Pub Date : 2026-01-01Epub Date: 2023-06-29DOI: 10.1016/j.ecosta.2023.06.007
Eiji Kurozumi
A fluctuation-type monitoring test for a bubble is proposed. The initial value is dealt with by either OLS or quasi-difference demeaning. The asymptotic property of the test under mildly explosive and local alternatives is investigated. It is shown that the fluctuation-type test has an advantage over the existing methods when the bubble appears mid- to late in the monitoring period or the bubble period is relatively long, whereas the CUSUM monitoring scheme performs better in view of power for an early bubble in the monitoring period. This theoretical property is supported in finite samples by Monte Carlo simulations. As none of the existing tests uniformly outperforms the others, the union of rejections strategy by combining the two or three monitoring tests is also proposed, which is shown to work well in finite samples.
{"title":"Fluctuation-type monitoring test for explosive behavior","authors":"Eiji Kurozumi","doi":"10.1016/j.ecosta.2023.06.007","DOIUrl":"10.1016/j.ecosta.2023.06.007","url":null,"abstract":"<div><div>A fluctuation-type monitoring test for a bubble is proposed. The initial value is dealt with by either OLS or quasi-difference demeaning. The asymptotic property of the test under mildly explosive and local alternatives is investigated. It is shown that the fluctuation-type test has an advantage over the existing methods when the bubble appears mid- to late in the monitoring period or the bubble period is relatively long, whereas the CUSUM monitoring scheme performs better in view of power for an early bubble in the monitoring period. This theoretical property is supported in finite samples by Monte Carlo simulations. As none of the existing tests uniformly outperforms the others, the union of rejections strategy by combining the two or three monitoring tests is also proposed, which is shown to work well in finite samples.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 230-249"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83908081","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}
Pub Date : 2026-01-01Epub Date: 2023-06-22DOI: 10.1016/j.ecosta.2023.06.004
Yu Bai , Massimiliano Marcellino , George Kapetanios
The large heterogeneous panel data models are extended to the setting where the heterogenous coefficients are changing over time and the regressors are endogenous. Kernel-based non-parametric time-varying parameter instrumental variable mean group (TVP-IV-MG) estimator is proposed for the time-varying cross-sectional mean coefficients. The uniform consistency is shown and the pointwise asymptotic normality of the proposed estimator is derived. A data-driven bandwidth selection procedure is also proposed. The finite sample performance of the proposed estimator is investigated through a Monte Carlo study and an empirical application on multi-country Phillips curve with time-varying parameters.
{"title":"Mean group instrumental variable estimation of time-varying large heterogeneous panels with endogenous regressors","authors":"Yu Bai , Massimiliano Marcellino , George Kapetanios","doi":"10.1016/j.ecosta.2023.06.004","DOIUrl":"10.1016/j.ecosta.2023.06.004","url":null,"abstract":"<div><div><span>The large heterogeneous panel data models<span> are extended to the setting where the heterogenous coefficients are changing over time and the regressors are endogenous. Kernel-based non-parametric time-varying parameter </span></span>instrumental variable<span> mean group (TVP-IV-MG) estimator is proposed for the time-varying cross-sectional mean coefficients. The uniform consistency is shown and the pointwise asymptotic normality of the proposed estimator is derived. A data-driven bandwidth selection procedure is also proposed. The finite sample performance of the proposed estimator is investigated through a Monte Carlo study and an empirical application on multi-country Phillips curve with time-varying parameters.</span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 26-41"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85391343","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}
Pub Date : 2026-01-01Epub Date: 2023-03-04DOI: 10.1016/j.ecosta.2023.02.004
Henri Nyberg , Christos S. Savva
The fundamental risk-return relation is examined with a flexible regime switching model combining the impact of skewness and business cycle regimes in stock returns. Key methodological and empirical findings point out the need for a highly nonlinear and non-Gaussian model to get a reliable picture on the risk-return relationship. With an international dataset of major countries to global financial markets, the empirical results show that accounting especially for skewness patterns leads to the expected positive risk-return relation, which is importantly also maintained over different business cycle conditions.
{"title":"Risk-return trade-off in international stock returns: Skewness and business cycles","authors":"Henri Nyberg , Christos S. Savva","doi":"10.1016/j.ecosta.2023.02.004","DOIUrl":"10.1016/j.ecosta.2023.02.004","url":null,"abstract":"<div><div>The fundamental risk-return relation is examined with a flexible regime switching model combining the impact of skewness and business cycle regimes in stock returns. Key methodological and empirical findings point out the need for a highly nonlinear and non-Gaussian model to get a reliable picture on the risk-return relationship. With an international dataset of major countries to global financial markets, the empirical results show that accounting especially for skewness patterns leads to the expected positive risk-return relation, which is importantly also maintained over different business cycle conditions.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 42-60"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136051658","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}
Pub Date : 2026-01-01Epub Date: 2023-02-20DOI: 10.1016/j.ecosta.2023.02.003
Jose Olmo , Marcos Sanso-Navarro
Conventional spatial regression models are extended by modelling the spatial effects of the exogenous regressor model (SLX) as a functional coefficient. This coefficient is estimated by partitioning the domain of the spatial variable into a set of disjoint intervals and approximating the function using local Taylor expansions. The asymptotic properties of the proposed partitioning estimator are derived, and pointwise and uniform tests for the presence of spatial effects are developed. An empirical application of this work is used to study environmental Engel curves and provides strong evidence of neighbouring effects in the relationship between households’ income and the amount of pollution embodied in the goods and services they consume.
{"title":"A nonparametric spatial regression model using partitioning estimators","authors":"Jose Olmo , Marcos Sanso-Navarro","doi":"10.1016/j.ecosta.2023.02.003","DOIUrl":"10.1016/j.ecosta.2023.02.003","url":null,"abstract":"<div><div><span>Conventional spatial regression models are extended by modelling the spatial effects of the exogenous regressor model (SLX) as a functional coefficient. This coefficient is estimated by partitioning the domain of the spatial variable into a set of disjoint intervals and approximating the function using local Taylor expansions. The </span>asymptotic properties<span> of the proposed partitioning estimator are derived, and pointwise and uniform tests for the presence of spatial effects are developed. An empirical application of this work is used to study environmental Engel curves and provides strong evidence of neighbouring effects in the relationship between households’ income and the amount of pollution embodied in the goods and services they consume.</span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 126-153"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79414951","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}
Pub Date : 2026-01-01Epub Date: 2023-07-03DOI: 10.1016/j.ecosta.2023.06.006
Zhihao Xu , Clifford M. Hurvich
A unified frequency domain cross-validation (FDCV) method is proposed to obtain a heteroskedasticity and autocorrelation consistent (HAC) standard error. This method enables model/tuning parameter selection across both parametric and nonparametric spectral estimators simultaneously. The candidate class for this approach consists of restricted maximum likelihood-based (REML) autoregressive spectral estimators and lag-weights estimators with the Parzen kernel. Additionally, an efficient technique for computing the REML estimators of autoregressive models is provided. Through simulations, the reliability of the FDCV method is demonstrated, comparing favorably with popular HAC estimators such as Andrews-Monahan and Newey-West.
{"title":"A Unified Frequency Domain Cross-Validatory Approach to HAC Standard Error Estimation","authors":"Zhihao Xu , Clifford M. Hurvich","doi":"10.1016/j.ecosta.2023.06.006","DOIUrl":"10.1016/j.ecosta.2023.06.006","url":null,"abstract":"<div><div><span>A unified frequency domain cross-validation (FDCV) method is proposed to obtain a heteroskedasticity and autocorrelation<span><span> consistent (HAC) standard error. This method enables model/tuning parameter selection across both parametric and nonparametric spectral estimators simultaneously. The candidate class for this approach consists of restricted maximum likelihood-based (REML) autoregressive spectral estimators and lag-weights estimators with the Parzen kernel. Additionally, an efficient technique for computing the REML estimators of </span>autoregressive models is provided. Through simulations, the reliability of the FDCV method is demonstrated, comparing favorably with popular </span></span>HAC estimators such as Andrews-Monahan and Newey-West.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 214-229"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80038692","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}
Pub Date : 2026-01-01Epub Date: 2023-11-03DOI: 10.1016/j.ecosta.2023.11.001
Alexander Chudik , M. Hashem Pesaran , Ron P. Smith
Using a transformation of the autoregressive distributed lag model due to Bewley, a novel pooled Bewley (PB) estimator of long-run coefficients for dynamic panels with heterogeneous short-run dynamics is proposed. The PB estimator is directly comparable to the widely used Pooled Mean Group (PMG) estimator, and is shown to be consistent and asymptotically normal. Monte Carlo simulations show good small sample performance of PB compared to the existing estimators in the literature, namely PMG, panel dynamic OLS (PDOLS), and panel fully-modified OLS (FMOLS). Application of two bias-correction methods and a bootstrapping of critical values to conduct inference robust to cross-sectional dependence of errors are also considered. The utility of the PB estimator is illustrated in an empirical application to the aggregate consumption function.
通过对自回归分布滞后模型的变换,提出了一种具有异质短期动态的动态面板长期系数池Bewley (PB)估计方法。PB估计量与广泛使用的PMG (Pooled Mean Group)估计量具有直接可比性,并被证明是一致的和渐近正态的。蒙特卡罗模拟表明,与文献中现有的估计器(即PMG、面板动态OLS (pols)和面板全修正OLS (FMOLS))相比,PB具有良好的小样本性能。还考虑了两种偏差校正方法的应用和临界值的自举来对误差的横截面依赖性进行鲁棒推断。PB估计器的效用在总消费函数的经验应用中得到说明。
{"title":"Pooled Bewley Estimator of Long Run Relationships in Dynamic Heterogenous Panels","authors":"Alexander Chudik , M. Hashem Pesaran , Ron P. Smith","doi":"10.1016/j.ecosta.2023.11.001","DOIUrl":"10.1016/j.ecosta.2023.11.001","url":null,"abstract":"<div><div>Using a transformation of the autoregressive distributed lag model due to Bewley, a novel pooled Bewley (PB) estimator of long-run coefficients for dynamic panels with heterogeneous short-run dynamics is proposed. The PB estimator is directly comparable to the widely used Pooled Mean Group (PMG) estimator, and is shown to be consistent and asymptotically normal. Monte Carlo simulations show good small sample performance of PB compared to the existing estimators in the literature, namely PMG, panel dynamic OLS (PDOLS), and panel fully-modified OLS (FMOLS). Application of two bias-correction methods and a bootstrapping of critical values to conduct inference robust to cross-sectional dependence of errors are also considered. The utility of the PB estimator is illustrated in an empirical application to the aggregate consumption function.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 1-25"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135411092","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}
Pub Date : 2026-01-01Epub Date: 2023-06-01DOI: 10.1016/j.ecosta.2023.05.003
Matei Demetrescu , Christoph Hanck , Robinson Kruse-Becher
Time-varying volatility arises in many macroeconomic and financial applications. While “fixed-” arguments provide refinements in the use of estimators for the asymptotic variance of GMM estimators, the resulting fixed- distributions of test statistics are not pivotal under time-varying volatility. Three approaches to robustify inference are investigated: (i) wild bootstrapping, (ii) time transformations and (iii) selection of test statistics and critical values according to the outcome of a pretest for heteroskedasticity. Simulations quantify the distortions from using the original fixed- approach and compare the effectiveness of the proposed corrections. Overall, the wild bootstrap is to be recommended. An empirical application to the Fama & French five factor model illustrates the relevance of the procedures.
{"title":"Robust Fixed-b Inference in the Presence of Time-Varying Volatility","authors":"Matei Demetrescu , Christoph Hanck , Robinson Kruse-Becher","doi":"10.1016/j.ecosta.2023.05.003","DOIUrl":"10.1016/j.ecosta.2023.05.003","url":null,"abstract":"<div><div><span>Time-varying volatility arises in many macroeconomic and financial applications. While “fixed-</span><span><math><mi>b</mi></math></span>” arguments provide refinements in the use of estimators for the asymptotic variance of GMM estimators, the resulting fixed-<span><math><mi>b</mi></math></span> distributions of test statistics are not pivotal under time-varying volatility. Three approaches to robustify inference are investigated: (i) wild bootstrapping, (ii) time transformations and (iii) selection of test statistics and critical values according to the outcome of a pretest for heteroskedasticity. Simulations quantify the distortions from using the original fixed-<span><math><mi>b</mi></math></span> approach and compare the effectiveness of the proposed corrections. Overall, the wild bootstrap is to be recommended. An empirical application to the Fama & French five factor model illustrates the relevance of the procedures.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 154-173"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88515536","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}
Pub Date : 2026-01-01Epub Date: 2023-06-21DOI: 10.1016/j.ecosta.2023.06.005
Galina Besstremyannaya , Sergei Golovan
The purpose is to enable inference in case of quantile regression with endogenous covariates and clustered data. It is proven that the instrumental variable quantile regression estimator is consistent where there is correlation of errors within clusters, and an asymptotic distribution for the estimator, which may be used for inference for a given quantile is derived. As regards inference based on the entire instrumental variable quantile regression process, it is proven that cluster-based resampling of a statistic of a certain class offers a computationally tractable approach for implementing asymptotic tests. The theoretical results concerning the asymptotic properties of the instrumental variable quantile regression estimator for clustered data are supported by simulation analysis. An empirical illustration shows the use of the proposed technique in order to estimate the earning equations of US men and women where female labor supply is endogenous and subject to the shock of World War II.
{"title":"Instrumental variable quantile regression for clustered data","authors":"Galina Besstremyannaya , Sergei Golovan","doi":"10.1016/j.ecosta.2023.06.005","DOIUrl":"10.1016/j.ecosta.2023.06.005","url":null,"abstract":"<div><div><span>The purpose is to enable inference in case of quantile<span> regression with endogenous covariates and clustered data. It is proven that the instrumental variable<span> quantile regression estimator is consistent where there is correlation of errors within clusters, and an asymptotic distribution for the estimator, which may be used for inference for a given quantile </span></span></span><span><math><mrow><mi>τ</mi><mo>,</mo></mrow></math></span><span> is derived. As regards inference based on the entire instrumental variable quantile regression process, it is proven that cluster-based resampling of a statistic of a certain class offers a computationally tractable approach for implementing asymptotic tests. The theoretical results concerning the asymptotic properties of the instrumental variable quantile regression estimator for clustered data are supported by simulation analysis. An empirical illustration shows the use of the proposed technique in order to estimate the earning equations of US men and women where female labor supply is endogenous and subject to the shock of World War II.</span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 199-213"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75554052","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}
Pub Date : 2026-01-01Epub Date: 2023-08-12DOI: 10.1016/j.ecosta.2023.08.001
Zhongfang He
The mixture innovation (MI) model places a spike-and-slab mixture distribution for the innovations of time-varying regression coefficients and permits flexible time variation patterns while allowing for dynamic shrinkage. Despite its appeal, the standard Bayesian algorithm to block sample the vector of 0/1 mixture indicators at each time needs to evaluate the model likelihood over all its scenarios for a regression model with regressors and becomes impractical when grows. As an alternative, a new specification of the MI model is proposed in which the 0/1 mixture indicators in the original MI model are approximated by a logistic function of latent continuous variables. As such the model likelihood only needs to be evaluated twice in an Metropolis-Hastings step to block update the latent variables and hence the approximated mixture indicators at each time , offering large improvement in computational efficiency while keeping the benefits of the MI model. An efficient MCMC algorithm is developed to estimate the new model. A simulation study shows that the new model can achieve the same level of estimation accuracy as the original MI model but at a much smaller computation cost. The new model is further tested in two empirical applications where block sampling the mixture indicators at each time in the original MI model is practically infeasible.
{"title":"A computationally efficient mixture innovation model for time-varying parameter regressions","authors":"Zhongfang He","doi":"10.1016/j.ecosta.2023.08.001","DOIUrl":"10.1016/j.ecosta.2023.08.001","url":null,"abstract":"<div><div><span>The mixture innovation (MI) model places a spike-and-slab mixture distribution for the innovations of time-varying regression coefficients and permits flexible time variation patterns while allowing for dynamic shrinkage. Despite its appeal, the standard Bayesian algorithm to block sample the vector of 0/1 mixture indicators at each time </span><span><math><mi>t</mi></math></span> needs to evaluate the model likelihood over all its <span><math><msup><mn>2</mn><mi>K</mi></msup></math></span> scenarios for a regression model with <span><math><mi>K</mi></math></span><span> regressors and becomes impractical when </span><span><math><mi>K</mi></math></span><span> grows. As an alternative, a new specification of the MI model is proposed in which the 0/1 mixture indicators in the original MI model are approximated by a logistic function of latent continuous variables. As such the model likelihood only needs to be evaluated twice in an Metropolis-Hastings step to block update the latent variables and hence the approximated mixture indicators at each time </span><span><math><mi>t</mi></math></span>, offering large improvement in computational efficiency while keeping the benefits of the MI model. An efficient MCMC algorithm is developed to estimate the new model. A simulation study shows that the new model can achieve the same level of estimation accuracy as the original MI model but at a much smaller computation cost. The new model is further tested in two empirical applications where block sampling the mixture indicators at each time <span><math><mi>t</mi></math></span> in the original MI model is practically infeasible.</div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 250-269"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","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}
Pub Date : 2026-01-01Epub Date: 2023-01-09DOI: 10.1016/j.ecosta.2023.01.001
Etienne Theising, Dominik Wied
Monitoring statistics for structural changes in systems of cointegrating relationships are proposed. The approach is based on parameter estimation over a calibration period. In case of homogenous systems and cross-sectional independence the pooled fully modified OLS estimator takes into account the effects of error serial correlation and regressor endogeneity. Cross-sectional dependence is allowed by using the pooled fully modified GLS estimator for homogenous systems and the fully modified SUR estimator for inhomogenous systems. The detectors show decent behaviour under the null hypothesis with controlled rejection probabilities and power against two alternatives for different data generating processes. An empirical application investigates deviations from the arbitrage parity condition for exchange rate triplets including Bitcoin. The procedures detect breakpoints in May to August 2014 and in January to May 2015 indicating an instability in arbitrage parities. Following this, a promising portfolio trading strategy based on the breakdates is constructed.
{"title":"Monitoring cointegration in systems of cointegrating relationships","authors":"Etienne Theising, Dominik Wied","doi":"10.1016/j.ecosta.2023.01.001","DOIUrl":"10.1016/j.ecosta.2023.01.001","url":null,"abstract":"<div><div>Monitoring statistics for structural changes in systems of cointegrating relationships are proposed. The approach is based on parameter estimation over a calibration period. In case of homogenous systems and cross-sectional independence the pooled fully modified OLS estimator takes into account the effects of error serial correlation and regressor<span> endogeneity. Cross-sectional dependence is allowed by using the pooled fully modified GLS estimator for homogenous systems and the fully modified SUR estimator for inhomogenous systems. The detectors show decent behaviour under the null hypothesis with controlled rejection probabilities and power against two alternatives for different data generating processes. An empirical application investigates deviations from the arbitrage parity condition for exchange rate triplets including Bitcoin. The procedures detect breakpoints in May to August 2014 and in January to May 2015 indicating an instability in arbitrage parities. Following this, a promising portfolio trading strategy based on the breakdates is constructed.</span></div></div>","PeriodicalId":54125,"journal":{"name":"Econometrics and Statistics","volume":"37 ","pages":"Pages 61-86"},"PeriodicalIF":2.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81830881","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}