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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]

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]

Estimation of a function, or its derivatives via nonparametric regression requires selection of one or more tuning parameters. In the present work, we propose a tuning parameter selection criterion called DCp for nonparametric derivative estimation in random design. Our criterion is general in that it can be applied with any nonparametric estimation method which is linear in the observed outcomes. Charnigo et al. [A generalized $ C_p $ C p criterion for derivative estimation. Technometrics. 2011;53(3):238–253] had proposed a GCp criterion for a similar purpose, assuming values of the covariate to be fixed and constant error variance. Here we consider the setting with random design and non-constant error variance since the covariate values will not generally be fixed and equally spaced in real data applications. We justify DCp in this setting both theoretically and by simulation. We also illustrate use of DCp with two economics data sets. [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]

A Zero-drift GARCH (ZD-GARCH) model is recently proposed to study conditional and unconditional heteroskedasticity together. Despite its attractive statistical properties, our research demonstrates that the stability test based on this model fails when structural changes are present. To overcome this issue, we allow the Markov regime-switching (MRS) feature within the ZD-GARCH framework and propose an MRS-ZD-GARCH model. A revised stability estimator is further derived. The effectiveness of our proposed approach to test the stability with and without structural changes is evidenced via simulation studies. Using the empirical data of the S&P 500, NASDAQ and Apple returns, we show that the new model can also outperform the ZD-GARCH model in practice and provide more informative results. Therefore, the MRS-ZD-GARCH model could be a widely useful tool to study the stability of financial data and help address risk management issues in other contexts. [ABSTRACT FROM AUTHOR]

Background: The non-inferiority test is a reasonable approach to assessing a new treatment in a three-arm trial. The three-arm trial consists of a placebo, reference, and an experimental treatment. The non-inferiority is often measured by the mean differences between the experimental and the placebo groups relative to the mean differences between the reference and the placebo groups. Methods: To cope with possible estimation distortion due to the allowance of heteroskedasticity, we adjust the measurement of non-inferiority by the incorporation of coefficient of variation (CV) of the experimental, the reference and the placebo groups. In this research, we propose a generalized p -value based method (GPV-based method) to facilitate non-inferiority tests for the means with unknown coefficient of variation in a three-arm trial. Results: The simulation results show that the GPV-based method can not only adequately control type I error rate at nominal level better but also provide power higher than those from Delta method and the empirical bootstrap method, which verifies the feasibility of our adjustment. Conclusions: We revise the measurement of non-inferiority by deducting the CV of each kind of treatment from the average effect of trials. CVs are included in the non-inferiority explicitly to help prevent possible estimating distortion if heteroskedasticity is allowed. Through the simulation study, the performance of GPV-based method for facilitating non-inferiority tests for the means with unknown CV in a three-arm trial is better than those from empirical bootstrap method and Delta method for small, medium and large sample sizes. Hence, the GPV-based method is recommended to be used to conduct the non-inferiority test for the means with unknown CV in a three-arm trial. The GPV-based method still performs well in non-normality cases. [ABSTRACT FROM AUTHOR]

Homogeneity of variance (HOV) is a well-known but often untested assumption in the context of multilevel models (MLMs). However, depending on how large the violation is, how different group sizes are, and the variance pairing, standard errors can be over or underestimated even when using MLMs, resulting in questionable inferential tests. We evaluate several tests (e.g., the H statistic, Breusch Pagan, Levene's test) that can be used with MLMs to assess violations of HOV. Although the traditional robust standard errors used with MLMs require at least 50 clusters to be effective, we assess a robust standard error adjustment (i.e., the CR2 estimator) that can be used even with a few clusters. Findings are assessed using a Monte Carlo simulation and are further illustrated using an applied example. We show that explicitly modeling the heterogenous variance structures or using the CR2 estimator are both effective at ameliorating the issues associated with the fixed effects of the regression model related to violations of HOV resulting from between-group differences. [ABSTRACT FROM AUTHOR]

Test equating is a statistical procedure to make scores from different test forms comparable and interchangeable. Focusing on an IRT approach, this paper proposes a novel method that simultaneously links the item parameter estimates of a large number of test forms. Our proposal differentiates itself from the current state of the art by using likelihood-based methods and by taking into account the heteroskedasticity and the correlation of the item parameter estimates of each form. Simulation studies show that our proposal yields equating coefficient estimates which are more efficient than what is currently available in the literature. [ABSTRACT FROM AUTHOR]

This paper proposes estimating parameters in higher-order spatial autoregressive models, where the error term also follows a spatial autoregression and its innovations are heteroskedastic, by matching the simple ordinary least squares estimator with its analytical approximate expectation, following the principle of indirect inference. The resulting estimator is shown to be consistent, asymptotically normal, simulation-free, and robust to unknown heteroskedasticity. Monte Carlo simulations demonstrate its good finite-sample properties in comparison with existing estimators. An empirical study of Airbnb rental prices in the city of Asheville illustrates that the structure of spatial correlation and effects of various factors at the early stage of the COVID-19 pandemic are quite different from those during the second summer. Notably, during the pandemic, safety is valued more and on-line reviews are valued much less. [ABSTRACT FROM AUTHOR]

The stock market is a chaotic system, and stock forecasting has been the research focus. This paper proposes a multi-factor model based on DeepForest-CQP to make it more applicable to the stock domain. A t-test is used for selecting factors, and orthogonalization and heteroskedasticity tests are performed for the combined factors, which are particularly important in stock forecasting. DeepForest-CQP was combined with the multi-factor model to construct a stock selection model that can achieve higher returns. The obtained multi-factor quantitative stock selection model is used to study stock selection strategies, and simulated trading is used to evaluate the multi-factor model and stock selection strategies and compare them with various machine learning multi-factor models. The experimental results show that the DeepForest-CQP-based multi-factor stock selection model achieves significant performance advantages in all backtesting metrics. [ABSTRACT FROM AUTHOR]

Background: Preference heterogeneity in health valuation has become a topic of greater discussion among health technology assessment agencies. To better understand heterogeneity within a national population, valuation studies may identify latent groups that place different absolute and relative importance (i.e., scale and taste parameters) on the attributes of health profiles. Objective: Using discrete choice responses from a Peruvian valuation study, we estimated EQ-5D-5L values on a quality-adjusted life-year (QALY) scale accounting for latent heterogeneity in scale and taste, as well as controlling heteroskedasticity at task level variation. Method: We conducted a series of latent class analyses, each including the 20 main effects of the EQ-5D-5L and a power function that relaxes the constant proportionality assumption (i.e., discounting) between value and lifespan. Taste class membership was conditional on respondent-specific characteristics and their experience with the composite time trade-off (cTTO) tasks. Scale class membership was conditional on behavioral characteristics such as survey duration and self-stated difficulty level in understanding tasks. Each analysis allowed the scale factor to vary by task type and completion time (i.e., heteroskedasticity). Results: The results indicated three taste classes: a quality-of-life oriented class (33.35%) that placed the highest value on levels of severity, a length-of-life oriented class (26.72%) that placed the highest value on lifespan, and a middle class (39.71%) with health attribute effects lower than the quality class and lifespan effect lower than the length-of-life oriented class. The EQ-5D-5L values ranged from − 2.11 to 0.86 (quality-of-life oriented class), from − 0.38 to 1.02 (middle class), and from 0.36 to 1.01 (length-of-life oriented class). The likelihood of being a member of the quality-of-life class was highly dependent on whether the respondent completed the cTTO tasks (p-value < 0.001), which indicated that the cTTO tasks might cause the Peru respondents to inflate the burden of health problems on a QALY scale compared to those who did not complete the cTTO tasks. The results also showed two scale classes as well as heteroskedasticity within each scale class. Conclusion: Accounting for taste and scale classes simultaneously improveds understanding of preference heterogeneity in health valuation. Future studies may confirm the differences in taste between classes in terms of the effect of quality of life and lifespan attributes. Furthermore, confirmatory evidence is needed on how behavioral variables captured within a study protocol may enhance analyses of preference heterogeneity. [ABSTRACT FROM AUTHOR]

The recent price crash of the New York Mercantile Exchange (NYMEX) crude oil futures contract, which occurred on 20 April 2020, has caused history-writing movements of relative prices. For instance, the West Texas Intermediate (WTI) experienced a negative price. Explosive heteroskedasticity is also evidenced in associated products, such as the Intercontinental Exchange Brent (BRE) and Shanghai International Energy Exchange (INE) crude oil futures. Those movements indicate potential non-stationarity in the conditional volatility with an asymmetric influence of negative shocks. To incorporate those features, which cannot be accommodated by the existing generalized autoregressive conditional heteroskedasticity (GARCH) models, we propose a threshold zero-drift GARCH (TZD-GARCH) model. Our empirical studies of the daily INE returns from March 2018 to April 2020 demonstrate the usefulness of the TZD-GARCH model in understanding the empirical features and in precisely forecasting the volatility of INE. Robust checks based on BRE and WTI over various periods further lead to highly consistent results. Applications of news impact curves and Value-at-Risk (VaR) analyses indicate the usefulness of the proposed TZD-GARCH model in practice. Implications include more effectively hedging risks of crude oil futures for policymakers and market participants, as well as the potential market inefficiency of INE relative to WTI and BRE. [ABSTRACT FROM AUTHOR]

As the building sector contributes approximately three-quarters of the U.S. electricity load, analyzing buildings' energy consumption patterns and establishing their effective operational strategy become of great importance. To achieve those goals, a physics-based building energy model (BEM), which can simulate a building's energy demand under various weather conditions and operational scenarios, has been developed. To obtain accurate simulation outputs, it is necessary to calibrate some parameters required for the BEM's pre-configuration. The BEM calibration is usually accomplished by matching the simulated energy use with the measured one. However, even with the efforts to calibrate the BEM at best, a systematic discrepancy between the two quantities is often observed, preventing the precise estimation of the energy demand. Such discrepancy is referred to as bias in this study. We present a new calibration approach that models the discrepancy to correct the relationship between the simulated and measured energy use. We show that our bias correction can improve predictive performance. Additionally, we observe the heterogeneous variance in the electricity loads, especially in the afternoon hours, which often reduces prediction accuracy and increases uncertainty. To address this issue, we incorporate heterogeneous weights into the least squares loss function. To implement the bias-correction procedure with the weighted least squares formulation, we propose a newly devised iteratively reweighted least squares algorithm. The effectiveness of the proposed calibration methodology is evaluated with a real-world dataset collected from a residential building in Texas. • Accurate estimation of building energy model parameters is significantly important. • Building energy model parameters are calibrated using the novel modeling approach. • The approach corrects the computer model bias and addresses the heterogeneous variance. • A case study demonstrates the superiority of the proposed calibration methodology. [ABSTRACT FROM AUTHOR]

The aim of this study was to model the behavior of particles with aerodynamic diameter lower or equal to 10 μ m (PM10) in the Caribbean area according to African dust seasonality. To carry out this study, PM10 measurement from Guadeloupe (GPE) and Puerto Rico (PR) between 2006 and 2010 were used. Firstly, the missing data issues were addressed using algorithms that we elaborated. Thereafter, the coupled SARIMA-GARCH (Seasonal Autoregressive Integrated Moving Average and Generalized Autoregressive Conditional Heteroscedastic) model was developed and compared to PM10 empirical data. The SARIMA process is representative of the main PM10 sources, while the heteroskedasticity is also taken into account by the G A R C H process. In this framework, PM10 data from GPE and PR are decomposed into the sum of the background atmosphere ( B t = anthropogenic activities + marine aerosol), African dust seasonality ( S t = mineral dust), and extreme events processes ( C t ). Akaike's information criterion (AIC) helped us to choose the best model. Forecast evaluation indexes such as the Mean Absolute Percentage Error (MAPE), the Mean Absolute Scale Error (MASE), and Theil's U statistic provided significant results. Specifically, the MASE and U values were found to be almost zero. Thus, these indexes validated the forecasts of the coupled SARIMA-GARCH model. To sum up, the SARIMA-GARCH combination is an efficient tool to forecast PM10 behavior in the Caribbean area. [ABSTRACT FROM AUTHOR]

Background: Respondents in a health valuation study may have different sources of error (i.e., heteroskedasticity), tastes (differences in the relative effects of each attribute level), and scales (differences in the absolute effects of all attributes). Although prior studies have compared values by preference-elicitation tasks (e.g., paired comparison [PC] and best-worst scaling case 2 [BWS]), no study has yet controlled for heteroskedasticity and heterogeneity (taste and scale) simultaneously in health valuation.Methods: Preferences on EQ-5D-5L profiles were elicited from a random sample of 380 adults from the general population of the Netherlands, using 24 PC and 25 BWS case 2 tasks. To control for heteroskedasticity and heterogeneity (taste and scale) simultaneously, we estimated Dutch EQ-5D-5L values using conditional, heteroskedastic, and scale-adjusted latent class (SALC) logit models by maximum likelihood.Results: After controlling for heteroskedasticity, the PC and BWS values were highly correlated (Pearson's correlation: 0.9167, CI: 0.9109-0.9222) and largely agreed (Lin's concordance: 0.7658, CI: 0.7542-0.7769) on a pits scale. In terms of preference heterogeneity, some respondents (mostly young men) failed to account for any of the EQ-5D-5L attributes (i.e., garbage class), and others had a lower scale (59%; p-value: 0.123). Overall, the SALC model produced a consistent Dutch EQ-5D-5L value set on a pits scale, like the original study (Pearson's correlation:0.7295; Lin's concordance: 0.6904).Conclusions: This paper shows the merits of simultaneously controlling for heteroskedasticity and heterogeneity in health valuation. In this case, the SALC model dispensed with a garbage class automatically and adjusted the scale for those who failed the PC dominant task. Future analysis may include more behavioral variables to better control heteroskedasticity and heterogeneity in health valuation.Highlights: The Dutch EQ-5D-5L values based on paired comparison [PC] and best-worst scaling [BWS] responses were highly correlated and largely agreed after controlling for heteroskedasticity. Controlling for taste and scale heterogeneity simultaneously enhanced the Dutch EQ-5D-5Lvalues by automatically dispensing with a garbage class and adjusting the scale for those who failed the dominant task. After controlling for heteroskedasticity and heterogeneity, this study produced Dutch EQ-5D-5L values on a pits scale moderately concordant with the original values. [ABSTRACT FROM AUTHOR]

In analysis of variance (ANOVA) models, it is generally assumed that the distribution of the error terms is normal with mean zero and constant variance σ 2. Traditionally, a least square (LS) method is used for estimating the unknown parameters and testing the null hypothesis. It is known that, when the normality assumption is not satisfied, LS estimators of the parameters and the test statistics based on them lose their efficiency, see Tukey. On the other hand, a non constant variance problem which is called heteroskedasticity is another serious issue for LS estimators. The LS estimators still remain unbiased but the estimated standard error (SE) is wrong. Because of this, confidence intervals and hypotheses tests cannot be relied on. Welch's ANOVA is the most popular method to solve this problem. In this paper, we assume that the distribution of the error terms is skew-t with non constant variance in one-way ANOVA. We also propose a new test statistics based on the maximum likelihood (ML) estimators of skew-t distribution. A Monte Carlo simulation study is performed to compare traditional LS and Welch's method with the proposed method in terms of Type I errors and the powers. At the end of this study, an example is given for the illustration of the methods. [ABSTRACT FROM AUTHOR]

There has been a recent upsurge of interest in testing for structural changes in heteroskedastic time series, as changes in the variance invalidate the asymptotic distribution of conventional structural change tests. Several tests have been proposed that are robust to general form of heteroskedastic errors. The most popular use a two‐steps approach: first estimate the residuals assuming no changes in the regression coefficients; second, use the residuals to approximate the heteroskedastic asymptotic distribution or take an entire sample average to construct a test for which the variance process is averaged out. An alternative approach was proposed by Perron et al. (Perron et al. (2020). Quantitative Economics11: 1019–1057) who provided a test for changes in the coefficients allowing for changes in the variance of the error term. We show that it transforms the variance profile into one that effectively has very little impact on the size of the test. With respect to the power properties, the two‐steps procedures can suffer from non‐monotonic power problems in dynamic models and in static models with a correction for serial correlation in the error. Most have power equals to size with zero‐mean regressors. Even when the two‐steps tests have power, it is generally lower than that of the latter test. [ABSTRACT FROM AUTHOR]

Structural vector autoregressive analysis aims to trace the contemporaneous linkages among multiple economic time series back to underlying orthogonal structural shocks. Traditionally, researchers rely on economically motivated restrictions to identify these shocks. However, in the presence of heteroskedasticity or non‐Gaussian independent components, only these statistical properties allow a locally unique identification. In this paper, we compare alternative statistical identification procedures under distinct covariance changes and distributional frameworks. We find that statistical identification schemes are robust under distinct data structures to some extent and support researchers in detecting shocks that feature an economic underpinning. The detection of independent components appears most flexible. [ABSTRACT FROM AUTHOR]

In pursuit of efficiency, we propose a new way to construct least squares estimators, as the minimizers of an augmented objective function that takes explicitly into account the variability of the error term and the resulting uncertainty, as well as the possible existence of heteroskedasticity. We initially derive an infeasible estimator which we then approximate using Ordinary Least Squares (OLS) residuals from a first-step regression to obtain the feasible "HOLS" estimator. This estimator has negligible bias, is consistent and outperforms OLS in terms of finite-sample Mean Squared Error, but also in terms of asymptotic efficiency, under all skedastic scenarios, including homoskedasticity. Analogous efficiency gains are obtained for the case of Instrumental Variables estimation. Theoretical results are accompanied by simulations that support them. [ABSTRACT FROM AUTHOR]

Microdata are required to evaluate the distributive impact of the taxation system as a whole (direct and indirect taxes) on individuals or households. However, in European Union countries this information is usually distributed into two separate surveys: the Household Budget Surveys (HBS), including total household expenditure and its composition, and EU Statistics on Income and Living Conditions (EU-SILC), including detailed information about households' income and direct (but not indirect) taxes paid. We present a parametric statistical matching procedure to merge both surveys. For the first stage of matching, we propose estimating total household expenditure in HBS (Engel curves) using a GLM estimator, instead of the traditionally used OLS method. It is a better alternative, insofar as it can deal with the heteroskedasticity problem of the OLS estimates, while making it unnecessary to retransform the regressors estimated in logarithms. To evaluate these advantages of the GLM estimator, we conducted a computational Monte Carlo simulation. In addition, when an error term is added to the deterministic imputation of expenditure in the EU-SILC, we propose replacing the usual Normal distribution of the error with a Chi-square type, which allows a better approximation to the original expenditures variance in the HBS. An empirical analysis is provided using Spanish surveys for years 2012–2016. In addition, we extend the empirical analysis to the rest of the European Union countries, using the surveys provided by Eurostat (EU-SILC, 2011; HBS, 2010). [ABSTRACT FROM AUTHOR]

The Schoenfeld residual-based test for proportional-hazards violations in the Cox duration model is predicated on a key assumption pertaining to homoskedasticity in the residuals. This assumption is likely to be violated in the presence of stratified hazards, which is noted in estat phtest's help file. We provide a wrapper command, stratph, that implements a straightforward modification to the residual-based diagnostic that corrects for the potential assumption violation. We use the stratified hazards example from the stcox help file to demonstrate the stratph command's workings. [ABSTRACT FROM AUTHOR]

In this paper, we consider standard as well as instrumental variables regression. Specification problems related to autocorrelation, heteroskedasticity, neglected non-linearity, unsatisfactory out-of-small performance and endogeneity can be addressed in the context of multi-criteria optimization. The new technique performs well, it minimizes all these problems simultaneously, and eliminates them for the most part. Markov Chain Monte Carlo techniques are used to perform the computations. An empirical application to NASDAQ returns is provided. [ABSTRACT FROM AUTHOR]

Objective: Most of the bodily functions are regulated by multiple interactions between the parasympathetic (PNS) and sympathetic (SNS) nervous system. In this study, we propose a novel framework to quantify the causal flow of information between PNS and SNS through the analysis of heart rate variability (HRV) and electrodermal activity (EDA) signals. Methods: Our method is based on a time-varying (TV) multivariate autoregressive model of EDA and HRV time-series and incorporates physiologically inspired assumptions by estimating the Directed Coherence in a specific frequency range. The statistical significance of the observed interactions is assessed by a bootstrap procedure purposely developed to infer causalities in the presence of both TV model coefficients and TV model residuals (i.e., heteroskedasticity). We tested our method on two different experiments designed to trigger a sympathetic response, i.e., a hand-grip task (HG) and a mental-computation task (MC). Results: Our results show a parasympathetic driven interaction in the resting state, which is consistent across different studies. The onset of the stressful stimulation triggers a cascade of events characterized by the presence or absence of the PNS-SNS interaction and changes in the directionality. Despite similarities between the results related to the two tasks, we reveal differences in the dynamics of the PNS-SNS interaction, which might reflect different regulatory mechanisms associated with different stressors. Conclusion: We estimate causal coupling between PNS and SNS through MVAR modeling of EDA and HRV time-series. Significance: Our results suggest promising future applicability to investigate more complex contexts such as affective and pathological scenarios. [ABSTRACT FROM AUTHOR]

In models with endogenous regressors, a standard regression approach is to exploit just-identifying or overidentifying orthogonality conditions by using instrumental variables. In just-identified models, the identifying orthogonality assumptions cannot be tested without the imposition of other nontestable assumptions. While formal testing of overidentifying restrictions is possible, its interpretation still hinges on the validity of an initial set of untestable just-identifying orthogonality conditions. We present the kinkyreg command for kinky least-squares inference, which adopts an alternative approach to identification. By exploiting nonorthogonality conditions in the form of bounds on the admissible degree of endogeneity, feasible test procedures can be constructed that do not require instrumental variables. The kinky least-squares confidence bands can be more informative than confidence intervals obtained from instrumental-variables estimation, especially when the instruments are weak. Moreover, the approach facilitates a sensitivity analysis for standard instrumental-variables inference. In particular, it allows the user to assess the validity of previously untestable just-identifying exclusion restrictions. Further instrument-free tests include linear hypotheses, functional form, heteroskedasticity, and serial correlation tests. [ABSTRACT FROM AUTHOR]

In this paper, we derive the exact finite sample distribution of the F ( = t 2 ) statistic for a single linear restriction on the regression parameters. We show that the F statistic can be expressed as a ratio of quadratic forms, and therefore its exact cumulative distribution under the null hypothesis can be derived from the result of Imhof [Computing the distribution of quadratic forms in normal variables. Biometrika. 1961;48(3/4):419–426]. A numerical calculation is carried out for the exact distribution of the F statistic using various HC covariance matrix estimators, and the rejection probability under the null hypothesis (size) based on the exact distribution is examined. The results show the exact finite sample distribution is remarkably reliable, while, in comparison, the use of the F-table leads to a serious over-rejection when the sample is not large or leveraged/unbalanced. [ABSTRACT FROM AUTHOR]

In this paper we consider adaptive estimation of a panel data model with unknown heteroskedasticity in both the idiosyncratic and the individual specific random components. We use the kernel estimator for the unknown variances first and then implement the GLS estimator. We also examine the finite sample performance of the adaptive estimators and compare them with several widely used estimators via Monte Carlo experiments. We find that with a proper bandwidth, our adaptive estimator performs much better than other estimators in terms of both estimation efficiency and test size. Besides, a larger bandwidth yields better estimation efficiency and lower test size. [ABSTRACT FROM AUTHOR]

A unit root test is proposed for time series with a general nonlinear deterministic trend component. It is shown that asymptotically the pooled OLS estimator of overlapping blocks filters out any trend component that satisfies some Lipschitz condition. Under both fixed‐b and small‐b block asymptotics, the limiting distribution of the t‐statistic for the unit root hypothesis is derived. Nuisance parameter corrections provide heteroskedasticity‐robust tests, and serial correlation is accounted for by pre‐whitening. A Monte Carlo study that considers slowly varying trends yields both good size and improved power results for the proposed tests when compared to conventional unit root tests. [ABSTRACT FROM AUTHOR]

This study compared two single-group approaches for assessing measurement invariance across an observed background variable: restricted factor analysis (RFA) and moderated nonlinear factor analysis (MNLFA). In MNLFA models, heteroskedasticity can be accounted for by allowing the common-factor variance and the residual variances to differ as a function of the background variable. In contrast, RFA models assume homoskedasticity of both the common factor and the residuals. We conducted a simulation study to examine the performance of RFA and MNLFA under common-factor and residual homoskedasticity and heteroskedasticity. Results suggest that MNLFA and RFA with product indicators outperform RFA with latent moderated structural equations in conditions with heteroskedastic common-factors, and MNLFA outperforms RFA in conditions with residual heteroskedasticity. We provide an explanation for the robustness of RFA with product indicators to violations of common-factor homoskedasticity. [ABSTRACT FROM AUTHOR]

We study the problem of estimating the parameters of a linear median regression without any assumption on the shape of the error distribution – including no condition on the existence of moments – allowing for heterogeneity (or heteroskedasticity) of unknown form, noncontinuous distributions, and very general serial dependence (linear and nonlinear). This is done through a reverse inference approach, based on a distribution-free sign-based testing theory, from which confidence sets and point estimators are subsequently generated. We propose point estimators, which have a natural association with confidence distributions. These estimators are based on maximizing test p-values and inherit robustness properties from the generating distribution-free tests. Both finite-sample and large-sample properties of the proposed estimators are established under weak regularity conditions. We show that they are median-unbiased (under symmetry and estimator unicity) and possess equivariance properties. Consistency and asymptotic normality are established without any moment existence assumption on the errors. A Monte Carlo study of bias and RMSE shows sign-based estimators perform better than LAD-type estimators in various heteroskedastic settings. We illustrate the use of sign-based estimators on an example of β-convergence of output levels across U.S. states. [ABSTRACT FROM AUTHOR]

This article proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by non‐stationary volatility. The assumed volatility process can accommodate discrete breaks, smooth transition variation as well as trending volatility. We develop wild bootstrap sup‐Wald tests of the null hypothesis that the process is either stationary [I(0)] or has a unit root [I(1)] throughout the sample. We also propose a sequential procedure to estimate the number of persistence breaks based on ordering the regime‐specific bootstrap p‐values. The asymptotic validity of the advocated procedures is established both under the null of stability and a variety of persistence change alternatives. A comparison with existing tests that assume homoskedasticity illustrates the finite sample improvements offered by our methods. An application to OECD inflation rates highlights the empirical relevance of the proposed approach and weakens the case for persistence change relative to existing procedures. [ABSTRACT FROM AUTHOR]

In this paper, we consider two different cases of spillover effects: the first is a case where the model does not contain any additional endogenous regressors. Related to this, we give a variance formula that can be used to make inference for estimated spillover effects. In the second case, we extend the discussion of spillover effects to a model containing additional endogenous variables. We suggest approximations to the spillover effects that according to the results of our Monte Carlo experiment are quite accurate. However, our variance formula can not be determined unless the equations of the entire system are known. Suggestions for approximations in this case are left for future research. [ABSTRACT FROM AUTHOR]

This article studies the adaptive estimation of the heteroskedastic functional-coefficient regressions. The motivation for such a theoretical study originates from the empirical analysis of Jansen et al., where the role of fiscal policy on the U.S. asset markets (treasury bonds) is evaluated via the functional-coefficient model. It is found that this model is subject to time-varying heteroskedasticity. As a result, the local least square (LLS) estimator suffers from efficiency loss. To overcome this problem, we propose an adaptive LLS (ALLS) estimator, which can adapt to heteroskedasticity of unknown form asymptotically. Simulation studies confirm that the ALLS estimator can achieve significant efficiency gain in finite samples, compared to the LLS estimator. Real data analysis reveals that the heteroskedastic functional-coefficient model provides adequate fit and better out-of-sample forecasting. [ABSTRACT FROM AUTHOR]

We introduce the command xtserialpm to perform the portmanteau test developed in Jochmans (2019, Cambridge Working Papers in Economics No. 1993, University of Cambridge, Faculty of Economics). The procedure tests for serial correlation of arbitrary form in the errors of a linear panel model after estimation of the regression coefficients by the within-group estimator. The test is designed for short panels and can deal with general missing-data patterns. The test is different from the related portmanteau test of Inoue and Solon (2006, Econometric Theory 22: 835–851), which is performed by xtistest (Wursten, 2018, Stata Journal 18: 76–100), in that it allows for heteroskedasticity. In simulations documented below, xtserialpm is found to provide a more powerful test than xthrtest (Wursten 2018), which performs the test for first-order autocorrelation of Born and Breitung (2016, Econometric Reviews 35: 1290–1316). We also provide comparisons with xtistest and xtserial (Drukker, 2003, Stata Journal 3: 168–177). These tests perform well under stationarity but break down under even mild forms of heteroskedasticity. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for testing heteroskedasticity in two-way fixed effects panel data models under two important scenarios where the cross-sectional dimension is large and the temporal dimension is either large or fixed. Specifically, we will develop test statistics for both cases under the conditional moment framework, and derive their asymptotic distributions under both the null and alternative hypotheses. The proposed tests are distribution free and can easily be implemented using the simple auxiliary regressions. Simulation studies and two real data analyses demonstrate that our proposed tests perform well in practice, and may have the potential for wide application in econometric models with panel data. [ABSTRACT FROM AUTHOR]

Lewbel (2012, Journal of Business and Economic Statistics 30: 67–80) provides a heteroskedasticity-based estimator for linear regression models containing an endogenous regressor when no external instruments or other such information is available. The estimator is implemented in the command ivreg2h by Baum and Schaffer (2012, Statistical Software Components S457555, Department of Economics, Boston College). In this article, we give advice and instructions to researchers who want to use this estimator. [ABSTRACT FROM AUTHOR]

Objective: We present a novel modeling framework for identifying time-varying (TV) couplings between time-series of biomedical relevance. Methods: The proposed methodology is based on multivariate autoregressive (MVAR) models, which have been extensively used to study couplings between biosignals. Contrary to the standard estimation methods that assume time-invariant relationships, we propose a modified recursive Kalman filter (KF) to track changes in the model parameters. We perform model order selection and hyperparameter optimization simultaneously using Genetic Algorithms, greatly improving accuracy and computation time. In addition, we address the effect of residual heteroscedasticity, possibly associated with event-related changes or phase transitions during a given experimental protocol, on the TV-MVAR coupling measures by using Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to fit the TV-MVAR residuals. Results: Using simulated data, we show that the proposed framework yields more accurate parameter estimates compared to the conventional KF, particularly when the true system parameters exhibit different rate of variations over time. Furthermore, by accounting for heteroskedasticity, we obtain more accurate estimates of the strength and directionality of the underlying couplings. We also use our approach to investigate TV hemodynamic interactions during exercise in young and old healthy adults, as well as individuals with chronic stroke. We extract TV coupling patterns that reflect well known exercise-induced effects on the underlying regulatory mechanisms with excellent time resolution. Conclusion and Significance: The proposed modeling framework can be used to efficiently quantify TV couplings between biosignals. It is fully automated and does not require prior knowledge of the system TV characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we consider the instrumental variables (IV) estimation of factor models. In the psychometrics literature, although the two-stage least squares (2SLS) estimator is routinely used in IV estimation of factor models, alternative estimators have been proposed in the econometrics literature. Therefore, in this paper, we compare the performance of these alternative IV estimators in the context of factor models. Monte Carlo simulation results reveal that the HLIM/HFUL estimator by Hausman et al. (2012) outperforms the 2SLS estimator and performs best in many cases. [ABSTRACT FROM AUTHOR]

We consider the issue of performing testing inferences on the parameters that index the linear regression model under heteroskedasticity of unknown form. Quasi-t test statistics use asymptotically correct standard errors obtained from heteroskedasticity-consistent covariance matrix estimators. An alternative approach involves making an assumption about the functional form of the response variances and jointly modelling mean and dispersion effects. In this paper we compare the accuracy of testing inferences made using the two approaches. We consider several different quasi-t tests and also z tests performed after estimated generalized least squares estimation which was carried out using three different estimation strategies. The numerical evidence shows that some quasi-t tests are typically considerably less size distorted in small samples than the tests carried out after the jointly modelling of mean and dispersion effects. Finally, we present and discuss two empirical applications. [ABSTRACT FROM AUTHOR]

Unit root test statistics may not have the usual asymptotic properties when the variance of innovations is unstable. In particular, persistent changes in volatility can cause the size to differ from the nominal level. We propose a class of modified unit root test statistics that are robust to the presence of unstable volatility. The modification is achieved by purging heteroskedasticity from the data using a kernel estimate of volatility before the application of standard tests. In the absence of deterministic trend components, this approach delivers test statistics that achieve standard asymptotics under the null hypothesis of a unit root. When the data are homoskedastic, the local power of unit root tests is unchanged by our modification. We use Monte Carlo simulations to compare the finite sample performance of our modified tests with that of existing methods of correcting for unstable volatility. [ABSTRACT FROM AUTHOR]

Compositional data are known as a sort of complex multidimensional data with the feature that reflect the relative information rather than absolute information. There are a variety of models for regression analysis with compositional variables. Similar to the traditional regression analysis, the heteroskedasticity still exists in these models. However, the existing heteroskedastic regression analysis methods cannot apply in these models with compositional error term. In this paper, we mainly study the heteroskedastic linear regression model with compositional response and covariates. The parameter estimator is obtained through weighted least squares method. For the hypothesis test of parameter, the test statistic is based on the original least squares estimator and corresponding heteroskedasticity-consistent covariance matrix estimator. When the proposed method is applied to both simulation and real example, we use the original least squares method as a comparison during the whole process. The results implicate the model's practicality and effectiveness in regression analysis with heteroskedasticity. [ABSTRACT FROM AUTHOR]

In this paper, we present a new heteroskedastic consistent (HC) covariance matrix estimator which considers the effect of leverage observations and which has a better approximation of its true asymptotic distribution. We point out that the basic motivation behind this new modified HC estimator is to provide an estimator which does not require any user specified values. In terms of bias and mean squared error (MSE), a Monte Carlo simulation study provided evidence that this new estimator has better small sample properties over some existing estimators. A real-life example also evaluated the finite sample behavior in comparison to those existing estimators. [ABSTRACT FROM AUTHOR]

Wind power curve describes the relationship between wind speed and wind power output, which is useful for wind farm design and wind turbine condition monitoring. However, most research on power curves modeling neglected the effect of historical meteorological factors. Also, the research on probabilistic power curve is still limited. Therefore, this paper proposes a novel probabilistic power curve modeling approach. The effect of both current and historical meteorological variables, such as wind speed, wind direction, ambient temperature and turbulence intensity, on the power curve is studied by binning method and kernel density estimation. Next, instead of forecasting the wind power or its quantiles, a new probabilistic power curve model, Density LSTM with Negative Log-Likelihood Loss, is proposed to forecast the parameters of the probability density function of wind power directly. Finally, different probability distribution of wind power output is studied. Gamma, Laplace and Weibull distributions prove to be more suitable than Gaussian distribution. Based on the datasets of inland and offshore wind farms, it is verified that adding useful historical meteorological variables can improve the forecasting performance of the test dataset. Besides, the proposed probabilistic power curve can effectively improve the prediction performance in the probabilistic prediction task and can improve the prediction precision of the annual energy production. • Temporal effect of historical wind speed, wind direction and ambient temperature on wind power is validated. • LSTM with negative log likelihood loss function is used to predict the probability density function of power output. • Four probability distribution of (Gaussian, Laplace, t and Gamma) of wind power output is discussed. [ABSTRACT FROM AUTHOR]

Noting that standard panel unit root tests (PURTs) are not reliable in the presence of time varying volatility, recent papers have suggested a few heteroskedasticity-robust PURTs. These tests do not remain pivotal, however, if they are applied on detrended data. Building on recent asymptotic results for bootstrap approximations (Smeekes and Urbain in A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing, 2014), we provide simulation evidence that recursive detrending followed by a wild bootstrap correction leads to very good size precision for a variety of PURTs designed for testing against panel stationarity formalized with a cross sectionally homogenous autoregressive parameter. With respect to power, the bootstrap variant of the original nonrobust test of Levin et al. (J Econom 108(1):1-24, 2002) turns out to be the most effective among alternative tests. At the implementation side, performing the wild bootstrap correction using the so-called Rademacher distribution is found to be the most effective for both size and power properties of panel unit root inference by means of wild bootstrap based critical values. The empirical illustration shows that GDP per capita is best characterized as a unit root process. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new method which corrects residual variances for the butterfly distributed residuals (BDR). Distribution theory, confidence intervals, and tests of hypotheses are valid and meaningful only if the standard regression assumptions are satisfied. Heteroskedasticity is one of the violations of these assumptions and BDR is another type of heteroskedasticity. This study reveals an alternative approach to correct the BDR type of heteroskedasticity by the weighting re-estimated absolute residuals (WRAR). After giving brief information about heteroskedasticity and BDR type of heteroskedasticity, WRAR is introduced. WRAR and the usual variance stabilizing techniques are compared on multiple and simple regression models. [ABSTRACT FROM AUTHOR]

The hypothesis of structural stability that the regression coefficients do not change over time is central to all applications of linear regression models. It is rather surprising that existing theory as well as practice focus on testing for structural change under homoskedasticity – that is, regression coefficients may change, but the variances remain the same. Since structural change can, and often does, involve changes in variances, this is a puzzling gap in the literature. Our main focus in this paper is to utilize a newly developed test (MZ) by Maasoumi et al. (2010) that tests simultaneously for break in regression coefficients as well as in variance. Currently, the supFtest is most widely used for structural change. This has certain optimality properties shown by Andrews (1993). However, this test assumes homoskedasticity across the structural change. We introduce the sup MZ test which caters to unknown breakpoints, and also compare it to the supF. Our Monte Carlo results show that sup MZ test incurs only a low cost in case of homoskedasticity while having hugely better performance in case of heteroskedasticity. The simulation results are further supported by providing a real-world application. In real-world datasets, we find that structural change often involves heteroskedasticity. In such cases, the supFtest can fail to detect structural breaks and give misleading results, while the sup MZ test works well. We conclude that the sup MZ test is superior to current methodology for detecting structural change. [ABSTRACT FROM PUBLISHER]

This paper compares the performance between regression analysis and a clustering based neural network approach when the data deviates from the homoscedasticity assumption of regression. Heteroskedasticity is a problem that arises in linear regression due to the unequal error variances. One of the methods to deal heteroskedasticity in classical regression theory is weighted least-square regression (WLS). In order to deal the problem of heteroskedasticity, backpropagation neural network is applied. In this context, an algorithm is proposed which is based on robust estimates of location and dispersion matrix that helps in preserving the error assumption of the linear regression. Analysis is carried out with appropriate designs using simulated data and the results are presented. [ABSTRACT FROM AUTHOR]

In official economic statistics, the goal of surveys is often to estimate the mean or the total of a heteroskedastic lognormal variable. For this purpose, ratio imputation has been often used to treat missing values. However, there are three competing ratio estimators in the literature: ordinary least squares (OLS); ratio of means (RoM); and mean of ratios (MoR). It is not quite obvious which of the estimators is best, thus leading to a gap between theory and practice. The objective of this article is to fill in this gap by unifying ratio imputation models and by proposing a novel estimation strategy for selecting a ratio imputation model based on the magnitude of heteroskedasticity. The proposed method estimates the magnitude of heteroskedasticity under the framework of weighted least squares (WLS). Using the 135,000 simulated datasets that cover different parameter settings, the results in the Monte Carlo simulation give a strong support for the proposed method. If the estimated magnitude of heteroskedasticity is moderate, RoM should be used. If the estimated magnitude is severe, MoR should be used. If the estimated magnitude is mild, either OLS or RoM may be used. [ABSTRACT FROM AUTHOR]

This paper contrasts two approaches to estimating quantile regression models: traditional semi-parametric methods and partially adaptive estimators using flexible probability density functions (pdfs). While more general pdfs could have been used, the skewed Laplace was selected for pedagogical purposes. Monte Carlo simulations are used to compare the behavior of the semi-parametric and partially adaptive quantile estimators in the presence of possibly skewed and heteroskedastic data. Both approaches accommodate skewness and heteroskedasticity which are consistent with linear quantiles; however, the partially adaptive estimator considered allows for non linear quantiles and also provides simple tests for symmetry and heteroskedasticity. The methods are applied to the problem of estimating conditional quantile functions for wages corresponding to different levels of education. [ABSTRACT FROM AUTHOR]