Pub Date : 2025-10-13DOI: 10.1016/j.jeconom.2025.106108
Frank Kleibergen , Zhaoguo Zhan
We propose the continuous updating estimator (CUE) for estimating ex-post risk premia from large cross-sections of individual asset returns over limited time periods. We analyze its properties while also allowing for an unknown number of unobserved factors. The CUE then provides an estimator of its, so-called, pseudo-true value, the risk premia on the observed factors without assuming that they comprise all priced factors. We develop size-correct procedures for testing hypotheses on the estimand of the CUE, which are more precise than existing ones. The proposed methodology is used to examine risk factors widely analyzed using a small number of portfolios. Our findings are that market, size, and momentum factors carry largely positive risk premia, while many other factors much less so. Different factors therefore stand out in the cross-section of individual assets.
{"title":"Risk premia from the cross-section of individual assets","authors":"Frank Kleibergen , Zhaoguo Zhan","doi":"10.1016/j.jeconom.2025.106108","DOIUrl":"10.1016/j.jeconom.2025.106108","url":null,"abstract":"<div><div>We propose the continuous updating estimator (CUE) for estimating ex-post risk premia from large cross-sections of individual asset returns over limited time periods. We analyze its properties while also allowing for an unknown number of unobserved factors. The CUE then provides an estimator of its, so-called, pseudo-true value, <span><math><mrow><mi>i</mi><mo>.</mo><mi>e</mi><mo>.</mo><mo>,</mo></mrow></math></span> the risk premia on the observed factors without assuming that they comprise all priced factors. We develop size-correct procedures for testing hypotheses on the estimand of the CUE, which are more precise than existing ones. The proposed methodology is used to examine risk factors widely analyzed using a small number of portfolios. Our findings are that market, size, and momentum factors carry largely positive risk premia, while many other factors much less so. Different factors therefore stand out in the cross-section of individual assets.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106108"},"PeriodicalIF":4.0,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-10DOI: 10.1016/j.jeconom.2025.106111
Gregory Fletcher Cox
When parameters are weakly identified, bounds on the parameters may provide a valuable source of information. Existing weak identification estimation and inference results are unable to combine weak identification with bounds. Within a class of minimum distance models, this paper proposes identification-robust inference that incorporates information from bounds when parameters are weakly identified. This paper demonstrates the value of the bounds and identification-robust inference in a simple latent factor model and a simple GARCH model. This paper also demonstrates the identification-robust inference in an empirical application, a factor model for parental investments in children.
{"title":"Weak identification with bounds in a class of minimum distance models","authors":"Gregory Fletcher Cox","doi":"10.1016/j.jeconom.2025.106111","DOIUrl":"10.1016/j.jeconom.2025.106111","url":null,"abstract":"<div><div>When parameters are weakly identified, bounds on the parameters may provide a valuable source of information. Existing weak identification estimation and inference results are unable to combine weak identification with bounds. Within a class of minimum distance models, this paper proposes identification-robust inference that incorporates information from bounds when parameters are weakly identified. This paper demonstrates the value of the bounds and identification-robust inference in a simple latent factor model and a simple GARCH model. This paper also demonstrates the identification-robust inference in an empirical application, a factor model for parental investments in children.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106111"},"PeriodicalIF":4.0,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-09DOI: 10.1016/j.jeconom.2025.106100
Alexandre Belloni , Mingli Chen , Victor Chernozhukov
We propose two types of Quantile Graphical Models: (i) Conditional Independence Quantile Graphical Models (CIQGMs) characterize the conditional independence by evaluating the distributional dependence structure at each quantile index, as such, those can be used for validation of the graph structure in the causal graphical models; (ii) Prediction Quantile Graphical Models (PQGMs) characterize the statistical dependencies through the graphs of the best linear predictors under asymmetric loss functions. PQGMs make weaker assumptions than CIQGMs as they allow for misspecification. One advantage of these models is that we can apply them to large collections of variables driven by non-Gaussian and non-separable shocks. Because of QGMs’ ability to handle large collections of variables and focus on specific parts of the distributions, we could apply them to quantify tail interdependence. The resulting tail risk network can be used for measuring systemic risk contributions that help make inroads in understanding international financial contagion and dependence structures of returns under downside market movements.
We develop estimation and inference methods focusing on the high-dimensional case, where the number of nodes in the graph is large as compared to the number of observations. For CIQGMs, these results include valid simultaneous choices of penalty functions, uniform rates of convergence, and confidence regions that are simultaneously valid. We also derive analogous results for PQGMs, which include new results for penalized quantile regressions in high-dimensional settings to handle misspecification, many controls, and a continuum of additional conditioning events.
{"title":"Quantile graphical models: Prediction and conditional independence with applications to systemic risk","authors":"Alexandre Belloni , Mingli Chen , Victor Chernozhukov","doi":"10.1016/j.jeconom.2025.106100","DOIUrl":"10.1016/j.jeconom.2025.106100","url":null,"abstract":"<div><div>We propose two types of Quantile Graphical Models: (i) Conditional Independence Quantile Graphical Models (CIQGMs) characterize the conditional independence by evaluating the distributional dependence structure at each quantile index, as such, those can be used for validation of the graph structure in the causal graphical models; (ii) Prediction Quantile Graphical Models (PQGMs) characterize the statistical dependencies through the graphs of the best linear predictors under asymmetric loss functions. PQGMs make weaker assumptions than CIQGMs as they allow for misspecification. One advantage of these models is that we can apply them to large collections of variables driven by non-Gaussian and non-separable shocks. Because of QGMs’ ability to handle large collections of variables and focus on specific parts of the distributions, we could apply them to quantify tail interdependence. The resulting tail risk network can be used for measuring systemic risk contributions that help make inroads in understanding international financial contagion and dependence structures of returns under downside market movements.</div><div>We develop estimation and inference methods focusing on the high-dimensional case, where the number of nodes in the graph is large as compared to the number of observations. For CIQGMs, these results include valid simultaneous choices of penalty functions, uniform rates of convergence, and confidence regions that are simultaneously valid. We also derive analogous results for PQGMs, which include new results for penalized quantile regressions in high-dimensional settings to handle misspecification, many controls, and a continuum of additional conditioning events.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106100"},"PeriodicalIF":4.0,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-10-04DOI: 10.1016/j.jeconom.2025.106103
James A. Duffy , Sophocles Mavroeidis , Sam Wycherley
In the literature on nonlinear cointegration, a long-standing open problem relates to how a (nonlinear) vector autoregression, which provides a unified description of the short- and long-run dynamics of a vector of time series, can generate ‘nonlinear cointegration’ in the profound sense of those series sharing common nonlinear stochastic trends. We consider this problem in the setting of the censored and kinked structural VAR (CKSVAR), which provides a flexible yet tractable framework within which to model time series that are subject to threshold-type nonlinearities, such as those arising due to occasionally binding constraints, of which the zero lower bound (ZLB) on short-term nominal interest rates provides a leading example. We provide a complete characterisation of how common linear and nonlinear stochastic trends may be generated in this model, via unit roots and appropriate generalisations of the usual rank conditions, providing the first extension to date of the Granger–Johansen representation theorem to a nonlinearly cointegrated setting, and thereby giving the first successful treatment of the open problem. The limiting common trend processes include regulated, censored and kinked Brownian motions, none of which have previously appeared in the literature on cointegrated VARs. Our results and running examples illustrate that the CKSVAR is capable of supporting a far richer variety of long-run behaviour than is a linear VAR, in ways that may be particularly useful for the identification of structural parameters.
{"title":"Cointegration with occasionally binding constraints","authors":"James A. Duffy , Sophocles Mavroeidis , Sam Wycherley","doi":"10.1016/j.jeconom.2025.106103","DOIUrl":"10.1016/j.jeconom.2025.106103","url":null,"abstract":"<div><div>In the literature on nonlinear cointegration, a long-standing open problem relates to how a (nonlinear) vector autoregression, which provides a unified description of the short- and long-run dynamics of a vector of time series, can generate ‘nonlinear cointegration’ in the profound sense of those series sharing common nonlinear stochastic trends. We consider this problem in the setting of the censored and kinked structural VAR (CKSVAR), which provides a flexible yet tractable framework within which to model time series that are subject to threshold-type nonlinearities, such as those arising due to occasionally binding constraints, of which the zero lower bound (ZLB) on short-term nominal interest rates provides a leading example. We provide a complete characterisation of how common linear and <em>nonlinear</em> stochastic trends may be generated in this model, via unit roots and appropriate generalisations of the usual rank conditions, providing the first extension to date of the Granger–Johansen representation theorem to a nonlinearly cointegrated setting, and thereby giving the first successful treatment of the open problem. The limiting common trend processes include regulated, censored and kinked Brownian motions, none of which have previously appeared in the literature on cointegrated VARs. Our results and running examples illustrate that the CKSVAR is capable of supporting a far richer variety of long-run behaviour than is a linear VAR, in ways that may be particularly useful for the identification of structural parameters.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106103"},"PeriodicalIF":4.0,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-26DOI: 10.1016/j.jeconom.2025.106105
Clifford Lam , Zetai Cen
We introduce the matrix-valued time-varying Main Effects Factor Model (MEFM). MEFM is a generalization to the traditional matrix-valued factor model (FM). We give rigorous definitions of MEFM and its identifications, and propose estimators for the time-varying grand mean, row and column main effects, and the row and column factor loading matrices for the common component. Rates of convergence for different estimators are spelt out, with asymptotic normality shown. The core rank estimator for the common component is also proposed, with consistency of the estimators presented. As time series, the row and column main effects and can be non-stationary without affecting the estimation accuracy of our estimators. The number of main effects factors contributing to row or column main effects is also consistently estimated by our proposed estimators. We propose a test for testing if FM is sufficient against the alternative that MEFM is necessary, and demonstrate the power of such a test in various simulation settings. We also demonstrate numerically the accuracy of our estimators in extended simulation experiments. A set of NYC Taxi traffic data is analyzed and our test suggests that MEFM is indeed necessary for analyzing the data against a traditional FM.
{"title":"Matrix-valued factor model with time-varying main effects","authors":"Clifford Lam , Zetai Cen","doi":"10.1016/j.jeconom.2025.106105","DOIUrl":"10.1016/j.jeconom.2025.106105","url":null,"abstract":"<div><div>We introduce the matrix-valued time-varying Main Effects Factor Model (MEFM). MEFM is a generalization to the traditional matrix-valued factor model (FM). We give rigorous definitions of MEFM and its identifications, and propose estimators for the time-varying grand mean, row and column main effects, and the row and column factor loading matrices for the common component. Rates of convergence for different estimators are spelt out, with asymptotic normality shown. The core rank estimator for the common component is also proposed, with consistency of the estimators presented. As time series, the row and column main effects <span><math><mrow><mo>{</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>}</mo></mrow></math></span> and <span><math><mrow><mo>{</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>}</mo></mrow></math></span> can be non-stationary without affecting the estimation accuracy of our estimators. The number of main effects factors contributing to row or column main effects is also consistently estimated by our proposed estimators. We propose a test for testing if FM is sufficient against the alternative that MEFM is necessary, and demonstrate the power of such a test in various simulation settings. We also demonstrate numerically the accuracy of our estimators in extended simulation experiments. A set of NYC Taxi traffic data is analyzed and our test suggests that MEFM is indeed necessary for analyzing the data against a traditional FM.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106105"},"PeriodicalIF":4.0,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-23DOI: 10.1016/j.jeconom.2025.106101
Luis A.F. Alvarez , Chang Chiann , Pedro A. Morettin
This paper studies parameter estimation using L-moments, an alternative to traditional moments with attractive statistical properties. The estimation of model parameters by matching sample L-moments is known to outperform maximum likelihood estimation (MLE) in small samples from popular distributions. The choice of the number of L-moments used in estimation remains ad-hoc, though: researchers typically set the number of L-moments equal to the number of parameters, which is inefficient in larger samples. In this paper, we show that, by properly choosing the number of L-moments and weighting these accordingly, one is able to construct an estimator that outperforms MLE in finite samples, and yet retains asymptotic efficiency. We do so by introducing a generalised method of L-moments estimator and deriving its properties in an asymptotic framework where the number of L-moments varies with sample size. We then propose methods to automatically select the number of L-moments in a sample. Monte Carlo evidence shows our approach can provide mean-squared-error improvements over MLE in smaller samples, whilst working as well as it in larger samples. We consider extensions of our approach to the estimation of conditional models and a class semiparametric models. We apply the latter to study expenditure patterns in a ridesharing platform in Brazil.
{"title":"Inference on model parameters with many L-moments","authors":"Luis A.F. Alvarez , Chang Chiann , Pedro A. Morettin","doi":"10.1016/j.jeconom.2025.106101","DOIUrl":"10.1016/j.jeconom.2025.106101","url":null,"abstract":"<div><div>This paper studies parameter estimation using L-moments, an alternative to traditional moments with attractive statistical properties. The estimation of model parameters by matching sample L-moments is known to outperform maximum likelihood estimation (MLE) in small samples from popular distributions. The choice of the number of L-moments used in estimation remains <em>ad-hoc</em>, though: researchers typically set the number of L-moments equal to the number of parameters, which is inefficient in larger samples. In this paper, we show that, by properly choosing the number of L-moments and weighting these accordingly, one is able to construct an estimator that outperforms MLE in finite samples, and yet retains asymptotic efficiency. We do so by introducing a generalised method of L-moments estimator and deriving its properties in an asymptotic framework where the number of L-moments varies with sample size. We then propose methods to automatically select the number of L-moments in a sample. Monte Carlo evidence shows our approach can provide mean-squared-error improvements over MLE in smaller samples, whilst working as well as it in larger samples. We consider extensions of our approach to the estimation of conditional models and a class semiparametric models. We apply the latter to study expenditure patterns in a ridesharing platform in Brazil.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106101"},"PeriodicalIF":4.0,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145118398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-22DOI: 10.1016/j.jeconom.2025.106102
Yuya Shimizu
This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya–Watson kernel regression, and local linear estimation. Our theory accommodates growing and heterogeneous cluster sizes. We derive asymptotic conditional bias and variance, establish uniform consistency, and prove asymptotic normality. Our findings reveal that under heterogeneous cluster sizes, the asymptotic variance includes a new term reflecting within-cluster dependence, which is overlooked when cluster sizes are presumed to be bounded. We propose valid approaches for bandwidth selection and inference, introduce estimators of the asymptotic variance, and demonstrate their consistency. In simulations, we verify the effectiveness of the cluster-robust bandwidth selection and show that the derived cluster-robust confidence interval improves the coverage ratio. We illustrate the application of these methods using a policy-targeting dataset in development economics.
{"title":"Nonparametric regression under cluster sampling","authors":"Yuya Shimizu","doi":"10.1016/j.jeconom.2025.106102","DOIUrl":"10.1016/j.jeconom.2025.106102","url":null,"abstract":"<div><div>This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya–Watson kernel regression, and local linear estimation. Our theory accommodates growing and heterogeneous cluster sizes. We derive asymptotic conditional bias and variance, establish uniform consistency, and prove asymptotic normality. Our findings reveal that under heterogeneous cluster sizes, the asymptotic variance includes a new term reflecting within-cluster dependence, which is overlooked when cluster sizes are presumed to be bounded. We propose valid approaches for bandwidth selection and inference, introduce estimators of the asymptotic variance, and demonstrate their consistency. In simulations, we verify the effectiveness of the cluster-robust bandwidth selection and show that the derived cluster-robust confidence interval improves the coverage ratio. We illustrate the application of these methods using a policy-targeting dataset in development economics.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106102"},"PeriodicalIF":4.0,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145118399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-18DOI: 10.1016/j.jeconom.2025.106099
Daniel Dzikowski, Carsten Jentsch
While seasonality inherent to raw macroeconomic data is commonly removed by seasonal adjustment techniques before it is used for structural inference, this may distort valuable information in the data. As an alternative method to commonly used structural vector autoregressions (SVARs) for seasonally adjusted data, we propose to model potential periodicity in seasonally unadjusted (raw) data directly by structural periodic vector autoregressions (SPVARs). This approach does not only allow for periodically time-varying intercepts, but also for periodic autoregressive parameters and innovations variances. As this larger flexibility leads to an increased number of parameters, we propose linearly constrained estimation techniques. Moreover, based on SPVARs, we provide two novel identification schemes and propose a general framework for impulse response analyses that allows for direct consideration of seasonal patterns. We provide asymptotic theory for SPVAR estimators and impulse responses under flexible linear restrictions and introduce a test for seasonality in impulse responses. For the construction of confidence intervals, we discuss several residual-based (seasonal) bootstrap methods and prove their bootstrap consistency under different assumptions. A real data application shows that useful information about the periodic structure in the data may be lost when relying on common seasonal adjustment methods.
{"title":"Structural periodic vector autoregressions","authors":"Daniel Dzikowski, Carsten Jentsch","doi":"10.1016/j.jeconom.2025.106099","DOIUrl":"10.1016/j.jeconom.2025.106099","url":null,"abstract":"<div><div>While seasonality inherent to raw macroeconomic data is commonly removed by seasonal adjustment techniques before it is used for structural inference, this may distort valuable information in the data. As an alternative method to commonly used structural vector autoregressions (SVARs) for seasonally adjusted data, we propose to model potential periodicity in seasonally unadjusted (raw) data directly by structural periodic vector autoregressions (SPVARs). This approach does not only allow for periodically time-varying intercepts, but also for periodic autoregressive parameters and innovations variances. As this larger flexibility leads to an increased number of parameters, we propose linearly constrained estimation techniques. Moreover, based on SPVARs, we provide two novel identification schemes and propose a general framework for impulse response analyses that allows for direct consideration of seasonal patterns. We provide asymptotic theory for SPVAR estimators and impulse responses under flexible linear restrictions and introduce a test for seasonality in impulse responses. For the construction of confidence intervals, we discuss several residual-based (seasonal) bootstrap methods and prove their bootstrap consistency under different assumptions. A real data application shows that useful information about the periodic structure in the data may be lost when relying on common seasonal adjustment methods.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106099"},"PeriodicalIF":4.0,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-12DOI: 10.1016/j.jeconom.2025.106097
Antoine A. Djogbenou , Ulrich Hounyo
This paper examines the applicability of the bootstrap approach to test for irrelevant risk factors that are potentially useless in misspecified linear stochastic discount factor (SDF) models. In the literature, the misspecification-robust inference with useless factors is known to give rise to nonstandard limiting distributions bounded stochastically to compute critical values. We show how and to what extent the wild bootstrap yields a more accurate approximation of the distribution of -statistics when testing for an unpriced factor in the context of linear SDF models. Simulation experiments and empirical tests are also used to document the relevance of the bootstrap method.
{"title":"Misspecification-robust bootstrap t-test for irrelevant factor in linear stochastic discount factor models","authors":"Antoine A. Djogbenou , Ulrich Hounyo","doi":"10.1016/j.jeconom.2025.106097","DOIUrl":"10.1016/j.jeconom.2025.106097","url":null,"abstract":"<div><div>This paper examines the applicability of the bootstrap approach to test for irrelevant risk factors that are potentially useless in misspecified linear stochastic discount factor (SDF) models. In the literature, the misspecification-robust inference with useless factors is known to give rise to nonstandard limiting distributions bounded stochastically to compute critical values. We show how and to what extent the wild bootstrap yields a more accurate approximation of the distribution of <span><math><mi>t</mi></math></span>-statistics when testing for an unpriced factor in the context of linear SDF models. Simulation experiments and empirical tests are also used to document the relevance of the bootstrap method.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106097"},"PeriodicalIF":4.0,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145046142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-08DOI: 10.1016/j.jeconom.2025.106089
Torben G. Andersen , Yingwen Tan , Viktor Todorov , Zhiyuan Zhang
We devise an on-line detector for temporal instability in the shape of average intraday volatility curves under a general semimartingale setup for the price-volatility dynamics. We adopt a block-based strategy to estimate volatility nonparametrically from the intraday observations over local time windows with asymptotically shrinking size. Our detector then tracks sequential changes in running means of the intraday volatility curve estimates. Asymptotic size and power properties of the detector follow from a weak form invariance principle, which is established under the strong mixing condition aligned with our semimartingale setup. Simulation and empirical results demonstrate good finite-sample performance of the proposed detection method.
{"title":"On-line detection of changes in the shape of intraday volatility curves","authors":"Torben G. Andersen , Yingwen Tan , Viktor Todorov , Zhiyuan Zhang","doi":"10.1016/j.jeconom.2025.106089","DOIUrl":"10.1016/j.jeconom.2025.106089","url":null,"abstract":"<div><div>We devise an on-line detector for temporal instability in the shape of average intraday volatility curves under a general semimartingale setup for the price-volatility dynamics. We adopt a block-based strategy to estimate volatility nonparametrically from the intraday observations over local time windows with asymptotically shrinking size. Our detector then tracks sequential changes in running means of the intraday volatility curve estimates. Asymptotic size and power properties of the detector follow from a weak form invariance principle, which is established under the strong mixing condition aligned with our semimartingale setup. Simulation and empirical results demonstrate good finite-sample performance of the proposed detection method.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106089"},"PeriodicalIF":4.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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