Pub Date : 2026-03-01Epub Date: 2026-02-11DOI: 10.1016/j.jeconom.2026.106195
Songnian Chen , Qian Wang
In this paper, we consider estimation of an accelerated failure time model with time-varying regressors and fixed effects for duration data. We propose computationally simple profiled estimators for both fixed and random censoring cases. Under regularity conditions, we establish consistency and asymptotic normality of the estimators. Simulation studies demonstrate that our estimators perform well in finite samples. Finally, we use data from the First Malaysian Family Life Survey to illustrate our proposed estimation method.
{"title":"Semiparametric estimation of duration model with time-varying regressors and fixed effects","authors":"Songnian Chen , Qian Wang","doi":"10.1016/j.jeconom.2026.106195","DOIUrl":"10.1016/j.jeconom.2026.106195","url":null,"abstract":"<div><div>In this paper, we consider estimation of an accelerated failure time model with time-varying regressors and fixed effects for duration data. We propose computationally simple profiled estimators for both fixed and random censoring cases. Under regularity conditions, we establish consistency and asymptotic normality of the estimators. Simulation studies demonstrate that our estimators perform well in finite samples. Finally, we use data from the First Malaysian Family Life Survey to illustrate our proposed estimation method.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106195"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171159","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 : 2026-03-01Epub Date: 2025-12-31DOI: 10.1016/j.jeconom.2025.106175
Lukas Bauer , Roxana Halbleib , Richard Olsen , Torben G. Andersen , Ingmar Nolte
{"title":"Introduction to the Issue on High Frequency Econometrics","authors":"Lukas Bauer , Roxana Halbleib , Richard Olsen , Torben G. Andersen , Ingmar Nolte","doi":"10.1016/j.jeconom.2025.106175","DOIUrl":"10.1016/j.jeconom.2025.106175","url":null,"abstract":"","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106175"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147399261","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 : 2026-03-01Epub Date: 2025-11-18DOI: 10.1016/j.jeconom.2025.106132
Qiyuan Li , Yifan Li , Ingmar Nolte , Sandra Nolte , Shifan Yu
This paper introduces a novel nonparametric high-frequency jump test for discretely observed Itô semimartingales. Based on observations sampled recursively at first exit times from a symmetric double barrier, our method distinguishes between threshold exceedances caused by the Brownian component and jumps, which enables the construction of a feasible, noise-robust statistical test. Simulation results demonstrate superior finite-sample performance of our test compared to existing methods. An empirical analysis of NYSE-traded stocks provides clear statistical evidence for jumps, with the results highly robust to spurious detections.
{"title":"Testing for jumps in a discretely observed price process with endogenous sampling times","authors":"Qiyuan Li , Yifan Li , Ingmar Nolte , Sandra Nolte , Shifan Yu","doi":"10.1016/j.jeconom.2025.106132","DOIUrl":"10.1016/j.jeconom.2025.106132","url":null,"abstract":"<div><div>This paper introduces a novel nonparametric high-frequency jump test for discretely observed Itô semimartingales. Based on observations sampled recursively at first exit times from a symmetric double barrier, our method distinguishes between threshold exceedances caused by the Brownian component and jumps, which enables the construction of a feasible, noise-robust statistical test. Simulation results demonstrate superior finite-sample performance of our test compared to existing methods. An empirical analysis of NYSE-traded stocks provides clear statistical evidence for jumps, with the results highly robust to spurious detections.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106132"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147399601","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 : 2026-03-01Epub Date: 2024-04-19DOI: 10.1016/j.jeconom.2024.105732
Viktor Todorov , Yang Zhang
We propose a nonparametric estimator for the deterministic periodic component of volatility from short-dated options within an in-fill asymptotic setting. The estimator uses options with zero and one day to expiration sampled at high-frequency during a trading day. At each point in time, we aggregate the options to form nonparametric estimates of conditional risk-neutral expectations of future integrated return variation for the two available option tenors. A suitable ratio of these estimates removes the stochastic components of the conditional expectations of future volatility, up to asymptotically higher-order terms, and allows to form estimates of the deterministic periodic component of volatility. We derive a Central Limit Theorem for the estimator, with its rate of convergence determined from the mesh of the strike grid and the length of the time to expiration of the options. The newly-developed estimation procedure is applied to S&P 500 index options data.
{"title":"Intraday volatility patterns from short-dated options","authors":"Viktor Todorov , Yang Zhang","doi":"10.1016/j.jeconom.2024.105732","DOIUrl":"10.1016/j.jeconom.2024.105732","url":null,"abstract":"<div><div>We propose a nonparametric estimator for the deterministic periodic component of volatility from short-dated options within an in-fill asymptotic setting. The estimator uses options with zero and one day to expiration sampled at high-frequency during a trading day. At each point in time, we aggregate the options to form nonparametric estimates of conditional risk-neutral expectations of future integrated return variation for the two available option tenors. A suitable ratio of these estimates removes the stochastic components of the conditional expectations<span><span> of future volatility, up to asymptotically higher-order terms, and allows to form estimates of the deterministic periodic component of volatility. We derive a Central Limit Theorem for the estimator, with its </span>rate of convergence determined from the mesh of the strike grid and the length of the time to expiration of the options. The newly-developed estimation procedure is applied to S&P 500 index options data.</span></div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 105732"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140769219","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 : 2026-03-01Epub Date: 2026-02-10DOI: 10.1016/j.jeconom.2026.106204
Bin Chen , Yuefeng Han , Qiyang Yu
In this paper, we consider diffusion index forecasting with both tensor and non-tensor predictors, where the tensor structure is preserved with a Canonical Polyadic (CP) tensor factor model. When the number of non-tensor predictors is small, we study the asymptotic properties of the least squares estimator in this tensor factor-augmented regression, allowing for factors with different strengths. We derive an analytical formula for prediction intervals that accounts for the estimation uncertainty of the latent factors. In addition, we propose a novel thresholding estimator for the high-dimensional covariance matrix that is robust to cross-sectional dependence. When the number of non-tensor predictors exceeds or diverges with the sample size, we introduce a multi-source factor-augmented sparse regression model and establish the consistency of the corresponding penalized estimator. Simulation studies validate our theoretical results and an empirical application to U.S. trade flows demonstrates the advantages of our approach over other popular methods in the literature.
{"title":"Diffusion index forecasting with tensor data","authors":"Bin Chen , Yuefeng Han , Qiyang Yu","doi":"10.1016/j.jeconom.2026.106204","DOIUrl":"10.1016/j.jeconom.2026.106204","url":null,"abstract":"<div><div>In this paper, we consider diffusion index forecasting with both tensor and non-tensor predictors, where the tensor structure is preserved with a Canonical Polyadic (CP) tensor factor model. When the number of non-tensor predictors is small, we study the asymptotic properties of the least squares estimator in this tensor factor-augmented regression, allowing for factors with different strengths. We derive an analytical formula for prediction intervals that accounts for the estimation uncertainty of the latent factors. In addition, we propose a novel thresholding estimator for the high-dimensional covariance matrix that is robust to cross-sectional dependence. When the number of non-tensor predictors exceeds or diverges with the sample size, we introduce a multi-source factor-augmented sparse regression model and establish the consistency of the corresponding penalized estimator. Simulation studies validate our theoretical results and an empirical application to U.S. trade flows demonstrates the advantages of our approach over other popular methods in the literature.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106204"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171157","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 : 2026-03-01Epub Date: 2025-11-10DOI: 10.1016/j.jeconom.2025.106122
Andrew J. Patton , Haozhe Zhang
Standard realized volatility (RV) measures estimate the latent volatility of an asset price using high frequency data with no reference to how or where the estimate will subsequently be used. This paper presents methods for “tailoring” the estimate of volatility to the application in which it will be used. For example, if the volatility measure will be used in a specific parametric forecasting model, it may be possible to exploit that knowledge to construct a better measure of volatility. We use methods from machine learning to estimate optimal “bespoke” RVs for heterogeneous autoregressive (HAR) and GARCH-X forecasting applications. We apply the methods to 886 U.S. stock returns and find that bespoke RVs significantly improve out-of-sample forecast performance. We find that, across a variety of volatility models, the bespoke RV places more weight on data from the end of the trade day, and that the optimal bespoke weights can be well-approximated by a simple parametric function.
{"title":"Bespoke realized volatility: Tailored measures of risk for volatility prediction","authors":"Andrew J. Patton , Haozhe Zhang","doi":"10.1016/j.jeconom.2025.106122","DOIUrl":"10.1016/j.jeconom.2025.106122","url":null,"abstract":"<div><div>Standard realized volatility (RV) measures estimate the latent volatility of an asset price using high frequency data with no reference to how or where the estimate will subsequently be used. This paper presents methods for “tailoring” the estimate of volatility to the application in which it will be used. For example, if the volatility measure will be used in a specific parametric forecasting model, it may be possible to exploit that knowledge to construct a better measure of volatility. We use methods from machine learning to estimate optimal “bespoke” RVs for heterogeneous autoregressive (HAR) and GARCH-X forecasting applications. We apply the methods to 886 U.S. stock returns and find that bespoke RVs significantly improve out-of-sample forecast performance. We find that, across a variety of volatility models, the bespoke RV places more weight on data from the end of the trade day, and that the optimal bespoke weights can be well-approximated by a simple parametric function.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106122"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147399101","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 : 2026-03-01Epub Date: 2025-02-04DOI: 10.1016/j.jeconom.2025.105954
Michael Stollenwerk
Realized covariance measures (RCs) are an essential input for assessing the risks of different investment allocations. Thus, it is useful to model and forecast them. To this end, a realistic distributional assumption is needed. In this paper, we compare all probability distributions that have so far in the literature been applied to time-series of RCs. We derive them in a unified framework based on their stochastic representations using random lower and upper triangular matrices. These matrices are composed of standard normal distributions in the off-diagonal elements and -distributions on the diagonals (Barlett matrices). Furthermore, we derive a novel family of probability distributions (the -Riesz distribution family), which has a property we call tail-homogeneity. This property means that in crisis periods, i.e. large RCs, our distribution family realistically assumes high dependence between the individual entries of the RCs. We show theoretically how all the distributions differ from each other, and how they are related to each other. In the empirical part, we demonstrate how the theoretical differences translate into differences in fit and forecasting performance. We show that our novel distribution family achieves the best fit. Out-of-sample forecasting comparisons further corroborate the excellent performance of our novel distribution family.
{"title":"Probability distributions for realized covariance measures","authors":"Michael Stollenwerk","doi":"10.1016/j.jeconom.2025.105954","DOIUrl":"10.1016/j.jeconom.2025.105954","url":null,"abstract":"<div><div>Realized covariance measures (RCs) are an essential input for assessing the risks of different investment allocations. Thus, it is useful to model and forecast them. To this end, a realistic distributional assumption is needed. In this paper, we compare all probability distributions that have so far in the literature been applied to time-series of RCs. We derive them in a unified framework based on their stochastic representations using random lower and upper triangular matrices. These matrices are composed of standard normal distributions in the off-diagonal elements and <span><math><mi>χ</mi></math></span>-distributions on the diagonals (Barlett matrices). Furthermore, we derive a novel family of probability distributions (the <span><math><mi>t</mi></math></span>-Riesz distribution family), which has a property we call <em>tail-homogeneity</em>. This property means that in crisis periods, i.e. large RCs, our distribution family realistically assumes high dependence between the individual entries of the RCs. We show theoretically how all the distributions differ from each other, and how they are related to each other. In the empirical part, we demonstrate how the theoretical differences translate into differences in fit and forecasting performance. We show that our novel distribution family achieves the best fit. Out-of-sample forecasting comparisons further corroborate the excellent performance of our novel distribution family.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 105954"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147399102","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 : 2026-03-01Epub Date: 2026-02-28DOI: 10.1016/j.jeconom.2026.106217
Kai Feng , Han Hong , Denis Nekipelov
In this paper, we develop a functional differentiability approach for solving statistical optimal allocation problems. We derive Hadamard differentiability of the value functions through analyzing the properties of the sorting operator using tools from geometric measure theory. Building on our Hadamard differentiability results, we apply the functional delta method to obtain the asymptotic properties of the value function process for the binary constrained optimal allocation problem and the plug-in ROC curve estimator. Moreover, the convexity of the optimal allocation value functions facilitates demonstrating the degeneracy of first order derivatives with respect to the policy. We then present a double / debiased estimator for the value functions. Importantly, the conditions that validate Hadamard differentiability justify the margin assumption from the statistical classification literature for the fast convergence rate of plug-in methods.
{"title":"Statistical inference of optimal allocations I: Regularities and their implications","authors":"Kai Feng , Han Hong , Denis Nekipelov","doi":"10.1016/j.jeconom.2026.106217","DOIUrl":"10.1016/j.jeconom.2026.106217","url":null,"abstract":"<div><div>In this paper, we develop a functional differentiability approach for solving statistical optimal allocation problems. We derive Hadamard differentiability of the value functions through analyzing the properties of the sorting operator using tools from geometric measure theory. Building on our Hadamard differentiability results, we apply the functional delta method to obtain the asymptotic properties of the value function process for the binary constrained optimal allocation problem and the plug-in ROC curve estimator. Moreover, the convexity of the optimal allocation value functions facilitates demonstrating the degeneracy of first order derivatives with respect to the policy. We then present a double / debiased estimator for the value functions. Importantly, the conditions that validate Hadamard differentiability justify the margin assumption from the statistical classification literature for the fast convergence rate of plug-in methods.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106217"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147384790","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 : 2026-03-01Epub Date: 2023-12-01DOI: 10.1016/j.jeconom.2023.105614
Z. Merrick Li , Oliver Linton
We introduce a new method to estimate the integrated volatility (IV) and the spot volatility (SV) based on noisy high-frequency data. Our method employs the ReMeDI approach introduced by Li and Linton (2022) to estimate the moments of microstructure noise and thereby eliminate their influence, and the pre-averaging method to target the volatility parameter. The method is robust: it can be applied when the efficient price exhibits stochastic volatility and jumps, the observation times are random, and the noise process is nonstationary, autocorrelated, asymptotically vanishing and dependent on the efficient price. We derive the limit distributions for the proposed estimators under the infill asymptotics in a general setting. Our extensive simulation studies demonstrate the robustness, accuracy and computational efficiency of our estimators compared to several alternative estimators recently proposed in the literature. Empirically, we show that neglecting the complexities of noise and the random observation times generates substantial biases in volatility estimation and may yield a different intraday volatility pattern.
{"title":"Robust estimation of integrated and spot volatility","authors":"Z. Merrick Li , Oliver Linton","doi":"10.1016/j.jeconom.2023.105614","DOIUrl":"10.1016/j.jeconom.2023.105614","url":null,"abstract":"<div><div>We introduce a new method to estimate the integrated volatility (IV) and the spot volatility (SV) based on noisy high-frequency data. Our method employs the ReMeDI approach introduced by <span><span>Li and Linton (2022)</span></span> to estimate the moments of microstructure noise and thereby eliminate their influence, and the pre-averaging method to target the volatility parameter. The method is robust: it can be applied when the efficient price exhibits stochastic volatility and jumps, the observation times are random, and the noise process is nonstationary, autocorrelated, asymptotically vanishing and dependent on the efficient price. We derive the limit distributions for the proposed estimators under the infill asymptotics in a general setting. Our extensive simulation studies demonstrate the robustness, accuracy and computational efficiency of our estimators compared to several alternative estimators recently proposed in the literature. Empirically, we show that neglecting the complexities of noise and the random observation times generates substantial biases in volatility estimation and may yield a different intraday volatility pattern.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 105614"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516586","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 : 2026-03-01Epub Date: 2026-01-28DOI: 10.1016/j.jeconom.2026.106186
Anders Bredahl Kock , David Preinerstorfer
A decision maker typically (i) incorporates training data to learn about the relative effectiveness of treatments, and (ii) chooses an implementation mechanism that implies an “optimal” predicted outcome distribution according to some target functional. Nevertheless, a fairness-aware decision maker may not be satisfied achieving said optimality at the cost of being “unfair” against a subgroup of the population, in the sense that the outcome distribution in that subgroup deviates too strongly from the overall optimal outcome distribution. We study a framework that allows the decision maker to regularize such deviations, while allowing for a wide range of target functionals and fairness measures to be employed. We establish regret and consistency guarantees for empirical success policies with (possibly) data-driven preference parameters, and provide numerical results. Furthermore, we briefly illustrate the methods in two empirical settings.
{"title":"Regularizing fairness in optimal policy learning with distributional targets","authors":"Anders Bredahl Kock , David Preinerstorfer","doi":"10.1016/j.jeconom.2026.106186","DOIUrl":"10.1016/j.jeconom.2026.106186","url":null,"abstract":"<div><div>A decision maker typically (i) incorporates training data to learn about the relative effectiveness of treatments, and (ii) chooses an implementation mechanism that implies an “optimal” predicted outcome distribution according to some target functional. Nevertheless, a fairness-aware decision maker may not be satisfied achieving said optimality at the cost of being “unfair” against a subgroup of the population, in the sense that the outcome distribution in that subgroup deviates too strongly from the overall optimal outcome distribution. We study a framework that allows the decision maker to regularize such deviations, while allowing for a wide range of target functionals and fairness measures to be employed. We establish regret and consistency guarantees for empirical success policies with (possibly) data-driven preference parameters, and provide numerical results. Furthermore, we briefly illustrate the methods in two empirical settings.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106186"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146076155","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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