{"title":"Calibrating with a smile: A Mellin transform approach to volatility surface calibration","authors":"M. Rodrigo , A. Lo","doi":"10.1016/j.ecosta.2022.05.004","DOIUrl":"10.1016/j.ecosta.2022.05.004","url":null,"abstract":"<div><div>The implied volatility<span><span> in the Black-Scholes framework is not a constant but a function of both the strike price (“smile/skew”) and the time to expiry. A popular approach to recovering the volatility surface is through the use of deterministic volatility function models via Dupire’s equation. A new method for volatility surface calibration based on the Mellin transform is proposed. An explicit formula for the volatility surface is obtained in terms of the Mellin transform of the </span>call option price with respect to the strike price, and a numerical algorithm is provided. Results of numerical simulations are presented and the stability of the method is numerically verified. The proposed Mellin transform approach provides a simpler and more direct fitting of generalised forms of the volatility surface given previously in the literature.</span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"36 ","pages":"Pages 73-80"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90997204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"GMM Model Averaging Using Higher Order Approximations","authors":"Luis F. Martins , Vasco J. Gabriel","doi":"10.1016/j.ecosta.2022.09.004","DOIUrl":"10.1016/j.ecosta.2022.09.004","url":null,"abstract":"<div><div><span>Moment conditions model averaging (MA) estimators in the GMM framework are considered. Under finite sample considerations, MA estimators with optimal weights are proposed, in the sense that weights minimize the corresponding higher-order asymptotic mean squared error (AMSE). It is shown that the higher-order AMSE objective function has a closed-form expression, which makes this procedure applicable in practice. In addition, and as an alternative, different averaging schemes based on moment selection criteria are considered, in which weights for averaging across GMM estimates can be obtained by direct smoothing or by numerical minimization of a specific criterion. Asymptotic properties assuming correctly specified models are derived and the performance of the proposed averaging approaches is contrasted with existing model selection alternatives </span><span><math><mrow><mi>i</mi><mo>)</mo></mrow></math></span> analytically, for a simple IV example, and <span><math><mrow><mi>i</mi><mi>i</mi><mo>)</mo></mrow></math></span> by means of Monte Carlo experiments in a nonlinear setting, showing that MA compares favourably in many relevant setups. The usefulness of MA methods is illustrated by studying the effect of institutions on economic performance.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"36 ","pages":"Pages 37-54"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77529352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nonparametric estimation of copulas and copula densities by orthogonal projections","authors":"Yves I. Ngounou Bakam , Denys Pommeret","doi":"10.1016/j.ecosta.2023.04.002","DOIUrl":"10.1016/j.ecosta.2023.04.002","url":null,"abstract":"<div><div><span>A nonparametric copula<span> density estimator based on Legendre orthogonal polynomials is proposed. A nonparametric copula estimator is then deduced by integration. Their asymptotic properties are reviewed. Both estimators are based on a sequence of moments that characterize the copulas and that we shall call the </span></span><em>copula coefficients</em>. A data-driven method is proposed to select the number of copula coefficients to use. An intensive simulation study shows the good performance of both copulas and copula densities estimators compared to a large panel of competitors. Two real datasets illustrate this approach.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"36 ","pages":"Pages 90-118"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82080471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Nearest neighbor matching: M-out-of-N bootstrapping without bias correction vs. the naive bootstrap","authors":"Christopher Walsh , Carsten Jentsch","doi":"10.1016/j.ecosta.2023.04.005","DOIUrl":"10.1016/j.ecosta.2023.04.005","url":null,"abstract":"<div><div><span>It is well known that the limiting variance of nearest neighbor matching estimators cannot be consistently estimated by a naive Efron-type bootstrap<span><span> as the conditional variance of the bootstrap estimator does not generally converge to the correct limit in expectation. In essence this is caused by the fact that the </span>bootstrap sample<span><span> contains ties with positive probability even when the </span>sample size becomes large. This negative result was originally derived in a simple setting by Abadie and Imbens (ECONOMETRICA, pp. 235–267, 76(6), 2008). A proof of concept for a direct M-out-of-N bootstrap on the data is provided in this setting. It is proven that in this setting the conditional variance of a direct M-out-of-N-type bootstrap estimator </span></span></span><em>without</em> bias-correction does converge to the correct limit in expectation. The key to the proof lies in the fact that asymptotically with probability one there are no ties in the bootstrap sample. The potential of the direct M-out-of-N-type bootstrap is investigated in simulations.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"36 ","pages":"Pages 81-89"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78326349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The benefits of returns and options in the estimation of GARCH models. A Heston-Nandi GARCH insight","authors":"Marcos Escobar-Anel , Lars Stentoft , Xize Ye","doi":"10.1016/j.ecosta.2022.12.001","DOIUrl":"10.1016/j.ecosta.2022.12.001","url":null,"abstract":"<div><div>In a controlled, simulated setting, the questions of what the benefits are of including option prices in the estimation of GARCH models<span>, the extent to which options can replace returns, and what the best type of options is for estimation, are addressed. The computational advantages of affine GARCH models for option pricing make these questions numerically tractable, therefore the experiments focus on the Heston-Nandi GARCH model. Three estimation methods, namely, returns-only estimation, options-only calibration and joint returns-options estimation-calibration are compared. The study reveals that, although the benefit is insignificant for the risk premium factor, adding options significantly reduces the standard errors of the GARCH dynamic parameters. This conclusion holds true under both linear and variance-dependent pricing kernels. The results suggest that, in a realistic setting, practitioners can use a large and recent sample of option prices to compensate for the lack of available return data. As a by-product, evidence also shows that out-of-the-money, short-maturity options are the best choice to improve the quality of the estimation.</span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"36 ","pages":"Pages 1-18"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72408877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Subal C. Kumbhakar , A. Peresetsky , Y. Shchetynin , A. Zaytsev
{"title":"Technical efficiency and inefficiency: Reliability of standard SFA models and a misspecification problem","authors":"Subal C. Kumbhakar , A. Peresetsky , Y. Shchetynin , A. Zaytsev","doi":"10.1016/j.ecosta.2021.12.006","DOIUrl":"10.1016/j.ecosta.2021.12.006","url":null,"abstract":"<div><div>It is formally proven that if inefficiency (<span><math><mi>u</mi></math></span>) is modelled through its variance, considered as a function of exogenous variables <span><math><mi>z</mi></math></span>, then the marginal effects of <span><math><mi>z</mi></math></span> on technical inefficiency (<span><math><mrow><mi>T</mi><mi>I</mi></mrow></math></span>) and technical efficiency (<span><math><mrow><mi>T</mi><mi>E</mi></mrow></math></span>) have opposite signs in the typical setup with a normally distributed random error and an exponentially or half-normally distributed <span><math><mi>u</mi></math></span>. This is true for both conditional and unconditional <span><math><mrow><mi>T</mi><mi>I</mi></mrow></math></span> and <span><math><mrow><mi>T</mi><mi>E</mi></mrow></math></span>. An example is provided to show that the signs of the marginal effects of <span><math><mi>z</mi></math></span> on <span><math><mrow><mi>T</mi><mi>I</mi></mrow></math></span> and <span><math><mrow><mi>T</mi><mi>E</mi></mrow></math></span> may coincide for some ranges of <span><math><mi>z</mi></math></span>. If the real data comes from a bimodal distribution of <span><math><mi>u</mi></math></span>, and a model is estimated with an exponential or half-normal distribution for <span><math><mi>u</mi></math></span>, the estimated efficiency and the marginal effect of <span><math><mi>z</mi></math></span> on <span><math><mrow><mi>T</mi><mi>E</mi></mrow></math></span> could be wrong. Moreover, the rank correlations between the true and the estimated values of <span><math><mrow><mi>T</mi><mi>E</mi></mrow></math></span> could be small and even negative for some subsamples of the data. This is a warning that in the case when the true (real life) distribution of the inefficiency is bimodal, commonly used standard SFA models could lead to wrong policy recommendations. The kernel density plot of the residuals is suggested as a diagnostic plot. The results are illustrated by simulations.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"36 ","pages":"Pages 55-72"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145223591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Approximation of BSDE with hidden forward equation and unknown volatility","authors":"Oleg V. Chernoyarov , Yury A. Kutoyants","doi":"10.1016/j.ecosta.2023.01.002","DOIUrl":"10.1016/j.ecosta.2023.01.002","url":null,"abstract":"<div><div>The focus is on the approximation of the solution of BSDE<span> in the case where the solution of forward equation is observed in the presence of small Gaussian<span> noise. The volatility of the forward equation is considered to depend on some unknown parameter. This approximation is made in several steps. First a preliminary estimator of the unknown volatility is obtained, then using Kalman-Bucy filtration equations and Fisher-score device one-step MLE-process of this parameter is constructed. The solution of BSDE is approximated by means of the solution of PDE and the One-step MLE-process. The error of approximation is described in different metrics.</span></span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"36 ","pages":"Pages 119-132"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72621678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Variable Selection in Macroeconomic Forecasting with Many Predictors","authors":"Zhenzhong Wang, Zhengyuan Zhu, Cindy Yu","doi":"10.1016/j.ecosta.2023.01.003","DOIUrl":"10.1016/j.ecosta.2023.01.003","url":null,"abstract":"<div><div><span><span>In the data-rich environment, using many economic predictors to forecast a few key variables has become a new trend in econometrics. The commonly used approach is factor augment (FA) approach. This paper pursues another direction, variable selection (VS) approach, to handle high-dimensional predictors. VS is an active topic in statistics and computer science. However, it does not receive as much attention as FA in economics. This paper introduces several cutting-edge VS methods to </span>economic forecasting, which includes: (1) classical greedy procedures; (2) </span><span><math><msub><mi>l</mi><mn>1</mn></msub></math></span><span><span> regularization; (3) false-discovery-rate control methods, (4) </span>gradient descent<span><span><span> with sparsification and (5) meta-heuristic algorithms. Comprehensive simulation studies are conducted to compare their variable selection accuracy and prediction performance under different scenarios. Among the reviewed methods, a meta-heuristic algorithm called sequential Monte Carlo algorithm performs the best. Surprisingly the classical forward selection is comparable to it and better than other more sophisticated algorithms. In addition, these VS methods are applied on economic forecasting<span> and compared with the popular FA approach. It turns out for employment rate and CPI </span></span>inflation, some VS methods can achieve considerable improvement over FA, and the selected predictors can be well explained by </span>economic theories.</span></span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"36 ","pages":"Pages 19-36"},"PeriodicalIF":2.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83123283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Joint Hypothesis Testing from Heterogeneous Samples under Cross-dependence","authors":"Uwe Hassler , Mehdi Hosseinkouchack","doi":"10.1016/j.ecosta.2022.07.004","DOIUrl":"10.1016/j.ecosta.2022.07.004","url":null,"abstract":"<div><div>A testing principle is introduced that allows to combine evidence from <span><math><mi>N</mi></math></span> potentially correlated samples. It builds on a (weighted) sum of entities from the individual samples, which is fed into a self-normalizing variance ratio type statistic. Due to self-normalization the (autoco)variances within each sample as well as the cross-covariances between the samples melt into one scaling parameter that cancels from the ratios asymptotically. Tests constructed from this principle are hence robust with respect to cross-dependence without having to estimate any nuisance parameters. The weighting and the entities from the individual samples depend on the testing problem at hand. Two cases are discussed in detail. The first one are tests of restrictions on a parameter vector (e. g. testing restrictions on expected values), while the second one focusses on time series: panel integration tests (unit root as well as stationarity tests). The validity of the asymptotic theory in finite samples is established by means of simulation evidence.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"35 ","pages":"Pages 41-54"},"PeriodicalIF":2.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79993938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Automatic Portmanteau Test For Nonlinear Dependence","authors":"Charisios Grivas","doi":"10.1016/j.ecosta.2022.12.003","DOIUrl":"10.1016/j.ecosta.2022.12.003","url":null,"abstract":"<div><div>A data-driven version of a portmanteau test for detecting nonlinear types of statistical dependence is considered. An attractive feature of the proposed test is that it properly controls the type I error without being sensitive with respect to the number of autocorrelations used. In addition, the automatic test is found to have higher power in simulations when compared to the standard portmanteau test, for both raw data and residuals.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"35 ","pages":"Pages 71-83"},"PeriodicalIF":2.0,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}