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on Econometrics |
| By: | Federico Carlini (LUISS Business School); Mirco Rubin (EDHEC Business School); Pierluigi Vallarino (Erasmus University Rotterdam and Tinbergen Institute) |
| Abstract: | We propose a new rank-based test for the number of common primitive shocks, q, in large panel data. After estimating a VAR(1) model on r static factors extracted by principal component analysis, we estimate the number of common primitive shocks by testing the rank of the VAR residuals’ covariance matrix. The new test is based on the asymptotic distribution of the sum of the smallest r − q eigenvalues of the residuals’ covariance matrix. We develop both plug-in and bootstrap versions of this eigenvalue-based test. The eigenvectors associated to the q largest eigenvalues allow us to construct an easy-to-implement estimator of the common primitive shocks. We illustrate our testing and estimation procedures with applications to panels of macroeconomic variables and individual stocks’ volatilities. |
| JEL: | C12 C23 C38 |
| Date: | 2025–03–07 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250016 |
| By: | Mirko Armillotta (University of Rome Tor Vergata); Paolo Gorgi (Vrije Universiteit Amsterdam and Tinbergen Institute); André Lucas (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | This paper presents a novel copula-based autoregressive framework for multilayer arrays of integer-valued time series with tensor structure. It complements recent advances in tensor time series that predominantly focus on real-valued data and overlook the unique properties of integer-valued time series, such as discreteness and non-negativity. Our approach incorporates feedback effects for the time-varying parameters that describe the counts’ temporal dynamics and introduces new identification constraints for parameter estimation. We provide an asymptotic theory for a Two-Stage Maximum Likelihood Estimator (2SMLE) tailored to the new tensor model. The estimator tackles the model’s multidimensionality and interdependence challenges for large-scale count datasets, while at the same time addressing computational challenges inherent to copula parameter estimation. In this way it significantly advances the modeling of count tensors. An application to crime time series demonstrates the practical utility of the proposed methodology. |
| Keywords: | INGARCH, tensor autoregression, parameter identification, quasi-likelihood, two-stage estimator |
| JEL: | C32 C55 |
| Date: | 2025–02–05 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250004 |
| By: | Janneke van Brummelen (Vrije Universiteit Amsterdam); Paolo Gorgi (Vrije Universiteit Amsterdam and Tinbergen Institute); Siem Jan Koopman (Vrije Universiteit Amsterdam and Tinbergen Institute) |
| Abstract: | We develop a score-driven time-varying parameter model where no particular parametric error distribution needs to be specified. The proposed method relies on a versatile spline-based density, which produces a score function that follows a natural cubic spline. This flexible approach nests the Gaussian density as a special case. It can also represent asymmetric and leptokurtic densities that produce outlier-robust updating functions for the time-varying parameter and are often appealing in empirical applications. As leading examples, we consider models where the time-varying parameters appear in the location or in the log-scale of the observations. The static parameter vector of the model can be estimated by means of maximum likelihood and we formally establish some of the asymptotic properties of such estimators. We illustrate the practical relevance of the proposed method in two empirical studies. We employ the location model to filter the mean of the U.S. monthly CPI inflation series and the scale model for volatility filtering of the full panel of daily stock returns from the S&P 500 index. The results show a competitive performance of the method compared to a set of competing models that are available in the existing literature. |
| JEL: | C13 C22 |
| Date: | 2025–02–16 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20250011 |
| By: | Guglielmo Maria Caporale; Luis Alberiko Gil-Alana |
| Abstract: | This paper puts forward a general statistical model in the time domain based on the concept of fractional integration. More specifically, in the proposed framework instead of imposing that the roots are strictly on the unit circle, we also allow them to be within the unit circle. This approach enables us to specify the time series in terms of its infinite past, with a rate of dependence between the observations much smaller than that produced by the classic I(d) representations. Both Monte Carlo experiments and empirical applications to climatological and financial data show that the proposed approach performs well. |
| Keywords: | fractional integration, unit roots, testing procedure |
| JEL: | C22 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11983 |
| By: | Ivan Fernandez-Val; Seoyun Hong |
| Abstract: | We develop a distribution regression model with a censored selection rule, offering a semi-parametric generalization of the Heckman selection model. Our approach applies to the entire distribution, extending beyond the mean or median, accommodates non-Gaussian error structures, and allows for heterogeneous effects of covariates on both the selection and outcome distributions. By employing a censored selection rule, our model can uncover richer selection patterns according to both outcome and selection variables, compared to the binary selection case. We analyze identification, estimation, and inference of model functionals such as sorting parameters and distributions purged of sample selection. An application to labor supply using data from the UK reveals different selection patterns into full-time and overtime work across gender, marital status, and time. Additionally, decompositions of wage distributions by gender show that selection effects contribute to a decrease in the observed gender wage gap at low quantiles and an increase in the gap at high quantiles for full-time workers. The observed gender wage gap among overtime workers is smaller, which may be driven by different selection behaviors into overtime work across genders. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.10814 |
| By: | Lin Deng; Michael Stanley Smith; Worapree Maneesoonthorn |
| Abstract: | Multivariate distributions that allow for asymmetry and heavy tails are important building blocks in many econometric and statistical models. The Unified Skew-t (UST) is a promising choice because it is both scalable and allows for a high level of flexibility in the asymmetry in the distribution. However, it suffers from parameter identification and computational hurdles that have to date inhibited its use for modeling data. In this paper we propose a new tractable variant of the unified skew-t (TrUST) distribution that addresses both challenges. Moreover, the copula of this distribution is shown to also be tractable, while allowing for greater heterogeneity in asymmetric dependence over variable pairs than the popular skew-t copula. We show how Bayesian posterior inference for both the distribution and its copula can be computed using an extended likelihood derived from a generative representation of the distribution. The efficacy of this Bayesian method, and the enhanced flexibility of both the TrUST distribution and its implicit copula, is first demonstrated using simulated data. Applications of the TrUST distribution to highly skewed regional Australian electricity prices, and the TrUST copula to intraday U.S. equity returns, demonstrate how our proposed distribution and its copula can provide substantial increases in accuracy over the popular skew-t and its copula in practice. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.10849 |
| By: | Shaobo Li; Ben Sherwood |
| Abstract: | This paper considers equity premium prediction, for which mean regression can be problematic due to heteroscedasticity and heavy-tails of the error. We show advantages of quantile predictions using a novel penalized quantile regression that offers a model for a full spectrum analysis on the equity premium distribution. To enhance model interpretability and address the well-known issue of crossing quantile predictions in quantile regression, we propose a model that enforces the selection of a common set of variables across all quantiles. Such a selection consistency is achieved by simultaneously estimating all quantiles with a group penalty that ensures sparsity pattern is the same for all quantiles. Consistency results are provided that allow the number of predictors to increase with the sample size. A Huberized quantile loss function and an augmented data approach are implemented for computational efficiency. Simulation studies show the effectiveness of the proposed approach. Empirical results show that the proposed method outperforms several benchmark methods. Moreover, we find some important predictors reverse their relationship to the excess return from lower to upper quantiles, potentially offering interesting insights to the domain experts. Our proposed method can be applied to other fields. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.16019 |
| By: | Elliot L. Epstein; Apaar Sadhwani; Kay Giesecke |
| Abstract: | In many financial prediction problems, the behavior of individual units (such as loans, bonds, or stocks) is influenced by observable unit-level factors and macroeconomic variables, as well as by latent cross-sectional effects. Traditional approaches attempt to capture these latent effects via handcrafted summary features. We propose a Set-Sequence model that eliminates the need for handcrafted features. The Set model first learns a shared cross-sectional summary at each period. The Sequence model then ingests the summary-augmented time series for each unit independently to predict its outcome. Both components are learned jointly over arbitrary sets sampled during training. Our approach harnesses the set nature of the cross-section and is computationally efficient, generating set summaries in linear time relative to the number of units. It is also flexible, allowing the use of existing sequence models and accommodating a variable number of units at inference. Empirical evaluations demonstrate that our Set-Sequence model significantly outperforms benchmarks on stock return prediction and mortgage behavior tasks. Code will be released. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.11243 |
| By: | Ramon van den Akker; Bas J. M. Werker; Bo Zhou |
| Abstract: | We establish an asymptotic framework for the statistical analysis of the stochastic contextual multi-armed bandit problem (CMAB), which is widely employed in adaptively randomized experiments across various fields. While algorithms for maximizing rewards or, equivalently, minimizing regret have received considerable attention, our focus centers on statistical inference with adaptively collected data under the CMAB model. To this end we derive the limit experiment (in the Hajek-Le Cam sense). This limit experiment is highly nonstandard and, applying Girsanov's theorem, we obtain a structural representation in terms of stochastic differential equations. This structural representation, and a general weak convergence result we develop, allow us to obtain the asymptotic distribution of statistics for the CMAB problem. In particular, we obtain the asymptotic distributions for the classical t-test (non-Gaussian), Adaptively Weighted tests, and Inverse Propensity Weighted tests (non-Gaussian). We show that, when comparing both arms, validity of these tests requires the sampling scheme to be translation invariant in a way we make precise. We propose translation-invariant versions of Thompson, tempered greedy, and tempered Upper Confidence Bound sampling. Simulation results corroborate our asymptotic analysis. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.13897 |
| By: | Cameron Cornell; Lewis Mitchell; Matthew Roughan |
| Abstract: | Causal networks offer an intuitive framework to understand influence structures within time series systems. However, the presence of cycles can obscure dynamic relationships and hinder hierarchical analysis. These networks are typically identified through multivariate predictive modelling, but enforcing acyclic constraints significantly increases computational and analytical complexity. Despite recent advances, there remains a lack of simple, flexible approaches that are easily tailorable to specific problem instances. We propose an evolutionary approach to fitting acyclic vector autoregressive processes and introduces a novel hierarchical representation that directly models structural elements within a time series system. On simulated datasets, our model retains most of the predictive accuracy of unconstrained models and outperforms permutation-based alternatives. When applied to a dataset of 100 cryptocurrency return series, our method generates acyclic causal networks capturing key structural properties of the unconstrained model. The acyclic networks are approximately sub-graphs of the unconstrained networks, and most of the removed links originate from low-influence nodes. Given the high levels of feature preservation, we conclude that this cryptocurrency price system functions largely hierarchically. Our findings demonstrate a flexible, intuitive approach for identifying hierarchical causal networks in time series systems, with broad applications to fields like econometrics and social network analysis. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.12806 |
| By: | Herault, Nicolas (University of Bordeaux); Jenkins, Stephen P. (London School of Economics) |
| Abstract: | Because finite sample inference for inequality indices based on asymptotic methods or the standard bootstrap does not perform well, Davidson and Flachaire (Journal of Econometrics, 2007) and Cowell and Flachaire (Journal of Econometrics, 2007) proposed inference based on semiparametric methods in which the upper tail of incomes is modelled by a Pareto distribution. Using simulations, they argue accurate inference is achievable with moderately large samples. We provide the first systematic application of these and other inferential approaches to real-world income data (high-quality UK household survey data covering 1977–2018), while also modifying them to deal with weighted data and a large portfolio of inequality indices. We find that the semiparametric asymptotic approach provides a greater number of statistically significant differences than the semiparametric bootstrap which in turn provides more than the conventional asymptotic approach and the ‘Student-t’ approach (Ibragimov et al., Econometric Reviews, 2025), especially for year-pair comparisons within the period from the late-1980s onwards. |
| Keywords: | semiparametric asymptotic approach, semiparametric bootstrap approach, asymptotic approach, Pareto distribution, income inequality, t-statistic approach |
| JEL: | C14 C46 C81 D31 |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:iza:izadps:dp17973 |
| By: | Gianluca De Nard; Damjan Kostovic |
| Abstract: | The paper introduces a new type of shrinkage estimation that is not based on asymptotic optimality but uses artificial intelligence (AI) techniques to shrink the sample eigenvalues. The proposed AI Shrinkage estimator applies to both linear and nonlinear shrinkage, demonstrating improved performance compared to the classic shrinkage estimators. Our results demonstrate that reinforcement learning solutions identify a downward bias in classic shrinkage intensity estimates derived under the i.i.d. assumption and automatically correct for it in response to prevailing market conditions. Additionally, our data-driven approach enables more efficient implementation of risk-optimized portfolios and is well-suited for real-world investment applications including various optimization constraints. |
| Keywords: | Covariance matrix estimation, linear and nonlinear shrinkage, portfolio management reinforcement learning, risk optimization |
| JEL: | C13 C58 G11 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:470 |
| By: | Browne, William John; Charlton, Christopher Michael John; Price, Toni; Leckie, George; Steele, Fiona |
| Abstract: | Simulation-based methods are an alternative approach to sample size calculations, particularly for complex multilevel models where analytical calculations may be less straightforward. A criticism of simulation-based approaches is that they are computationally intensive, so in this paper we contrast different approaches of using the information within each simulation and sharing information across scenarios. We describe the “standard error” method (using the known effect estimate and simulations to estimate the standard error for a scenario) and show that it requires far fewer simulations than other methods. We also show that transforming power calculations onto different scales results in linear relationships with a particular family of functions of the sample size to be optimized, resulting in an easy route to sharing information across scenarios. |
| Keywords: | sample size calculations; multilevel models; simulation methods; power |
| JEL: | C1 |
| Date: | 2025–07–17 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:128881 |
| By: | Li, Mengbing; Shi, Chengchun; Wu, Zhenke; Fryzlewicz, Piotr |
| Abstract: | We consider reinforcement learning (RL) in possibly nonstationary environments. Many existing RL algorithms in the literature rely on the stationarity assumption that requires the state transition and reward functions to be constant over time. However, this assumption is restrictive in practice and is likely to be violated in a number of applications, including traffic signal control, robotics and mobile health. In this paper, we develop a model-free test to assess the stationarity of the optimal Q-function based on pre-collected historical data, without additional online data collection. Based on the proposed test, we further develop a change point detection method that can be naturally coupled with existing state-of-the-art RL methods designed in stationary environments for online policy optimization in nonstationary environments. The usefulness of our method is illustrated by theoretical results, simulation studies, and a real data example from the 2018 Intern Health Study. A Python implementation of the proposed procedure is publicly available at https://github.com/limengbinggz/CUSUM-RL . |
| Keywords: | change point detection; hypothesis testing; nonstationarity; reinforcement learning |
| JEL: | C1 |
| Date: | 2025–06–30 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:127507 |
| By: | Pál, Tibor; Storti, Giuseppe |
| Abstract: | This paper analyses the dynamics of the natural rate of interest (r-star) in the US using a score-driven state-space model within the Laubach–Williams structural framework. Compared to standard score-driven specifications, the proposed model enhances flexibility in variance adjustment by assigning time-varying weights to both the conditional likelihood score and the inertia coefficient in the volatility updating equations. The improved state dependence of volatility dynamics effectively accounts for sudden shifts in volatility persistence induced by highly volatile unexpected events. In addition, allowing time variation in the IS and Phillips curve relationships enables the analysis of structural changes in the US economy that are relevant to monetary policy. The results indicate that the advanced models improve the precision of r-star estimates by responding more effectively to changes in macroeconomic conditions. |
| Keywords: | r-star, state-space, Kalman filter, score-driven models |
| JEL: | C13 C51 E52 |
| Date: | 2025–07–14 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:125338 |
| By: | Guglielmo Maria Caporale; Luis Alberiko Gil-Alana |
| Abstract: | This note puts forward a new modelling approach that includes both fractional integration and autoregressive processes in a unified framework. The proposed model is very general and includes other more standard approaches such as the AR(F)IMA models. Some Monte Carlo evidence shows that the suggested framework outperforms standard AR(F)IMA specifications in capturing the properties of the series examined. |
| Keywords: | time series modelling, stationarity, fractional integration, autoregressions |
| JEL: | C22 C50 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11984 |
| By: | Philippe Goulet Coulombe; Karin Klieber |
| Abstract: | Local projections (LPs) are widely used in empirical macroeconomics to estimate impulse responses to policy interventions. Yet, in many ways, they are black boxes. It is often unclear what mechanism or historical episodes drive a particular estimate. We introduce a new decomposition of LP estimates into the sum of contributions of historical events, which is the product, for each time stamp, of a weight and the realization of the response variable. In the least squares case, we show that these weights admit two interpretations. First, they represent purified and standardized shocks. Second, they serve as proximity scores between the projected policy intervention and past interventions in the sample. Notably, this second interpretation extends naturally to machine learning methods, many of which yield impulse responses that, while nonlinear in predictors, still aggregate past outcomes linearly via proximity-based weights. Applying this framework to shocks in monetary and fiscal policy, global temperature, and the excess bond premium, we find that easily identifiable events-such as Nixon's interference with the Fed, stagflation, World War II, and the Mount Agung volcanic eruption-emerge as dominant drivers of often heavily concentrated impulse response estimates. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.12422 |
| By: | Qingyu Li; Chiranjib Mukhopadhyay; Abolfazl Bayat; Ali Habibnia |
| Abstract: | Recent advances in quantum computing have demonstrated its potential to significantly enhance the analysis and forecasting of complex classical data. Among these, quantum reservoir computing has emerged as a particularly powerful approach, combining quantum computation with machine learning for modeling nonlinear temporal dependencies in high-dimensional time series. As with many data-driven disciplines, quantitative finance and econometrics can hugely benefit from emerging quantum technologies. In this work, we investigate the application of quantum reservoir computing for realized volatility forecasting. Our model employs a fully connected transverse-field Ising Hamiltonian as the reservoir with distinct input and memory qubits to capture temporal dependencies. The quantum reservoir computing approach is benchmarked against several econometric models and standard machine learning algorithms. The models are evaluated using multiple error metrics and the model confidence set procedures. To enhance interpretability and mitigate current quantum hardware limitations, we utilize wrapper-based forward selection for feature selection, identifying optimal subsets, and quantifying feature importance via Shapley values. Our results indicate that the proposed quantum reservoir approach consistently outperforms benchmark models across various metrics, highlighting its potential for financial forecasting despite existing quantum hardware constraints. This work serves as a proof-of-concept for the applicability of quantum computing in econometrics and financial analysis, paving the way for further research into quantum-enhanced predictive modeling as quantum hardware capabilities continue to advance. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.13933 |
| By: | Paker, Meredith; Stephenson, Judy; Wallis, Patrick |
| Abstract: | Understanding long-run economic growth requires reliable historical data, yet the vast majority of long-run economic time series are drawn from incomplete records with significant temporal and geographic gaps. Conventional solutions to these gaps rely on linear regressions that risk bias or overfitting when data are scarce. We introduce “past predictive modeling, ” a framework that leverages machine learning and out-of-sample predictive modeling techniques to reconstruct representative historical time series from scarce data. Validating our approach using nominal wage data from England, 1300-1900, we show that this new method leads to more accurate and generalizable estimates, with bootstrapped standard errors 72% lower than benchmark linear regressions. Beyond just bettering accuracy, these improved wage estimates for England yield new insights into the impact of the Black Death on inequality, the economic geography of pre-industrial growth, and productivity over the long-run. |
| Keywords: | machine learning; predictive modeling; wages; black death; industrial revolution |
| JEL: | J31 C53 N33 N13 N63 |
| Date: | 2025–06–13 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:128852 |