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on Econometrics |
| By: | Xuanjing Su |
| Abstract: | This paper studies quantile regression with an endogenous regressor and measurement error in the dependent variable. Standard quantile regression estimators ignoring these two elements can induce substantial bias. We adopt a control-function approach in a triangular system and show that the conditional quantile coefficient functions, together with all other distributional parameters, are nonparametrically identifiable. Building on this constructive identification result, we propose a two-step sieve ML estimator. The first step estimates the control function. The second step performs a sieve likelihood maximization that incorporates the generated control variable through copula weights. When the number of quantile grid knots grows at an appropriate speed, the estimator is consistent and asymptotically normal, permitting inference via bootstrap. Monte Carlo simulations demonstrate that the estimator markedly reduces bias relative to existing methods, confirming its effectiveness in settings with endogeneity and additive measurement error in the outcome. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.20601 |
| By: | Hayato Tagawa |
| Abstract: | This paper develops a difference-in-differences framework for staggered policy adoption when units can be affected by other units' adoption. For each treated cohort and event time, the framework separates the effect of own adoption, the spillover effect generated by other adopters, and the total effect under the realized rollout. Identification uses a prespecified summary of spillover exposure and parallel trends comparisons among units with the same exposure at the baseline and target dates. Spillover effects are learned from never-treated units and evaluated for treated cohorts under the exposure distribution they face. We construct estimators for these effects and an inference procedure that allows for spatial dependence. Monte Carlo simulations illustrate that standard DID estimators that ignore spillovers can miss the total effect, whereas the proposed estimators have small bias for these effects and the associated confidence intervals have coverage close to the nominal level. In an empirical study of the Community Health Centers rollout, estimated spillovers account for a substantial share of the effect on older-adult mortality. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.15119 |
| By: | Gao, Fengnan; Wang, Tengyao |
| Abstract: | We introduce a new methodology ‘charcoal’ for estimating the location of sparse changes in high-dimensional linear regression coefficients, without assuming that those coefficients are individually sparse. The procedure works by constructing different sketches (projections) of the design matrix at each time point so as to eliminate the possible dense nuisance parameters. The sequence of sketched design matrices is then compared against a single sketched response vector to form a sequence of test statistics whose behavior shows a surprising link to the well-known CUSUM statistics of univariate changepoint analysis. The procedure is computationally attractive, and strong theoretical guarantees are derived for its estimation accuracy. Simulations confirm that our methods perform well in extensive settings, and a real-world application to a large single-cell RNA sequencing dataset showcases the practical relevance. |
| Keywords: | high-dimensional regression; changepoint; nuisance parameter; sparsity |
| JEL: | C1 |
| Date: | 2026–06–30 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:130998 |
| By: | Tymon S{\l}oczy\'nski; Liyang Sun; S. Derya Uysal |
| Abstract: | Instrumental variables (IV) methods are central to applied microeconomics. While classical approaches assume linear models with constant effects, recent literature has shifted toward the local average treatment effect (LATE) framework to accommodate heterogeneous treatment effects. This paper provides a practical guide to aligning empirical practice with recent theory. We first examine how different specifications with covariates lead to distinct weighted averages of covariate-specific LATEs. We then discuss how parametric misspecification can undermine the causal interpretation of these estimands and suggest flexible specifications as essential robustness checks. Finally, we review formal tests for LATE assumptions and methods robust to monotonicity violations. We provide a guide to software implementations to help researchers apply the methods in practice. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.15115 |
| By: | Jonas F. Frederiksen; Muneya Matsui; Rasmus S. Pedersen |
| Abstract: | We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test statistic converges to a nonstandard limit involving non-Gaussian stable random variables. As a consequence, conventional critical values can yield severely distorted inference: a nominal 5$\%$ test may reject a true null as often as 70$\%$ of the time. To establish these results, we develop a new stable limit theorem for strongly mixing, infinite-variance time series processes. Building on this theory, we consider sub-sampling-based inference that remains valid irrespective of tail-heaviness and requires no estimation of long-run variances or tail indices. An application to risk forecasts for emerging-market exchange rates shows that accounting for heavy tails can substantially alter conclusions about predictive performance relative to standard procedures. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.16866 |
| By: | Zhen Xie |
| Abstract: | Empirical Bayes methods can improve inference on unobservable individual effects by borrowing strength across units. This paper proposes nonparametric empirical Bayes confidence intervals (NP-EBCIs) for unobservable individual effects in a normal means model. The oracle intervals are constructed from posterior quantiles under a point-identified, fully nonparametric prior; feasible intervals replace these quantiles with nonparametric estimates. The NP-EBCIs are asymptotically exact in the sense that both their conditional and marginal coverage probabilities converge to the nominal level. The flexibility of this nonparametric construction has an unavoidable statistical cost. We demonstrate that posterior quantiles, unlike posterior means, inherit the severe ill-posedness of nonparametric deconvolution: the minimax optimal estimation rate is logarithmic. This logarithmic rate is minimax optimal for errors in the conditional coverage probability, and the resulting errors in the marginal coverage probability also vanish at the same logarithmic rate. Despite these slow asymptotic rates, simulations show that the NP-EBCIs remain close to nominal coverage when the prior is non-Gaussian, and deliver substantial length reductions relative to intervals that treat each unit in isolation. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.08551 |
| By: | Xiaojun Song; Jichao Yuan |
| Abstract: | In this paper, we propose a novel approach to detect heteroskedasticity in regression models with regressors contaminated by measurement error. Specifically, inspired by the integrated conditional moment (ICM) approach, we construct test statistics based on a deconvolved residual-marked empirical process and establish their asymptotic properties in both ordinary smooth and supersmooth cases, assuming the measurement error distribution is known. The issue of an unknown measurement error distribution is addressed by employing estimators of the measurement error characteristic function based on repeated measurements. Furthermore, depending on whether the measurement error distribution is known or not, to obtain critical values from the case-dependent limiting null distributions, we propose two computationally attractive multiplier bootstrap methods where the "parameter estimation effect" is successfully addressed. Finally, simulation results and empirical studies about corn yields and household budget shares confirm the favorable properties of the proposed tests. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.20012 |
| By: | Denis Chetverikov; Jesper R. -V. ~S{\o}rensen; Bo Honor\'e |
| Abstract: | We study inference using trimmed least squares (TLS) and trimmed least absolute deviations (TLAD) estimators of \citet{honore_trimmed_1992} in censored two-period panel-data models with fixed effects. We show that the published asymptotic variance formulas rely on additional regularity conditions that are not fully stated in the original analysis. For TLS, the published Hessian formula requires that the regressor-difference index vanish only when the regressor difference itself is zero, a restriction not explicitly stated in the original paper and violated, for instance, with a zero parameter vector. We derive the correct Hessian, establish asymptotic normality without imposing this restriction, and obtain a consistent plug-in variance estimator. We also show that the Hessian estimator proposed in \citet{honore_trimmed_1992} {\em is} actually consistent for the {\em correct} TLS asymptotic variance. For TLAD, we show that the published variance formula omits a conditional-probability term and that asymptotic normality requires additional continuity conditions. Under these conditions, we derive the corrected asymptotic variance and provide a tuning-parameter-free bootstrap variance estimator. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.17052 |
| By: | Zulfiqar, Ammara; Aziz, Mahwish; Wahid, Abdul |
| Abstract: | Structural Equation Modeling (SEM) is a commonly used and prevalent method to describe the relationships between latent and observed variables. If these variables contain outliers and leverage-points, the estimation by existing SEM is problematic and leads to biased and inefficient estimators. In this article, we propose the Least Mahalanobis Distance-based Trimmed (LMDT) model which uses Mahalanobis distance for the identification of outliers in SEM and trimming approach for dealing with such types of influential observations. By using this suggested technique, instead of maximum likelihood and least squares criteria, the LMDT is resistant to outliers in both measurement error and latent factors. A FAST-iterative algorithm is constructed and implemented for computing the LMDT. Both a simulation study and a real data analysis indicate that the proposed robust method has good performance in terms of bias and efficiency on contaminated and non-normal skewed data and it outperforms the two non-robust and one robust existing estimation methods. |
| Keywords: | Structural equation modeling; outliers; non-normality; Mahalanobis distance; trimming |
| JEL: | C15 C51 J28 |
| Date: | 2026–05–11 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:129065 |
| By: | Yasumasa Matsuda; Michel F. C. Haddad |
| Abstract: | We propose a density-valued vector autoregressive model with latent factors for multivariate time series of density functions. Motivated by weekly regional distributions of SARS-CoV-2 cycle threshold (Ct) values in Brazil, we study their distributional dynamics across regions. The Ct value is the number of amplification cycles required for the viral signal to cross a detection threshold (lower Ct values correspond to higher viral load). We estimate each regional density by a B-spline mixture, mapping the mixture weights to a Euclidean space by a generalized logit transform equipped with an isometric inner product, and model the transformed series by a crossregional VAR with latent factors. This decomposition allows for the separation between strong common movements and directed idiosyncratic dynamics. Directed edges are identified from the idiosyncratic VAR component using one-sided tests with Benjamini–Yekutieli false discovery rate control. Simulations show that increasing the number of estimated factors does not mechanically eliminate genuine idiosyncratic dependence; rather, it mainly removes spuriously detected edges driven by common factor movements. In the real-world data application, the full sample yields only a weak directed network, whereas a substantial network emerges once the first six months are excluded and the density prior is kept weak. The estimated links suggest directed predictive relations from the northern region toward southeastern metropolitan areas. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:toh:dssraa:150 |
| By: | Safira, Dinda Ayu; Kuswanto, Heri; Ahsan, Muhammad; Sibbertsen, Philipp |
| Abstract: | This study proposes an optimized estimation approach for Self-Exciting Threshold Autoregressive (SETAR) models by integrating the Majorization-Minimization Group Least Absolute Shrinkage and Selection Operator (MM-gLASSO) algorithm, with a primary focus on improving forecasting performance in complex regime-switching environments. While SETAR models are powerful in capturing non-linear regimes and asymmetric dynamics in time series data, they often suffer from high-dimensional parameter spaces. This typically leads to high-dimensional parameter spaces that cause overfitting and reduced forecasting stability. We address this by employing the MM algorithm to simplify the complex, non-differentiable gLASSO penalty into a more manageable surrogate function. This ensures stable convergence and allows for simultaneous variable selection and parameter estimation across multiple regimes. The gLASSO penalty is specifically utilized to ensure that irrelevant lags are excluded consistently across the threshold structure. We provide a detailed derivation of the estimation procedure and evaluate its performance through extensive simulation studies. The results indicate that the MM-gLASSO framework significantly outperforms traditional methods, particularly in terms of sparsity recognition and parameter consistency. Finally, an empirical application on PM2.5 concentration demonstrates the model's superior forecasting capability and its effectiveness in identifying structural transitions in real-world time series data. |
| Keywords: | gLASSO, MM algorithm, nonlinear time series, regime detection, SETAR model |
| JEL: | C13 C32 C53 Q53 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:han:dpaper:dp-746 |
| By: | Ziyi Liu; Yiqing Xu |
| Abstract: | Synthetic control methods can produce misleading counterfactual predictions when outcome series contain unit-specific stochastic trends, a common feature of nonstationary macroeconomic data. Existing remedies, such as pre-filtering or differencing, reduce spurious matching but may discard shared nonstationary variation that helps estimate donor weights. We propose Harmonic Synthetic Control (HSC), which replaces this binary choice with a soft allocation mechanism. HSC jointly estimates donor weights and a treated-unit-specific smooth residual component, then extrapolates this component into post-treatment periods using a time-series forecaster. A tuning parameter, selected by rolling-origin cross-validation, governs the division between donor matching and forecasting. As it varies, HSC continuously interpolates between synthetic control applied to differenced outcomes and synthetic control applied to raw outcomes with an intercept or trend. We provide a spectral interpretation showing how HSC downweights low-frequency residual components in donor matching and assigns them to the forecasting branch. A prediction-error decomposition separates weight-estimation distortion from residual-forecasting error. Monte Carlo exercises show that HSC adapts across regimes, performing well when stochastic trends are predominantly common or idiosyncratic, while estimators fixed to one regime can fail in the other. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.20359 |
| By: | Ron Berman; Walter W. Zhang; Hangcheng Zhao |
| Abstract: | Decision-makers often deploy the best-performing treatment from a randomized experiment, creating a winner's curse: selection favors treatments whose observed outcomes are high partly because of statistical noise, so the na\"ive estimate of the winner is upward biased. We distinguish two forms of winner's curse, bias relative to the true best treatment (global) and bias relative to the selected treatment's true mean (selective), and link them to regret from deploying a suboptimal treatment. This framework defines seven decision-relevant evaluation targets: mean bias, mean squared error, and confidence interval coverage for the global and selective winner's curse, and mean regret. We then show that methods that perform well on one target can perform poorly on others, so corrections should be matched to the manager's objective. Across simulations with varying effect sizes, multiple-arm settings, and data calibrated to an online A/B testing platform, no method dominates uniformly: the plug-in estimator performs best when treatment differences are large, cross-fitting performs best when treatments are similar, and resampling methods often achieve low mean squared error for moderate differences. We also introduce an adaptive empirical likelihood procedure that delivers asymptotically valid confidence intervals across settings without the tuning sensitivity of resampling-based methods. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.18887 |
| By: | Yuan Liao; Xin Tong; Wanjie Wang; Dacheng Xiu |
| Abstract: | We develop asymptotic theory for principal component analysis (PCA) of a high-dimensional factor model in which the working dimension $R$ is fixed and only required to satisfy $R \ge r$, where $r$ is the true number of factors. Building on anisotropic local laws from random matrix theory, we show that the ``extra'' empirical eigencomponents beyond the $r$-th are asymptotically noise-governed, incoherent, and nearly orthogonal to the factor loadings. We introduce two rotations, an expanded $r\times R$ map $H'$ and a compressed $R\times r$ map $H^{+}$, and establish consistency of the estimated factors under both. As an application, we analyze a factor-augmented regression for treatment-effect inference and prove $\sqrt{T}$-asymptotic normality for every fixed $R \ge r$. These results provide a theoretical underpinning for the common empirical practice of adopting a conservative upper bound on the number of factors, and shift the analytical burden from consistent dimension selection to the milder requirement of bounding $r$ from above. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.18448 |
| By: | Irene Botosaru; James L. Powell |
| Abstract: | We consider a static linear panel model with both correlated and uncorrelated random coefficients, where the former can depend arbitrarily on observable regressors while the latter are independent of them. We provide sufficient conditions for identification of the distributions of the random coefficients without imposing restrictions on the time-series structure of the error terms in short panels. Our framework applies to regular and irregular designs. The distribution of the correlated coefficients follows via a deconvolution argument. In irregular designs, identification relies on a stayer-based argument exploiting near-singular realizations of the regressor matrix. We develop a two-step minimum distance sieve estimator, with tuning parameters selected by cross-validation. In an application to calorie-expenditure elasticities using data from the randomized evaluation of a conditional cash transfer program, we interpret the estimated distributions by program status as distributions of regime-specific structural calorie-expenditure elasticities. The estimated densities themselves reveal substantial heterogeneity in household-specific elasticities, with nontrivial mass concentrated near zero and a non-negligible share of negative realizations. This heterogeneity implies that responses to income or expenditure changes are not uniformly positive and vary widely across households. Taken together, these features support a framework in which households adjust along both quantity and quality margins, rather than conforming to a homogeneous Engel-curve response. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.21367 |
| By: | St\'ephane Bonhomme; Koen Jochmans; Whitney K. Newey; Martin Weidner |
| Abstract: | We construct moment functions that are Neyman-orthogonal to a chosen order in parametric moment condition models. These moment functions reduce sensitivity to nuisance estimation error and, as such, offer a unified and tractable route to higher-order debiasing in a wide range of econometric models. The number of additional nuisance parameters required by our construction, beyond those already present in the original moment conditions, is independent of the order of orthogonalization and can be reduced to a single scalar if desired. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.10842 |
| By: | Dongwoo Kim; Kyoo il Kim; Pallavi Pal |
| Abstract: | This paper extends the incomplete model of Haile and Tamer (2003) from static English auctions to sequential English auctions. Because bidders may wait for future opportunities, the static condition that bidders do not let rivals win at beatable prices need not hold. We replace it with a dynamic opportunity-cost restriction, yielding nonparametric valuation bounds without solving a dynamic equilibrium. Sharp bounds are also characterized. We propose a novel moment-condition inversion estimator that pools auctions with heterogeneous bidder counts, mitigating finite-sample instability of order statistics approaches and admitting analytical standard errors and smooth confidence intervals. Applications to Korean wholesale used-car auctions and Cars and Bids online auctions deliver informative bounds. Counterfactual analyses show that the option to wait lowers first-period revenue by 8--11% in the Korean market, that increasing effective competition from 8 to 20 serious bidders in Cars and Bids raises seller revenue by 40--65%, and that maximin reserve prices vary substantially across vehicle clusters. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.14400 |
| By: | Stevenson, Megan T.; Fischman, Joshua B. |
| Abstract: | Something is amiss in empirical economics. Despite the advances of the credibility revolution, published estimates tend to be inflated and overconfident. We argue that this stems from a weakness in the dominant econometric framework: treating the researcher like a calculator that mechanically implements the econometric method. We use several examples to show how properties of estimators change dramatically with humans-in-the-loop. Under plausible assumptions on researcher behavior, lowpower estimators such as instrumental variables exhibit high degrees of bias, even with a first-stage F-statistic of 200. Threshold testing on the first-stage F-statistic can reduce bias, contrary to Angrist and Koles'ar (2024). And standard errors understate uncertainty, since they ignore variation due to researchers' subjective choices. Ignoring the role of humans "in the research loop" can lead to highly biased and unreliable findings. Modifying econometric practices to address the human factor is a critical frontier of the credibility revolution. |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:i4rdps:296 |
| By: | Haonan Ye |
| Abstract: | I propose Nonparametric Bayesian Policy Learning (NBPL) as a framework for uncertainty-aware treatment choice. I consider a decision-maker (DM) seeking to select an expected welfare-maximizing treatment rule using observable characteristics. A key observation is that, for a given welfare criterion and policy class, uncertainty about welfare-relevant objects is entirely induced by uncertainty about a reduced-form distribution. I assume the DM places a nonparametric Dirichlet process prior on this reduced-form parameter and uses the resulting posterior to conduct inference on optimal treatment assignments, optimal welfare, and comparisons across policy classes. The NBPL framework is flexible, and its implementation via the Bayesian bootstrap is highly tractable. I establish two main theoretical properties of NBPL. First, posterior welfare regret under NBPL converges at the minimax-optimal rate. Second, posterior model comparison across policy classes is pointwise consistent. I illustrate NBPL in two empirical applications: the bednet subsidy experiment of Bhattacharya and Dupas (2012) and the JTPA experiment studied by Kitagawa and Tetenov (2018). |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.17068 |
| By: | Duy-Minh Dang; Volter Entoma |
| Abstract: | We propose a data-driven Fourier-trained neural-network method for estimating fixed-horizon probability densities from empirical characteristic-function (CF) information. The estimator is a positive Gaussian--Laplace mixture with closed-form CF, so training can be performed directly in Fourier space while preserving nonnegativity and unit mass. We consider two sampling settings. In the direct i.i.d. sampling setting, the method is trained against an empirical CF constructed from i.i.d. samples. In the resampling-based pseudo-sampling setting, it is trained against an empirical pseudo-CF constructed from dependent data by resampling. For the direct i.i.d. case, we derive an expected $L_2$ error bound that separates Fourier truncation, empirical training error, discretization, and CF sampling error. For the pseudo-sampling case, we obtain a conditional analogue with two additional pseudo-law discrepancy terms. We develop a multidimensional extension of the framework and analyze its computational complexity. Numerical experiments show competitive performance relative to Expectation--Maximization on Gaussian-mixture benchmarks, clear gains on heavy-tailed targets, $L_2$ error decay consistent with the theory in a well-specified setting, and effective estimation of one-year Australian equity return law from resampled dependent data. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.18019 |
| By: | Peter Reinhard Hansen; Chen Tong |
| Abstract: | Score-driven models update time-varying parameters using conditional likelihood scores. This paper gives a Bayesian interpretation based on Tweedie's formula. In Gaussian signal extraction, Tweedie's formula expresses the posterior correction as a scaled score of the marginal predictive density; in natural exponential families, the corresponding identity includes a base-measure adjustment. For general conditional densities, we show that inverse-Fisher-scaled conditional scores arise as local Gaussian posterior corrections based on Fisher scoring and precision discounting. For conjugate natural exponential families, the classical discounted Bayesian recursion has an exact score-driven representation: with steady-state precision discounting and expectation-space inverse-Fisher scaling, the score-driven correction equals the Bayesian posterior mean before transition dynamics are imposed. Tweedie's variance-function index further clarifies how conditional scores normalize forecast errors. The results link empirical Bayes, approximate filtering, dynamic generalized linear models, and score-driven models while distinguishing exact Bayesian updating from local score-based approximation. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.15902 |
| By: | Masahiro Tanaka |
| Abstract: | This paper introduces a quasi-Bayesian approach for local projection instrumental-variables (LP-IV) estimation. It builds a moment-based quasi-posterior using the generalized method of moments (GMM) objective and applies a roughness-penalty prior to smooth impulse responses over different horizons. The approach maintains the key first-order features of traditional LP-IV methods, while enhancing stability in finite samples and allowing for joint inference through simultaneous bands. Simulations indicate that this regularization decreases root mean squared error compared to standard GMM, especially at medium and longer horizons. An application to Danish electricity markets highlights the method's practical usefulness. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.15966 |
| By: | Yuji Komiyama; Yasumasa Matsuda; Masakazu Ishihara |
| Abstract: | This study proposes a mixture cure model that latently divides a population based on event occurrence within a finite time horizon. Conventional models rely on event occurrence over an infinite horizon, introducing untestable assumptions that often lead to issues with identifiability and interpretability. By shifting the estimand to a specific period of interest, the proposed approach reduces reliance on these infinite-tail assumptions and aligns interpretations more closely with finite-horizon decision-making objectives. Through simulation studies, we first evaluate the statistical properties of the proposed estimator, including estimation bias and variance. We further show that relying on conventional infinite-horizon models for finite-horizon decision-making can lead to erroneous judgments. Finally, we apply the model to transaction data from Mercari, a Japanese online flea market platform. The empirical results reveal that the proposed model identifies different significant variables compared to the conventional model, offering interpretations that better reflect seasonal variation in user behavior. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:toh:dssraa:151 |
| By: | Felix Reichel |
| Abstract: | We place three algorithms for computing the unbiased sample covariance matrix in streaming and distributed settings on a common algebraic, numerical, and statistical foundation. The Gram algorithm, derived from the variance reformulation, maintains the running cross-product matrix $G_t = \sum_{i=1}^t x_i x_i^\top$ and the column-sum vector $s_t = \sum_{i=1}^t x_i$, yielding the unbiased covariance estimator $S_t = (t-1)^{-1}(G_t - t^{-1}s_t s_t^\top)$ in $O(p^2)$ time per update. The Welford algorithm propagates a running mean $m_t$ and outer-product corrections $M_t$, with updates $m_t = m_{t-1} + (x_t - m_{t-1})/t$ and $M_t = M_{t-1} + (x_t - m_{t-1})(x_t - m_t)^\top$, achieving the same asymptotic cost with improved numerical stability under large data shifts. The Chan-Golub-LeVeque algorithm supports block-parallel merging through the exact identity $M = M_A + M_B + \frac{n_A n_B}{n_A+n_B}(m_B - m_A)(m_B - m_A)^\top$, making it the natural choice for distributed and map-reduce architectures. All three algorithms produce the same estimator $S_t = M_t/(t-1)$ in exact arithmetic, although their finite-precision behavior differs markedly. Beyond runtime and numerical comparisons, we introduce a conformal prediction framework for streaming covariance estimation that yields finite-sample, distribution-free confidence sets $C_{t, jk}$ for each entry $S_{t, jk}$ of the covariance matrix at any step $t$ of the data stream. Experiments confirm that the Gram algorithm is fastest for batch computation, Welford is uniquely robust to catastrophic cancellation under large mean shifts, CGL is optimal for distributed settings, and conformal intervals achieve the nominal coverage level across all three algorithms. |
| Date: | 2026–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.00247 |
| By: | Patrick Woitschig; Mike West |
| Abstract: | We present a new class of Bayesian dynamic models for bivariate price-realized volatility time series in financial forecasting. A novel dynamic gamma process model adopted for realized volatility is integrated with traditional Bayesian dynamic linear models (DLMs) for asset price series. This represents reduced-form volatility leverage and feedback effects through use of realized volatility proxies in conditional DLMs for prices or returns, coupled with the synthesis of higher frequency data to track and anticipate volatility fluctuations. Analysis is computationally straightforward, extending conjugate-form Bayesian analyses for sequential filtering and model monitoring with simple and direct simulation for forecasting. A main applied setting is equity return forecasting with daily prices and realized volatility from high-frequency, intraday data. Detailed empirical studies of multiple S&P sector ETFs highlight the improvements achievable in asset price forecasting relative to standard models and deliver contextual insights on the nature and practical relevance of volatility leverage and feedback effects. The analytic structure and negligible extra computational cost will enable scaling to higher dimensions for multivariate price series forecasting for decouple/recouple portfolio construction and risk management applications. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.12099 |
| By: | Andrea Carriero; Florian Huber; Davide Pettenuzzo |
| Abstract: | We study double descent and benign overfitting in macroeconomic forecasting. We document that double-descent risk curves arise in standard macroeconomic datasets that are driven by a small number of latent factors, and we characterize when the underlying benign-overfitting mechanism holds. The conditions of Bartlett et al. (2020) are satisfied under the exact factor model and can also hold under the more realistic approximate factor model, provided idiosyncratic variances are not too dispersed across series. Because macroeconomic panels have only moderate dimensions, the overparameterization ratio N/T required by the theory is not naturally available. Our solution is to augment the data with synthetic copies from an estimated factor model and we prove that this strategy converges to a kernel ridge regression with a factor-structured kernel. Using monthly (FRED-MD) and quarterly (FRED-QD) US data, the resulting estimator consistently outperforms the Stock-Watson factor model for point forecasting across all series and horizons, with gains that are pervasive, statistically significant, and increasing with the forecast horizon. Our results suggest that benign overfitting, when it works, succeeds because overparameterization implicitly constructs a well-behaved kernel, not because overparameterization is intrinsically desirable. |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2605.15358 |
| By: | Neil R. Ericsson; Andrew B. Martinez |
| Abstract: | In April 2025, the Department of Economics at the University of Oxford hosted the "Workshop to Celebrate Forty Years of Unit Roots and Cointegration", which commemorated the 40th anniversary of the Oxford Bulletin of Economics and Statistics’s 1986 special issue "Economic Modelling With Cointegrated Variables". The current article summarizes that workshop's panel discussion with major contributors to the literature on cointegration-David Hendry, Peter Phillips, Katarina Juselius, and Soren Johansen—and includes additional remarks by Martin Ellison and the conference's audience. The discussion highlights key roles that the panelists and the Bulletin have played in advancing the literature on cointegration. |
| Keywords: | cointegration; equilibrium correction; error correction; spurious regression; structural breaks; unit roots. |
| JEL: | C10 N1 |
| Date: | 2026–05 |
| URL: | https://d.repec.org/n?u=RePEc:gwc:wpaper:2026-009 |