–103, 2023). The data were aggregated into entropy scores. The research compared the prediction accuracy of the beta-proportion GLLAMM with the normal linear mixed model (LMM) (Holmes et al., 2019) and investigated its capacity to estimate a latent intelligibility from entropy scores. The study also illustrated how hypotheses concerning the impact of speaker-related factors on intelligibility can be explored with the proposed model. The beta-proportion GLLAMM was not free of challenges; its implementation required formulating assumptions about the data-generating process and knowledge of probabilistic programming languages, both central to Bayesian methods. Nevertheless, results indicated the superiority of the model in predicting empirical phenomena over the normal LMM, and its ability to quantify a latent potential intelligibility. Additionally, the proposed model facilitated the exploration of hypotheses concerning speaker-related factors and intelligibility. Ultimately, this research has implications for researchers and data analysts interested in quantitatively measuring intricate, unobservable constructs while accurately predicting the empirical phenomena. [ABSTRACT FROM AUTHOR]

We present a Bayesian approach for the analysis of rating data when a scaling component is taken into account, thus incorporating a specific form of heteroskedasticity. Model-based probability effect measures for comparing distributions of several groups, adjusted for explanatory variables affecting both location and scale components, are proposed. Markov Chain Monte Carlo techniques are implemented to obtain parameter estimates of the fitted model and the associated effect measures. An analysis on students' evaluation of a university curriculum counselling service is carried out to assess the performance of the method and demonstrate its valuable support for the decision-making process. [ABSTRACT FROM AUTHOR]

We propose a model for interval-valued time series that specifies the conditional joint distribution of the upper and lower bounds as a mixture of truncated bivariate normal distributions. It preserves the interval natural order and provides great flexibility on capturing potential conditional heteroscedasticity and non-Gaussian features. The standard expectation maximization (EM) algorithm applied to truncated mixtures does not provide a closed-form solution in the M step. A new EM algorithm solves this problem. The model applied to the interval-valued IBM daily stock returns exhibits superior performance over competing models in-sample and out-of-sample evaluation. A trading strategy showcases the usefulness of our approach. [ABSTRACT FROM AUTHOR]

We study two sources of heteroscedasticity in high-frequency financial data and estimate their contribution to overall volatility by means of a Markov switching (MS) structural VAR model. We achieve identification for all coefficients by assuming that the structural errors follow a GARCH-DCC process. Using transaction data of the EUR/USD interdealer market in 2016, we first detect three regimesof volatility. Then we show that both sources of volatility matter for the transmission of shocks, and that information is channeled to the market mostly through demand shocks. This suggests that, on the EUR/USD market, some liquidity takers (LTs) are better informed than both liquidity providers and those LTs who follow a feedback strategy. [ABSTRACT FROM AUTHOR]

In efficacy and safety studies, a vital research concern is to determine the therapeutic window of a pharmaceutical compound. The approach to finding minimum effective dose and maximum safe dose involves multiple comparisons. Generally, in such a problem, a family‐wise error rate is inherited if multiplicity adjustment is not handled properly. This article without a need for multiplicity adjustment formulates a stepwise confidence interval method to identify a therapeutic window of a pharmaceutical compound when equality of variances cannot be assumed and when ratios of variances are known. This article employed Fieller's method and obtained individual confidence intervals for the identification of the minimum effective dose and maximum safe dose. A simulation study was performed and the results show that the confidence interval method proposed in this article controls the family‐wise error rate strongly. Power increases whenever the ratio of means increases and decreases against higher clinical relevance margins. The proposed procedure was applied to real data and provided optimum results. It was also observed that as both the ratio of means and the sample sizes increase, power increases accordingly. [ABSTRACT FROM AUTHOR]

Multivariate regression is a widely used technique for large-scale statistical applications. In this paper, we propose a novel method for the multivariate regression model, called multivariate weighted lasso (MWL). We consider the heteroscedasticity in the noise matrix and introduce an adjustable weight to calibrate the fitting residuals of different responses. The proposed method shows an advantage in complex multivariate regressions with heteroscedasticity. To implement the procedure, an efficient algorithm is provided based on the multivariate coordinate descent. We provide theoretical guarantees for the proposed method. Numerical simulations and financial applications are conducted using the proposed and other existing methods. The results indicate that the proposed method performs well in both variable selection and coefficient estimation. [ABSTRACT FROM AUTHOR]

This study considers an estimator for the asymptotic variance-covariance matrix in time-series quantile regression models which is robust to the presence of heteroscedasticity and autocorrelation. When regression errors are serially correlated, the conventional quantile regression standard errors are invalid. The proposed solution is a quantile analogue of the Newey-West robust standard errors. We establish the asymptotic properties of the heteroscedasticity and autocorrelation consistent (HAC) covariance matrix estimator and provide an optimal bandwidth selection rule. The quantile sample autocorrelation coefficient is biased toward zero in finite sample which adversely affects the optimal bandwidth estimation. We propose a simple alternative estimator that effectively reduces the finite sample bias. Numerical simulations provide evidence that the proposed HAC covariance matrix estimator significantly improves the size distortion problem. To illustrate the usefulness of the proposed robust standard error, we examine the impacts of the expansion of renewable energy resources on electricity prices. for this article are available online. [ABSTRACT FROM AUTHOR]

We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular, it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of an experiment. [ABSTRACT FROM AUTHOR]

Multilevel modeling (MLM) is commonly used in psychological research to model clustered data. However, data in applied research usually violate one of the essential assumptions of MLM—homogeneity of variance. While the fixed-effect estimates produced by the maximum likelihood method remain unbiased, the standard errors for the fixed effects are misestimated, resulting in inaccurate inferences and inflated or deflated type I error rates. To correct the bias in fixed effects standard errors and provide valid inferences, small-sample corrections such as the Kenward-Roger (KR) adjustment and the adjusted cluster-robust standard errors (CR-SEs) with the Satterthwaite approximation for t tests have been used. The current study compares KR with random slope (RS) models and the adjusted CR-SEs with ordinary least squares (OLS), random intercept (RI) and RS models to analyze small, heteroscedastic, clustered data using a Monte Carlo simulation. Results show the KR procedure with RS models has large biases and inflated type I error rates for between-cluster effects in the presence of level 2 heteroscedasticity. In contrast, the adjusted CR-SEs generally yield results with acceptable biases and maintain type I error rates close to the nominal level for all examined models. Thus, when the interest is only in within-cluster effect, any model with the adjusted CR-SEs could be used. However, when the interest is to make accurate inferences of the between-cluster effect, researchers should use the adjusted CR-SEs with RS to have higher power and guard against unmodeled heterogeneity. We reanalyzed an example in Snijders & Bosker (2012) to demonstrate the use of the adjusted CR-SEs with different models. [ABSTRACT FROM AUTHOR]

Measuring stock market volatility and its determinants is critical for stock market participants, as volatility spillover effects affect corporate performance. This study adopted a novel approach to analysing and implementing GARCH-MIDAS modelling methods. The classical GARCH as a benchmark and the univariate GARCHMIDAS framework are the GARCH family models whose forecasting outcomes are examined. The outcome of GARCH-MIDAS analyses suggests that inflation, interest rate, exchange rate, and oil price are significant determinants of the volatility of the Johannesburg Stock Market All Share Index. While for Nigeria, the volatility reacts significantly to the exchange rate and oil price. Furthermore, inflation, exchange rate, interest rate, and oil price significantly influence Ghanaian equity volatility, especially for the long-term volatility component. The significant shock of the oil price and exchange rate to volatility is present in all three markets using the generalized autoregressive conditional heteroscedastic-mixed data sampling (GARCH-MIDAS) framework. The GARCH-MIDAS, with a powerful fusion of the GARCH model’s volatility-capturing capabilities and the MIDAS approach’s ability to handle mixed-frequency data, predicts the volatility for all variables better than the traditional GARCH framework. Incorporating these two techniques provides an innovative and comprehensive approach to modelling stock returns, making it an extremely useful tool for researchers, financial analysts, and investors. [ABSTRACT FROM AUTHOR]

This paper focuses on the factor-augmented panel regression models with missing data and individual-varying factors. A so-called CCEM estimator for the slope coefficient is proposed and its asymptotic properties are investigated under some regularity conditions. Furthermore, a joint test statistic is constructed for serial correlation and heteroscedasticity in the idiosyncratic errors. Under the null hypothesis, the test statistic can be shown to be asymptotically chi-square distributed. Monte Carlo simulation results show that the proposed estimator and test statistic have desired performance in finite samples. [ABSTRACT FROM AUTHOR]

Mendelian randomization (MR) addresses causal questions using genetic variants as instrumental variables. We propose a new MR method, G-Estimation under No Interaction with Unmeasured Selection (GENIUS)-MAny Weak Invalid IV, which simultaneously addresses the 2 salient challenges in MR: many weak instruments and widespread horizontal pleiotropy. Similar to MR-GENIUS, we use heteroscedasticity of the exposure to identify the treatment effect. We derive influence functions of the treatment effect, and then we construct a continuous updating estimator and establish its asymptotic properties under a many weak invalid instruments asymptotic regime by developing novel semiparametric theory. We also provide a measure of weak identification, an overidentification test, and a graphical diagnostic tool. [ABSTRACT FROM AUTHOR]

This study is directed at gauging the equity price risk of the Indian commercial banks for the period 2003–2020. Parametric value-at-risk (VaR) is employed to estimate the downside risk. Further, the univariate exponential generalized auto regressive conditional heteroskedasticity (EGARCH) model is also used to find out the existence of stylised aspects of volatility. The outcomes point towards the existence of volatility clustering, persistence and asymmetry, but differ from bank to bank. Furthermore, the parametric VaR model that assumes normal distribution and student's t -distribution is not found to be an accurate model for all the banks. Tail risk is also found to be significant, and thus, justifies the Basel Committee's decision to shift towards an expected shortfall. However, these conventional VaR models should be supplemented by internal models, taking into consideration, bank-specific characteristics. JEL: G01, G15, I15, G17, G28 [ABSTRACT FROM AUTHOR]

Abstract Background A platform trial approach allows adding arms to on-going trials to speed up intervention discovery programs. A control arm remains open for recruitment in a platform trial while intervention arms may be added after the onset of the study and could be terminated early for efficacy and/or futility when early stopping is allowed. The topic of utilising non-concurrent control data in the analysis of platform trials has been explored and discussed extensively. A less familiar issue is the presence of heterogeneity, which may exist for example due to modification of enrolment criteria and recruitment strategy. Method We conduct a simulation study to explore the impact of heterogeneity on the analysis of a two-stage platform trial design. We consider heterogeneity in treatment effects and heteroscedasticity in outcome data across stages for a normally distributed endpoint. We examine the performance of some hypothesis testing procedures and modelling strategies. The use of non-concurrent control data is also considered accordingly. Alongside standard regression analysis, we examine the performance of a novel method that was known as the pairwise trials analysis. It is similar to a network meta-analysis approach but adjusts for treatment comparisons instead of individual studies using fixed effects. Results Several testing strategies with concurrent control data seem to control the type I error rate at the required level when there is heteroscedasticity in outcome data across stages and/or a random cohort effect. The main parameter of treatment effects in some analysis models correspond to overall treatment effects weighted by stage wise sample sizes; while others correspond to the effect observed within a single stage. The characteristics of the estimates are not affected significantly by the presence of a random cohort effect and/ or heteroscedasticity. Conclusion In view of heterogeneity in treatment effect across stages, the specification of null hypotheses in platform trials may need to be more subtle. We suggest employing testing procedure of adaptive design as opposed to testing the statistics from regression models; comparing the estimates from the pairwise trials analysis method and the regression model with interaction terms may indicate if heterogeneity is negligible.

When one-way ANOVA is statistically significant, a multiple comparison problem arises, hence post-hoc tests are needed to elucidate between which groups significant differences are found. Different post-hoc tests have been proposed for each situation regarding heteroscedasticity and sample size groups. This study aims to compare the Type I error (α) rate of 10 post-hoc tests in four different conditions based on heteroscedasticity and balance between-group sample size. A Montecarlo simulation study was carried out on a total of 28 data sets, with 10,000 resamples in each, distributed through four conditions. One-way ANOVA tests and post-hoc tests were conducted to estimate the α rate at a 95% confidence level. The percentage of times the null hypothesis was falsely refused is used to compare the tests. Three out of four conditions demonstrated considerable variability among sample sizes. However, the best post-hoc test in the second condition (heteroscedastic and balance group) did not depend on simple size. In some cases, inappropriate post-hoc tests were more accurate. Homoscedasticity and balance between-group sample size should be considered for appropriate post-hoc test selection.

In this article, statistical tests concerning the trend coefficient in cointegrating regressions are addressed for the case when the stochastic regressors have deterministic linear trends. The self‐normalization (SN) approach is adopted for developing inferential methods in the integrated and modified ordinary least squares (IMOLS) estimation framework. Two different self‐normalizers are used to construct the SN test statistics: a functional of the recursive IMOLS estimators and a functional of the IMOLS residuals. These two self‐normalizers produce two SN tests, denoted by TSNϵ and τδ1η^T⊥ respectively. Neither test requires studentization with a heteroskedasticity and autocorrelation consistent (HAC) estimator. A trimming parameter ϵ must be chosen to implement the TSNϵ test, whereas the τδ1η^T⊥ test does not require any tuning parameter. In the simulation, the QSNϵ≡TSNϵ2 test exhibits the smallest size distortion among the inferential methods examined in this article. However, this may come with some loss of power, particularly in small samples. [ABSTRACT FROM AUTHOR]

An increase in location is often accompanied by an increase in variability. Moreover, in randomized studies, the presence of heteroscedasticity can indicate a treatment effect. In these cases a location-scale test is appropriate. A common approach of a location-scale test is to use the sum of a location and a scale test statistic. In this study, we focus on one-sided location-scale tests. We introduce a one-sided Lepage-type test statistic. Since right-skewed data are common in many real-world applications, we design test statistics that are powerful also for right-skewed data. Moreover, this paper introduces both a maximum test and an adaptive test utilizing the one-sided Lepage-type test statistics. The limiting distributions of the maximum test statistics are also derived. We assess the performance of the different test statistics in various scenarios for continuous distributions through Monte Carlo simulations. Our simulation results demonstrate that the proposed new test statistics can significantly increase and stabilize statistical power, making it strong competitors to existing location-scale tests. We present practical illustrations based on example data and conclude with some final remarks. [ABSTRACT FROM AUTHOR]

AbstractData heterogeneity is a challenging issue for modern statistical data analysis. There are different types of data heterogeneity in practice. In this article, we consider potential structural changes and complicated tail distributions. There are various existing methods proposed to handle either structural changes or heteroscedasticity. However, it is difficult to handle them simultaneously. To overcome this limitation, we consider statistically and computationally efficient change point detection and localization in high-dimensional quantile regression models. Our proposed framework is general and flexible since the change points and the underlying regression coefficients are allowed to vary across different quantile levels. The model parameters, including the data dimension, the number of change points, and the signal jump size, can be scaled with the sample size. Under this framework, we construct a novel two-step estimation of the number and locations of the change points as well as the underlying regression coefficients. Without any moment constraints on the error term, we present theoretical results, including consistency of the change point number, oracle estimation of change point locations, and estimation for the underlying regression coefficients with the optimal convergence rate. Finally, we present simulation results and an application to the S&P 100 dataset to demonstrate the advantage of the proposed method. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

This article introduces customized screening ensemble with shape‐adaptive quantile regression (CseAQR), a novel probabilistic interval forecasting method built upon the quantile regression model. CseAQR utilizes ensemble learning to perform adaptive quantile regression prediction, which can handle the heteroscedasticity feature in time series data by using a weighted adaptive allocation loss function to enhance the adaptability of the basic quantile regression model on the dataset. The model performance predictor is used to select the optimal ensemble learner combination, assign reasonable adaptive weights to it, and obtain a preliminary prediction interval through weighted aggregation. Combining ensemble learners not only improves the accuracy and robustness of prediction intervals but also ensures the commutativity required for conformal prediction. Finally, the conformal prediction method is applied to locally adjust the prediction interval, constructing a more consistently aligned prediction interval with the actual data on a narrower basis. [ABSTRACT FROM AUTHOR]

In one-way analysis of variance models, performing simultaneous multiple comparisons of treatment groups with a control group may be of interest. Dunnett's test is used to test such differences and assumes equal variances of the response variable for each group. This assumption is not always met even after transformation. A parametric bootstrap (PB) method is developed here for comparing multiple treatment group means against the control group with unequal variances and unbalanced data. In simulation studies, the proposed method outperformed Dunnett's test in controlling the type I error under various settings, particularly when data have heteroscedastic variance and unbalanced design. Simulations show that power is often lower for the PB method than for Dunnett's test under equal variance, balanced data, or smaller sample size, but similar to or higher than for Dunnett's test with unequal variance, unbalanced data and larger sample size. The method is applied to a dataset concerning isotope levels found in elephant tusks from various geographical areas. These data have very unbalanced group sizes and unequal variances. This example illustrates that the PB method is easy to implement and avoids the need for transforming data to meet the equal variance assumption, simplifying interpretation of results. [ABSTRACT FROM AUTHOR]

This study develops a novel approach for improving stock return volatility forecasts using volatility index information with the entropic tilting technique. Unlike traditional linear heteroskedasticity autoregressive methods with option‐implied information, we first derive predictive densities from traditional models, and then tilt using both the first and second moments of the risk‐neutral distribution, which enables us to capture the nonlinear effect in our specification. The empirical findings demonstrate a substantial enhancement in the forecasting accuracy of all models once the first‐ and second‐moment information is considered, where the improvement is both statistically and economically significant. These results have important implications for risk management in well‐established derivatives markets. [ABSTRACT FROM AUTHOR]

Summary: Heteroskedasticity is a common feature in empirical time series analysis, and in this paper, we consider the effects of heteroskedasticity on statistical tests for equal forecast accuracy. In such a context, we propose two new Diebold–Mariano‐type tests for equal accuracy that employ nonparametric estimation of the loss differential variance function. We demonstrate that these tests have the potential to achieve power improvements relative to the original Diebold–Mariano test in the presence of heteroskedasticity, for a quite general class of loss differential series. The size validity and potential power superiority of our new tests are studied theoretically and in Monte Carlo simulations. We apply our new tests to competing forecasts of changes in the dollar/sterling exchange rate and find the new tests provide greater evidence of differences in forecast accuracy than the original Diebold–Mariano test, illustrating the value of these new procedures for practitioners. [ABSTRACT FROM AUTHOR]

Purpose: Given the difficulties in finding significant exchange rate exposure in the extant literature, this paper attempts to resolve the so-called "exposure puzzle" by investigating whether currency movements have any significant impact on international industry returns. Design/methodology/approach: This paper utilizes the multivariate Generalized AutoRegressive Conditional Heteroskedasticity (MGARCH) methodology to estimate both symmetric and asymmetric exchange rate exposures for each industry common across 12 countries simultaneously. Findings: The empirical results show that exchange rate exposure is not only statistically significant but also economically important based on the estimation of an asymmetric three-factor exposure model using MGARCH methodology. This is an extremely important finding as it suggests that the "exposure puzzle" may not be a puzzle at all once a better methodology is utilized in the estimation. Research limitations/implications: Because this study tries to resolve the exchange rate exposure puzzle by focusing on whether exchange rate movements affect ex-post returns as opposed to ex ante expected returns and given the significant exposures with respect to different risk factors found in the study, it is interesting to see if any of these risk factors commands a risk premium. In other words, a natural extension of this study is to test whether any of these risk factors is priced in international industry returns. Practical implications: The findings of the study have interesting implications for international investors who would like to diversify their portfolios across different industries and are concerned about whether the unexpected movements in the bilateral exchange rates will affect their portfolio returns in addition to its interest rate and world market risk exposures. Originality/value: The study utilizes the MGARCH methodology, which has not been fully exploited in the exchange rate exposure literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scale-invariant test for linear hypothesis of mean vectors with heteroscedasticity in high-dimensional settings. Most existing tests impose strong conditions on covariance matrices so that null distributions of their tests are asymptotically normal, which restricts the application of test procedures. However, our proposed test has different null distributions under mild conditions. Additionally, the well-known Welch-Satterthwaite chi-square approximation we adopted can automatically mimic the shapes of the null distributions of the test statistic. The performances of the test are illustrated by simulation and real data in finite samples which show that it has robustness and is more powerful than three competitors. [ABSTRACT FROM AUTHOR]

Background: A platform trial approach allows adding arms to on-going trials to speed up intervention discovery programs. A control arm remains open for recruitment in a platform trial while intervention arms may be added after the onset of the study and could be terminated early for efficacy and/or futility when early stopping is allowed. The topic of utilising non-concurrent control data in the analysis of platform trials has been explored and discussed extensively. A less familiar issue is the presence of heterogeneity, which may exist for example due to modification of enrolment criteria and recruitment strategy. Method: We conduct a simulation study to explore the impact of heterogeneity on the analysis of a two-stage platform trial design. We consider heterogeneity in treatment effects and heteroscedasticity in outcome data across stages for a normally distributed endpoint. We examine the performance of some hypothesis testing procedures and modelling strategies. The use of non-concurrent control data is also considered accordingly. Alongside standard regression analysis, we examine the performance of a novel method that was known as the pairwise trials analysis. It is similar to a network meta-analysis approach but adjusts for treatment comparisons instead of individual studies using fixed effects. Results: Several testing strategies with concurrent control data seem to control the type I error rate at the required level when there is heteroscedasticity in outcome data across stages and/or a random cohort effect. The main parameter of treatment effects in some analysis models correspond to overall treatment effects weighted by stage wise sample sizes; while others correspond to the effect observed within a single stage. The characteristics of the estimates are not affected significantly by the presence of a random cohort effect and/ or heteroscedasticity. Conclusion: In view of heterogeneity in treatment effect across stages, the specification of null hypotheses in platform trials may need to be more subtle. We suggest employing testing procedure of adaptive design as opposed to testing the statistics from regression models; comparing the estimates from the pairwise trials analysis method and the regression model with interaction terms may indicate if heterogeneity is negligible. [ABSTRACT FROM AUTHOR]

Introduction: Crown width (CW) is a significant variable of tree growth, but measuring crown width is laborious and time-consuming. Diameter at breast height (D) is a commonly used growth variable in crown width prediction. Here, a CW-D model was developed to estimate the crown width of larch. Methods: The data of 1,515 larch trees were collected in Guandi mountain, the northern China. We chose linear function, quadratic function, and other form of base functions to develop the CW models, and we introduced non-linear least squares techniques (NLS), non-linear mixed-effect (NLME), and Bayesian method in modeling process. Because the data was from different plot, we added a plot level random effect in NLME method to predict the effect from environment. For equally comparing the Bayesian method with the NLME, we also added the plot level random effect to the Bayesian MCMC procedure. We selected Akaike's information criterion and logarithm likelihood to evaluate NLS and NLME models, and chose deviance information criterion and stationary test to test Bayesian method. These methods had another three same indicators (the determination coeffcient, rootmean square error, andmean absolute deviation) in model evaluation. Results and discussion: Heteroskedasticity wasn't occurred in this study. The model I.2 (quadratic formula) showed a best fitting effect in each method, and Bayesian method with random effect was slightly superior than other methods. Therefore, the selected final model was quadratic function by Bayesian method with plot level random effect, this combination had the highest prediction accuracy in the larch trees' crown width estimation of Guandi mountain. [ABSTRACT FROM AUTHOR]

Purpose: The 2016 EQ-5D-3L value set for Trinidad and Tobago (T&T) allows for the calculation of EQ-5D-5L values via the crosswalk algorithm. The 2016 value set was based on methods predating the EQ-VT protocol, now considered the gold standard for developing EQ-5D value sets. Furthermore, direct elicitation of EQ-5D-5L is preferred over crosswalked values. This study aimed to produce an EQ-5D-5L value set for T&T. Methods: A representative sample (age, sex, geography) of adults each completed 10 composite Time Trade-Off (cTTO) tasks and 12 Discrete Choice Experiment (DCE) tasks in face-to-face interviews. The cTTO data were analyzed using a Tobit model that corrects for heteroskedasticity. DCE data were analyzed using a mixed logit model. The cTTO and DCE data were combined in hybrid models. Results: One thousand and seventy-nine adults completed the valuation interviews. Among the modelling approaches that were explored, the hybrid heteroskedastic Tobit model produced all internally consistent, statistically significant coefficients, and performed best in terms of out-of-sample predictivity for single states. Compared to the existing EQ-5D-5L crosswalk set, the new value set had a higher number of negative values (236 or 7.6% versus 21 or 0.7%). The mean absolute difference was 0.157 and the correlation coefficient between the two sets was 0.879. Conclusion: This study provides a value set for the EQ-5D-5L for T&T using the EQ-VT protocol. We recommend this value set for QALY computations relating to T&T. [ABSTRACT FROM AUTHOR]

This article assesses the predictive accuracy of factor models utilizing Partial·Least·Squares (PLS) and Principal·Component·Analysis (PCA) in comparison to autometrics and penalization techniques. The simulation exercise examines three types of scenarios by introducing the issues of multicollinearity, heteroscedasticity, and autocorrelation. The number of predictors and sample size are adjusted to observe the effects. The accuracy of the models is evaluated by calculating the Root·Mean·Square·Error (RMSE) and the Mean·Absolute·Error (MAE). In the presence of severe multicollinearity, the factor approach utilizing (PLS demonstrates exceptional performance in comparison. Autometrics achieves the lowest RMSE and MAE values across all levels of heteroscedasticity. Autometrics provides better forecasts with low and moderate autocorrelation. However, Elastic·Smoothly·Clipped·Absolute·Deviation (E-SCAD) forecasts well with severe autocorrelation. In addition to the simulation, we employ a popular Pakistani macroeconomic dataset for empirical research. The dataset contains 79 monthly variables from January 2013 to December 2020. The competing approaches perform differently compared to the simulation datasets, although "The PLS factor approach outperforms its competing approaches in forecasting, with lower RMSE and MAE". It is more probable that the actual dataset exhibits a high degree of multicollinearity. [ABSTRACT FROM AUTHOR]

A covariate-driven random coefficient generalized conditional heteroscedasticity (GARCH) time series model with the form of the buffered autoregression (BRC-GARCH-X) for modeling financial time series data is considered. As an extension of the classical two-regime threshold process, the buffered autoregression enjoys a more flexible regime-switching mechanism. Furthermore, the main feature of this model is that the threshold variable for regime-switching is formulated as a weighted average of important auxiliary variables. The estimator for regression parameters is obtained by the quasi-maximum exponential likelihood (QMEL) estimator and the corresponding asymptotic properties are established. Moreover, a mixed portmanteau test is developed for diagnostic checking. And a reasonable method for selecting search ranges for thresholds is also proposed and simulation studies are considered. As an application, we bring attention to some features of of stock returns of SP500 which shows that our model is feasible. [ABSTRACT FROM AUTHOR]

Objective: We propose a simple approach to dealing with partial contestation in models of multiparty elections. Methods: Our proposed approach is to add a tiny value to the vote share of parties that do not contest a district and then to include dummy variables identifying those districts in which parties do not compete. We can then estimate a single system of equations using a seemingly unrelated regression (SUR) approach and Aitchison's log‐ratio transformation. In our SUR system, we interact the dummy variable for a party that partially contested districts with other predictors in the equation that uses the share of votes of the same party in the log‐ratio outcome. Finally, we estimate robust standard errors for predictors in this equation to address heteroscedasticity. Results: We demonstrate the utility of our approach using simulated data and election results from the English parliamentary elections in 2017. Conclusion: From our simulations, we find that our recommended approach performs as well as that proposed by Tom, Tucker, and Wittenberg. Our strategy is advantageous in that it is easy to estimate, uses information from all districts, and addresses partial contestation in real‐world elections with a single system of seemingly unrelated regressions. [ABSTRACT FROM AUTHOR]

Simulation-based optimization is an effective solution to complex transportation problems relying on stochastic simulations. However, existing studies generally perform a fixed number of evaluations for each decision vector across the design space, overlooking simulation heteroscedasticity and its effects on solution efficiency and robustness. In this paper, we treat the number of evaluations as an adaptive variable depending upon the simulation heteroscedasticity and the potential optimality of each decision vector. A statistical method, which automatically determines the variable number of evaluations, is presented for a range of derivative-free optimization methods. By fusing Bayesian inference with the probability of correct selection, it permits adaptive allocation of budgeted computational resources to achieve improved solution efficiency and robustness. The method is integrated with the deterministic global optimizer DIviding RECTangles (DIRECT) to yield NoisyDIRECT as a continuous simulation-based robust optimization method (which is open sourced). The key properties of the method are proved and discussed. Numerical experiments on difficult test functions are first conducted to verify the improvement of NoisyDIRECT compared with DIRECT and Bayesian optimization. Given the same computational budget, NoisyDIRECT can better locate the global optimum than the other two alternatives. Applications to representative simulation-based transportation problems, including an M/M/1 queueing problem and a parking pricing problem, are then presented. The results demonstrate the ability of NoisyDIRECT to pinpoint the optimal solution via adaptive computational resources allocation, achieving the desired level of robustness. Funding: This work was supported by the Youth Program [Grant 52102375] and the Key Project [Grant 52131203] of the National Natural Science Foundation of China, the Youth Program [Grant BK20210247] of the Natural Science Foundation of Jiangsu Province, and the High-Level Personnel Project of Jiangsu Province [Grant JSSCBS20220099]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0485. [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]

During periods of economic prosperity, increased profit opportunities lead to active transactions in the existing housing market and heightened consumer risk preferences. At this time, developers increase the launch of presale housing projects to expand business opportunities, indirectly filling the supply gap of existing homes and alleviating housing demand. However, in reality, prices in both the presale and existing housing markets mutually drive each other up, further delaying the stabilization of housing prices. Therefore, whether the launch of presale housing projects can alleviate the demand for existing homes and achieve the function of price moderation becomes a researchworthy question. This study aims to investigate whether the volume of presale housing projects moderates or exacerbates housing prices. We focus on the volatility of aggregate residential housing prices in Taichung City, Taiwan, using transaction data of monthly average prices for Apartmemt complexes Units (high-rise buildings and high-rise apartments) from August 2012 to June 2023. We employ the ARCH/GARCH models to analyze the impact of presale housing project volumes on housing price volatility. Stability and convergence indicate a moderating effect of presale housing project volumes on housing prices; otherwise, it indicates exacerbation. After model testing, this study selects the most appropriate model as the ARIMA(3,1,0)-GARCH(1,0) model. This study finds that during periods of economic prosperity, the volume of presale housing projects does not aid in stabilizing or converging residential housing prices; instead, it exacerbates market disruption. [ABSTRACT FROM AUTHOR]

Purpose: This study evaluates the Federal Reserve (Fed) initial and final forecasts of the unemployment rate for 1983Q1-2018Q4. The Fed initial forecasts in a typical quarter are made in the first month (or immediately after), and the final forecasts are made in the third month of the quarter. The analysis also includes the private forecasts, which are made close to the end of the second month of the quarter. Design/methodology/approach: In evaluating the multi-period forecasts, the study tests for systematic bias, directional accuracy, symmetric loss, equal forecast accuracy, encompassing and orthogonality. For every test equation, it employs the Newey–West procedure in order to obtain the standard errors corrected for both heteroscedasticity and inherent serial correlation. Findings: Both Fed and private forecasts beat the naïve benchmark and predict directional change under symmetric loss. Fed final forecasts are more accurate than initial forecasts, meaning that predictive accuracy improves as more information becomes available. The private and Fed final forecasts contain distinct predictive information, but the latter produces significantly lower mean squared errors. The results are mixed when the study compares the private with the Fed initial forecasts. Additional results indicate that Fed (private) forecast errors are (are not) orthogonal to changes in consumer expectations about future unemployment. As such, consumer expectations can potentially help improve the accuracy of private forecasts. Originality/value: Unlike many other studies, this study focuses on the unemployment rate, since it is an important indicator of the social cost of business cycles, and thus its forecasts are of special interest to policymakers, politicians and social scientists. Accurate unemployment rate forecasts, in particular, are essential for policymakers to design an optimal macroeconomic policy. [ABSTRACT FROM AUTHOR]

Most statistical methods in time series analytics assume that the residuals are independently and identically distributed with zero mean and constant variance. In real cases, this assumption may be violated. Nowadays, data are dynamic and highly volatile, particularly in finance. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model is a statistical method for nonconstant conditional variance that can capture the volatility data. Recently, artificial intelligence methods are gaining popularity and have promising performance, one of those is the Long Short-Term Memory (LSTM) method. However, due to the filtering process by forget gate in the LSTM cell some information is missing, which can decrease the prediction’s accuracy. This study proposes a method, namely Hybrid GARCH-LSTM, to overcome those limitation. The performance of the proposed method is evaluated in the simulation and empirical data and compared with GARCH and LSTM model. The results show that the Hybrid GARCH–LSTM model is able to recognize the volatility pattern of data well and outperforms all the other models. [ABSTRACT FROM AUTHOR]