{"title":"Implicit Copulas: An Overview","authors":"Michael Stanley Smith","doi":"10.1016/j.ecosta.2021.12.002","DOIUrl":"https://doi.org/10.1016/j.ecosta.2021.12.002","url":null,"abstract":"<div><p><span>Implicit copulas<span> are the most common copula choice for modeling dependence in high dimensions. This broad class of copulas is introduced and surveyed, including elliptical copulas, skew </span></span><span><math><mi>t</mi></math></span><span> copulas, factor copulas, time series copulas and regression copulas. The common auxiliary representation of implicit copulas is outlined, and how this makes them both scalable and tractable for statistical modeling<span>. Issues such as parameter identification, extended likelihoods for discrete or mixed data, parsimony in high dimensions, and simulation from the copula model are considered. Bayesian<span> approaches to estimate the copula parameters, and predict from an implicit copula model, are outlined. Particular attention is given to implicit copula processes constructed from time series and regression models, which is at the forefront of current research. Two econometric<span> applications—one from macroeconomic time series and the other from financial asset pricing—illustrate the advantages of implicit copula models.</span></span></span></span></p></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"28 ","pages":"Pages 81-104"},"PeriodicalIF":1.9,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50198793","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":"Numerical Methods for Finding A-optimal Designs Analytically","authors":"Ping-Yang Chen , Ray-Bing Chen , Yu-Shi Chen , Weng Kee Wong","doi":"10.1016/j.ecosta.2022.09.005","DOIUrl":"https://doi.org/10.1016/j.ecosta.2022.09.005","url":null,"abstract":"<div><p><span>The traditional way in statistics<span> to find optimal designs for regression models is an analytical approach. Technical conditions that may be restrictive in practice are sometimes imposed to obtain the analytical results. Even then, the mathematical technique is invariably not amendable to find an optimal design under a different criterion or for the same criterion with a slightly changed model, suggesting that developing flexible and effective algorithms to search for the optimum is very useful. In particular, numerical results from an algorithm can be helpful to find analytical descriptions of optimal designs. As an example, particle swarm optimization has been shown to be quite effective for finding optimal designs for hard design problems and this paper demonstrates how its output can be used to find new analytic </span></span><span><math><mi>A</mi></math></span><span>-optimal approximate designs for the Gamma and inverse Gaussian models, each with the inverse link function. The methodology is quite general and may be applied to find analytical </span><span><math><mi>A</mi></math></span><span>-optimal designs for other models, like the Poisson model with the log link function, or other types of optimal designs.</span></p></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"28 ","pages":"Pages 155-162"},"PeriodicalIF":1.9,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50198657","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":"Testing Heteroskedasticity in High-Dimensional Linear Regression","authors":"Akira Shinkyu","doi":"10.1016/j.ecosta.2023.10.003","DOIUrl":"https://doi.org/10.1016/j.ecosta.2023.10.003","url":null,"abstract":"A new procedure that is based on the residuals of the Lasso is proposed for testing heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. The theoretical analysis demonstrates that the test statistic exhibits asymptotic normality under the null hypothesis of homoskedasticity, and the simulation results reveal that the proposed testing procedure obtains accurate empirical sizes and powers. Finally, the procedure is applied to real economic data.","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136093724","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}
Cathy W.S. Chen , Toshiaki Watanabe , Edward M.H. Lin
{"title":"Bayesian estimation of realized GARCH-type models with application to financial tail risk management","authors":"Cathy W.S. Chen , Toshiaki Watanabe , Edward M.H. Lin","doi":"10.1016/j.ecosta.2021.03.006","DOIUrl":"https://doi.org/10.1016/j.ecosta.2021.03.006","url":null,"abstract":"<div><p><span>Advances in the various realized GARCH models have proven effective in taking account of the bias in realized volatility (RV) introduced by microstructure noise and non-trading hours. They have been extended into nonlinear or long-memory patterns, including the realized exponential GARCH (EGARCH), realized heterogeneous autoregressive GARCH (HAR-GARCH), and realized threshold GARCH (TGARCH) models. These models with skew Student’s t-distribution are applied to </span>quantile<span> forecasts such as Value-at-Risk and expected shortfall of financial returns as well as volatility forecasting. Parameter estimation and quantile forecasting are built on Bayesian<span><span> Markov chain Monte Carlo sampling methods. Backtesting measures are presented for both Value-at-Risk and expected shortfall forecasts and employ two loss functions to assess volatility forecasts. Results taken from the S&P500 in the U.S. market with approximately 5-year out-of-sample periods covering the COVID-19 pandemic period are reported as follows: (1) The realized HAR-GARCH model performs best in respect of violation rates and expected shortfall at the 1% and 5% </span>significance levels. (2) The realized EGARCH model performs best with regard to volatility forecasts.</span></span></p></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"28 ","pages":"Pages 30-46"},"PeriodicalIF":1.9,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ecosta.2021.03.006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50198789","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":"A review of effective age models and associated non- and semiparametric methods","authors":"Eric Beutner","doi":"10.1016/j.ecosta.2021.12.005","DOIUrl":"https://doi.org/10.1016/j.ecosta.2021.12.005","url":null,"abstract":"<div><p>First an overview of a class of models for recurrent events is given. The class of models considered is known as virtual or effective age models. One of the strengths of this class of models is their ability to account for intervention effects after an event occurrence. Some of the models within this class allow to account for the effects of covariates and the impact of the number of already observed events. After having provided an overview of this class of models, non- and semiparametric inference methods for these models are reviewed. Several open problems in non- and semiparametric inference methods for these models are also described.</p></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"28 ","pages":"Pages 105-119"},"PeriodicalIF":1.9,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50198794","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":"Change point estimation under a copula-based Markov chain model for binomial time series","authors":"Takeshi Emura , Ching-Chieh Lai , Li-Hsien Sun","doi":"10.1016/j.ecosta.2021.07.007","DOIUrl":"https://doi.org/10.1016/j.ecosta.2021.07.007","url":null,"abstract":"<div><p><span>Estimation of a change point is a classical statistical problem in sequential analysis and process control. For binomial time series, the existing maximum likelihood estimators<span> (MLEs) for a change point are limited to independent observations. If the independence assumption is violated, the MLEs substantially lose their efficiency, and a likelihood function provides a poor fit to the data. A novel change point estimator<span> is proposed under a copula-based Markov chain model for serially dependent observations. The main novelty is the adaptation of a three-state </span></span></span>copula<span> model, consisting of the in-control state, out-of-control state, and transition state. Under this model, a MLE is proposed with the aid of profile likelihood. A parametric bootstrap method is adopted to compute a confidence set for the unknown change point. The simulation studies show that the proposed MLE is more efficient than the existing estimators when serial dependence in observations are specified by the model. The proposed method is illustrated by the jewelry manufacturing data, where the proposed model gives an improved fit.</span></p></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"28 ","pages":"Pages 120-137"},"PeriodicalIF":1.9,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ecosta.2021.07.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50198795","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":"Partially orthogonal blocked three-level response surface designs","authors":"Heiko Großmann , Steven G. Gilmour","doi":"10.1016/j.ecosta.2021.08.007","DOIUrl":"https://doi.org/10.1016/j.ecosta.2021.08.007","url":null,"abstract":"<div><p><span>When fitting second-order response surface models in a hypercuboidal region of experimentation, the variance matrices of </span><span><math><mi>D</mi></math></span><span>-optimal continuous designs have a particularly attractive structure, as do many regular unblocked exact designs. Methods for constructing blocked exact designs which preserve this structure and are orthogonal, or nearly orthogonal, are developed. Partially orthogonal designs are built using a small irregular fraction of a two- or three-level design and a regular fractional factorial design as building blocks. Results are derived which relate the properties of the blocked design to these components. Moreover, it is shown how the designs can be augmented to ensure that the model can be fitted and a method for constructing designs with small blocks is presented. Examples illustrate that partially orthogonal designs can compete with more traditional designs in terms of both efficiency and overall size of the experiment.</span></p></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"28 ","pages":"Pages 138-154"},"PeriodicalIF":1.9,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.ecosta.2021.08.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50198796","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":"Robust nonparametric multiple changepoint detection for multivariate variability","authors":"Kelly Ramsay, Shojaeddin Chenouri","doi":"10.1016/j.ecosta.2023.09.001","DOIUrl":"https://doi.org/10.1016/j.ecosta.2023.09.001","url":null,"abstract":"Two robust, nonparametric multiple changepoint detection algorithms are introduced: DWBS and MKWP. These algorithms can detect multiple changes in the variability of a sequence of independent multivariate observations, even when the number of changepoints is unknown. The algorithms DWBS and MKWP require minimal distributional assumptions and are robust to outlying observations and heavy tails. The DWBS algorithm uses a local search method based on depth-based ranks and wild binary segmentation. The MKWP algorithm estimates changepoints globally via maximizing a penalized version of the classical Kruskal–Wallis ANOVA test statistic. It is demonstrated that this objective function can be maximized via the well-known PELT algorithm. Under mild, nonparametric assumptions, both of these algorithms are shown to be consistent for the correct number of changepoints and the correct location(s) of the changepoint(s). A data driven thresholding method for multivariate data is introduced, based on the Schwartz information criteria. The robustness and accuracy of the new methods is demonstrated with a simulation study, where the algorithms are compared to several existing algorithms. These new methods can estimate the number of changepoints and their locations accurately when the data are heavy tailed or skewed and the sample size is large. Lastly, the proposed algorithms are applied to a four-dimensional sequence of European daily stock returns.","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134936298","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":"Vine Copula based Portfolio Level Conditional Risk Measure Forecasting","authors":"Emanuel Sommer, Karoline Bax, Claudia Czado","doi":"10.1016/j.ecosta.2023.08.002","DOIUrl":"https://doi.org/10.1016/j.ecosta.2023.08.002","url":null,"abstract":"Accurately estimating risk measures for financial portfolios and validating their robustness is critical for both financial institutions and regulators. However, many existing models operate at the aggregate portfolio level, hence they fail to capture the complex cross-dependencies between portfolio components and particularly provide no methodology to perform a sensitivity analysis on the estimates. To address both aspects, a new approach is presented that uses vine copulas in combination with univariate ARMA-GARCH models for marginal modelling to compute conditional portfolio-level risk measure estimates by simulating portfolio-level forecasts conditioned on a stress factor. A quantile-based approach is then presented to observe the behaviour of risk measures given a particular state of the conditioning asset(s). In an illustrative case study of Spanish equities with different stress factors, the results show that the portfolio is quite robust to a sharp downturn in the American market. At the same time, there is no evidence of this behaviour with respect to the European market. The novel algorithms presented are ready for use through the R package portvine, which is publicly available on CRAN.","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136221687","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":"A Computationally Efficient Mixture Innovation Model for Time-Varying Parameter Regressions","authors":"Zhongfang He","doi":"10.1016/j.ecosta.2023.08.001","DOIUrl":"https://doi.org/10.1016/j.ecosta.2023.08.001","url":null,"abstract":"","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"142 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75374122","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}