Heteroscedastic Errors Research Articles

Evidence of customer sophistication behaviour in deposit markets: the case of Qatar

PurposeThe paper investigates the interest rate policy transmission mechanism and the role of market structure of the banking industry in Qatar.Design/methodology/approachCompetitiveness indexes are used to measure the degree of market power in the banking industry in Qatar. The momentum threshold autoregressive model is applied over the monthly period from January 2005 to June 2018 to examine the magnitude of intermediation and adjustment to disequilibria in the deposit market. In addition, to model interest rate volatility and overcome the problem of heteroscedastic errors in the error correction standard models, an asymmetric EC-EGARCH-M model is applied.FindingsThe findings suggest incomplete pass-through and asymmetric response to monetary shocks. The asymmetric adjustment mechanism is found to be downward rigid which suggests a high degree of customer sophistication and an elastic supply of deposits. The results of the EC-EGARCH-M show that the impact of monetary policy shocks has a significant positive impact on deposit interest rates and that negative monetary shocks trigger more conditional interest rate volatility in the next period than positive monetary shocks for a short maturity rate.Originality/valueThe paper is the first to highlight the behaviour of the interest rate pass through channel and measures the degree of competitiveness of the banking industry for the case of a small, rich country. In addition, using recent data, the paper applies different econometric methodologies and overcomes the problem of heteroskedastic errors by modelling the interest rate volatility using the EC-EGARCH-M model.

Using Both Time Tradeoff and Discrete Choice Experiments in Valuing the EQ-5D: Impact of Model Misspecification on Value Sets.

Introduction. The EQ-5D-5L valuation protocol contains both time tradeoff (TTO) tasks and discrete choice experiments (DCE), raising the question of how to best use these in creating a value set. The hybrid model, which combines TTO and DCE data, has emerged as a commonly used approach. However, this model assumes independence among responses from the same individual, a linear relationship between TTO and DCE utilities, and, in many implementations, homoscedastic residuals. The aims of this study are to examine alternatives to these assumptions and determine the impact of misspecification on value sets. Methods. We performed a simulation study, parameterized using the US EQ-5D-5L valuation study, to assess the impact of model misspecification. We simulated TTO and DCE data with nonlinear relationships between TTO and DCE utilities, heteroscedastic errors, and correlated responses. Simulated data were analyzed using hybrid models with and without heteroscedasticity, Tobit models with and without heteroscedasticity, a latent class model, and a mixed model. Results. Mean absolute errors (MAEs) for correctly specified models were <0.05, whereas models that incorrectly assumed a linear relationship between TTO and DCE utilities or homoscedasticity of TTO responses featured states with an MAE >0.1. When a linear relationship between TTO and DCE utilities held, using both TTO and DCE data under correct specification yielded smaller MAEs compared with using TTO data alone but yielded larger MAEs when a linear relationship did not hold. Mistakenly assuming homoscedasticity led to increased MAEs, whereas ignoring dependence did not. Conclusions. Because heteroscedasticity in TTO utilities and nonlinear associations between DCE and TTO utilities have been noted, we recommend careful assessment of scedasticity and linearity to ascertain the suitability of a hybrid model.

Comparison of statistical and machine learning models for healthcare cost data: a simulation study motivated by Oncology Care Model (OCM) data

BackgroundThe Oncology Care Model (OCM) was developed as a payment model to encourage participating practices to provide better-quality care for cancer patients at a lower cost. The risk-adjustment model used in OCM is a Gamma generalized linear model (Gamma GLM) with log-link. The predicted value of expense for the episodes identified for our academic medical center (AMC), based on the model fitted to the national data, did not correlate well with our observed expense. This motivated us to fit the Gamma GLM to our AMC data and compare it with two other flexible modeling methods: Random Forest (RF) and Partially Linear Additive Quantile Regression (PLAQR). We also performed a simulation study to assess comparative performance of these methods and examined the impact of non-linearity and interaction effects, two understudied aspects in the field of cost prediction.MethodsThe simulation was designed with an outcome of cost generated from four distributions: Gamma, Weibull, Log-normal with a heteroscedastic error term, and heavy-tailed. Simulation parameters both similar to and different from OCM data were considered. The performance metrics considered were the root mean square error (RMSE), mean absolute prediction error (MAPE), and cost accuracy (CA). Bootstrap resampling was utilized to estimate the operating characteristics of the performance metrics, which were described by boxplots.ResultsRF attained the best performance with lowest RMSE, MAPE, and highest CA for most of the scenarios. When the models were misspecified, their performance was further differentiated. Model performance differed more for non-exponential than exponential outcome distributions.ConclusionsRF outperformed Gamma GLM and PLAQR in predicting overall and top decile costs. RF demonstrated improved prediction under various scenarios common in healthcare cost modeling. Additionally, RF did not require prespecification of outcome distribution, nonlinearity effect, or interaction terms. Therefore, RF appears to be the best tool to predict average cost. However, when the goal is to estimate extreme expenses, e.g., high cost episodes, the accuracy gained by RF versus its computational costs may need to be considered.

Supervised and semi-supervised twin parametric-margin regularized extreme learning machine

Twin extreme learning machine (TELM) has attracted considerable attention and achieved great success in the machine learning field. However, its performance will be severely affected when outliers exist in the dataset since TELM does not consider heteroscedasticity in practical applications. To improve the performance of TELM, a novel learning framework called twin parametric-margin extreme learning machine (TPMELM) was proposed. Further, to enhance the classification performance of our TPMELM in a semi-supervised learning setting, a Laplacian TPMELM (Lap-TPMELM) was developed by introducing manifold regularization into TPMELM. Using the geometric information of the marginal distribution embedded in unlabeled samples, Lap-TPMELM can effectively construct a more reasonable classifier. The TPMELM and Lap-TPMELM are suitable for many situations, especially when the data has heteroscedastic error structure. Moreover, the TPMELM and Lap-TPMELM are helpful in clarifying theoretical interpretation of parameters which control the bounds on proportions of support vectors and boundary errors. An efficient technique (successive over-relaxation, SOR) is applied in TPMELM and Lap-TPMELM, respectively. Experimental results show the effectiveness and reliability of the proposed methods.

Asymptotic Optimality of the Nonnegative Garrote Estimator Under Heteroscedastic Errors

This paper proposes the Nonnegative Garrote (NG) estimator for linear model with heteroscedastic errors. On the other hand, under some regularity conditions, the authors show the asymptotic optimality of the NG estimator by referring to the idea of the asymptotic optimality of the model average estimator. Simulation results and a real data analysis are reported for testing the results obtained previously. These results provide a stronger theoretical basis for the use of NG estimator by strengthening existing findings.

Applications of asymptotic inference in segmented line regression

This paper studies asymptotic properties of the estimators of the regression coefficients in segmented line regression, focusing on the multi-phase regression model with the continuity constraint at the unknown change-points. We first review the asymptotic distributions of the least squares estimators of the regression coefficients and discuss why the standard error estimates of the estimators derived under the assumption of known change-points do not serve as good estimates although the change-point estimators are consistent. Then, we provide some details on the asymptotic distributions of the estimated regression coefficients in three extended cases: (i) the model with heteroscedastic errors, (ii) the model with abrupt jumps either at known or unknown jump points, in addition to continuous changes, and (iii) the fit made under the constraint on the minimum size of the estimated slope changes. Empirical properties of the standard error estimates of the estimated regression coefficients are studied via simulations.

Integrated Bayesian Multi-model approach to quantify input, parameter and conceptual model structure uncertainty in groundwater modeling

A flexible Integrated Bayesian Multi-model Uncertainty Estimation Framework (IBMUEF) is presented to simultaneously quantify conceptual model structure, input and parameter uncertainty of a groundwater flow model. In this fully Bayesian framework, the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm with a novel likelihood function is combined with Bayesian Model Averaging (BMA). Four alternative conceptual models, representing different geological representations of an overexploited aquifer, have been developed. The uncertainty of the input of the model is represented by multipliers. A novel likelihood function based on a new heteroscedastic error model is included to extend the applicability of the framework. The results of the study confirm that neglecting conceptual model structure uncertainty results in unreliable prediction. Consideration of both model structure and input uncertainty are important to obtain confident parameter sets and better model predictions. This study shows that the IBMUEF provides more reliable model predictions and accurate uncertainty bounds.

Variable selection for high-dimensional regression models with time series and heteroscedastic errors

Although existing literature on high-dimensional regression models is rich, the vast majority of studies have focused on independent and homogeneous error terms. In this article, we consider the problem of selecting high-dimensional regression models with heteroscedastic and time series errors, which have broad applications in economics, quantitative finance, environmental science, and many other fields. The error term in our model is the product of two components: one time series component, allowing for a short-memory, long-memory, or conditional heteroscedasticity effect, and a high-dimensional dispersion function accounting for exogenous heteroscedasticity. By making use of the orthogonal greedy algorithm and the high-dimensional information criterion, we propose a new model selection procedure that consistently chooses the relevant variables in both the regression and the dispersion functions. The finite sample performance of the proposed procedure is also illustrated via simulations and real data analysis.

The adaptivity of thresholding wavelet estimators in heteroscedastic nonparametric model with negatively super-additive dependent errors

In this paper, we consider two estimators, a hard thresholding wavelet estimator and a block thresholding wavelet estimator, for the regression function in heteroscedastic nonparametric model with negatively super-additive dependent (NSD) errors. The random design distribution is known or unknown, and the corresponding adaptive properties of these estimators are investigated over Besov spaces, for the $${L^2}$$ risk. The results indicate that the block thresholding estimator is theoretically and computationally superior to the hard thresholding estimator with the former attains the optimal convergence rates, while the later achieves the nearly optimal convergence rates. Thus the block thresholding estimator provides extensive adaptivity to many irregular function classes even though with the presence of heteroscedastic NSD errors.

Degradation Modeling Based on Wiener Process Considering Multi-Source Heterogeneity

Degradation modeling using heterogeneous degradation data of a system population is critical for prognostics and health management. The heterogeneity may result from the inherent differences in the degrading systems and measuring instruments, as well as from the extrinsic environmental differences, making it difficult to predict the failure. Current studies have not considered the multiple sources of heterogeneity simultaneously, and consequently, have failed to capture the actual degradation process. To explain and quantify the combined effect of multi-source heterogeneity, we present a random effects Wiener process model with heteroscedastic measurement errors, where the parameters of the drift, diffusion, and error variance are assumed as random variables following a certain distribution. The Markov chain Monte Carlo method is adopted to estimate the posterior distributions of the actual degradation states and the model parameters under a hierarchical Bayesian framework. Based on the concept of first hitting time, the failure time distribution is estimated. To verify the presented approach, comparative studies are conducted with simulation and laser degradation data. The results show that considering multi-source heterogeneity can further eliminate the inter-individual variation in degradation data and improve the model fitting and prediction accuracy.

On Bootstrapping Tests of Equal Forecast Accuracy for Nested Models

The asymptotic distributions of the recursive out-of-sample forecast accuracy test statistics depend on stochastic integrals of Brownian motion when the models under comparison are nested. This often complicates their implementation in practice because the computation of their asymptotic critical values is costly. Hansen and Timmermann (2015, Econometrica) propose a Wald approximation of the commonly used recursive F-statistic and provide a simple characterization of the exact density of its asymptotic distribution. However, this characterization holds only when the larger model has one extra predictor or the forecast errors are homoscedastic. No such closed-form characterization is readily available when the nesting involves more than one predictor and heteroskedasticity is present. We first show both the recursive F-test and its Wald approximation have poor finite-sample properties, especially when the forecast horizon is greater than one. We then propose a hybrid bootstrap method consisting of a block moving bootstrap (which is nonparametric) and a residual based bootstrap for both statistics, and establish its validity. Simulations show that our hybrid bootstrap has good finite-sample performance, even in multi-step ahead forecasts with heteroscedastic or autocorrelated errors, and more than one predictor. The bootstrap method is illustrated on forecasting core inflation and GDP growth.

Forecasting core inflation: the case of South Africa

ABSTRACT Underlying, or core, inflation is likely the most important variable for monetary policy. It is considered to be the optimal nominal anchor as it is stable, excludes relative price shocks, and reflects underlying trends in the behaviour of price-setters and demand conditions in the economy. Despite its importance, there is sparse literature on estimating and forecasting core inflation in South Africa, with the focus still on measuring it. This paper emphasizes predicting core inflation from time-varying parameter vector autoregressive models (TVP-VARs), factor-augmented VARs (FAVAR), and structural break models using quarterly data from 1981Q1 to 2013Q4. We use mean squared forecast errors (MSFE) and predictive likelihoods to evaluate the forecasts. In general, we find that (i) time-varying parameter models consistently outperform constant coefficient models (ii) small TVP-VARs outperform all other models; (iii) models with heteroscedastic errors do better than models with homoscedastic errors; and (iv) allowing for structural breaks does not improve the predictability of core inflation. Overall, our results imply that additional information on the growth rate of the economy and the interest rate is sufficient to forecast core inflation accurately, but the relationship between these three variables needs to be modelled in a time-varying fashion.

Optimal designs for heteroscedastic regression models with two parameters

Optimal design problems for different criteria of optimality in case of two regression coefficients for fixed and random models with heteroscedastic errors are considered. The results obtained essentially generalize those from Wilk and Zaigraev [DS-optimal designs for random coefficient first-degree regression models with heteroscedastic errors. Statist Probab Lett. 2017;128:28–34].

Univariate and Multivariate Claims Reserving with Generalised Link Ratios

In this paper, a regression modelling setting is introduced to estimate loss development factors, and its multivariate counterpart considers contemporaneous correlation between each regression equation within the triangle with homoscedastic or heteroscedastic errors, respectively. Using now an appropriate econometric framework, the prediction error is derived in a matrix form avoiding the calculation of the corresponding developments using computationally expensive recursive formulas. In this regard, the classical loss development factors method is extended to the univariate Generalized Link Ratios one, where the appropriate method selection is related with the minimization of the prediction errors in the triangle. In addition, the multivariate Generalized Link Ratios method is proposed with contemporaneous correlations between each regression equation within the triangle, using also the minimization of the prediction error as a way to select the appropriate method for the triangle. Mathematical expressions for the case of homoscedastic and heteroscedastic errors derive for some labelled methods (such as the chain ladder, vector projector and simple average) as well as for many other unnamed methods. Finally, several numerical examples with irregular, regular, and real data illustrate the applicability of our treatment and check the assumptions made in the paper.

A multiple comparison procedure for dose‐finding trials with subpopulations

Identifying subgroups of patients with an enhanced response to a new treatment has become an area of increased interest in the last few years. When there is knowledge about possible subpopulations with an enhanced treatment effect before the start of a trial it might be beneficial to set up a testing strategy, which tests for a significant treatment effect not only in the full population, but also in these prespecified subpopulations. In this paper, we present a parametric multiple testing approach for tests in multiple populations for dose‐finding trials. Our approach is based on the MCP‐Mod methodology, which uses multiple comparison procedures (MCPs) to test for a dose–response signal, while considering multiple possible candidate dose–response shapes. Our proposed methods allow for heteroscedastic error variances between populations and control the family‐wise error rate over tests in multiple populations and for multiple candidate models. We show in simulations that the proposed multipopulation testing approaches can increase the power to detect a significant dose–response signal over the standard single‐population MCP‐Mod, when the specified subpopulation has an enhanced treatment effect.

Bayesian Updating of Structural Model with a Conditionally Heteroscedastic Error Distribution

AbstractThe existing literature on Bayesian updating of structural models has assigned equal variances (homoscedasticity) in the measured observables across all modes by assuming a Gaussian error d...

Locally D-optimal designs for heteroscedastic polynomial measurement error models

This paper considers constructions of optimal designs for heteroscedastic polynomial measurement error models. Corresponding approximate design theory is developed by using corrected score function approach, which leads to non-concave optimisation problems. For the weighted polynomial measurement error model of degree p with some commonly used heteroscedastic structures, the upper bounds for the number of support points of locally D-optimal designs can be determined explicitly. A numerical example is given to show how heteroscedastic structures affect the optimal designs.

Multivariate realized volatility forecasts of agricultural commodity futures

AbstractWe forecast the multivariate realized volatility of agricultural commodity futures by constructing multivariate heterogeneous autoregressive (MHAR) models with flexible heteroscedastic error structures that allow for non‐Gaussian distribution, stochastic volatility, and heteroscedastic and serial dependence. We evaluate the forecast performances of various models based on both statistical and economic criteria. The in‐sample and out‐of‐sample results suggest that the proposed MHAR models allowing for flexible heteroscedastic covariance structures outperform the benchmark MHAR models. In addition, the proposed Bayesian MHAR models allowing for t innovations improve both in‐sample and out‐of‐sample forecast performance of the corresponding MHAR models with Gaussian innovations.

Does eco-innovation lift firm value? The contingent role of institutions in emerging markets

PurposeDrawing on the literature of eco-innovation and institutional theory, this research aims to answer two fundamental questions: Does eco-innovation improve or harm firm value in emerging markets? and How institutional environments moderate the relationship between eco-innovation and firm value? We explicate the regulatory, normative and cognitive pillars of institutions, manifested as regulation intensity, environmental agency pressure and public pressure, respectively.Design/methodology/approachFor this study, a cross-sectional panel data set was assembled from multiple archival sources, including data coded from the corporate annual reports and social responsibility reports, statistical yearbooks, China Stock Market Financial Database (CSMAR) and other secondary sources. A hierarchical regression method was used to test the hypotheses. The data comprised 88 firms sampled over four years. The model using feasible generalized least squares (FGLSs) to control heteroscedasticity in errors due to unobserved heterogeneity was estimated.FindingsEmpirical findings from a data set compiled from multiple archival sources reveal that both eco-product and eco-process innovation negatively relate to firm value. The interactions between eco-innovation and regulation intensity, environmental agency pressure and public pressure are positively related to firm value.Originality/valueFirst, this study extends the literature of eco-innovation by investigating the impact of eco-innovation on firm value. Contrary to the conventional anecdotal evidence of the beneficial effect of eco-innovation, it was found that eco-innovation relates negatively to firm value. Second, this study develops and tests an institutional contingent view of eco-innovation by accounting for the moderating role of regulatory, normative and cognitive pressures.

CONDITIONAL PRICING MODEL WITH HETEROSCEDASTICITY: EVALUATION OF BRAZILIAN FUNDS

ABSTRACT Empirical studies have revealed that the conditional Capital Asset Pricing Model (CAPM) has a higher explanatory power than its unconditional version, particularly for the model in state-space form where the beta is estimated using Kalman filter. Most empirical analyses are based on stock portfolios to explain financial anomalies, but only a few studies proposed improving investment fund performance. The main contribution of this study is the assessment of Brazilian investment funds through traditional measures estimated from the CAPM model in state-space form with heteroscedastic and homoscedastic errors compared to alternative models, such as the unconditional CAPM and a four-factor model. Using a sample of stock funds from May 2005-April 2015, the results indicate that the conditional CAPM model produces better results than the alternative models, providing better performance evaluation practices for funds in both stock-picking and market-timing ability.