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on Econometric Time Series |
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Issue of 2025–06–23
nineteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Giuseppe Cavaliere; Thomas Mikosch; Anders Rahbek; Frederik Vilandt |
| Abstract: | Integrated autoregressive conditional duration (ACD) models serve as natural counterparts to the well-known integrated GARCH models used for financial returns. However, despite their resemblance, asymptotic theory for ACD is challenging and also not complete, in particular for integrated ACD. Central challenges arise from the facts that (i) integrated ACD processes imply durations with infinite expectation, and (ii) even in the non-integrated case, conventional asymptotic approaches break down due to the randomness in the number of durations within a fixed observation period. Addressing these challenges, we provide here unified asymptotic theory for the (quasi-) maximum likelihood estimator for ACD models; a unified theory which includes integrated ACD models. Based on the new results, we also provide a novel framework for hypothesis testing in duration models, enabling inference on a key empirical question: whether durations possess a finite or infinite expectation. We apply our results to high-frequency cryptocurrency ETF trading data. Motivated by parameter estimates near the integrated ACD boundary, we assess whether durations between trades in these markets have finite expectation, an assumption often made implicitly in the literature on point process models. Our empirical findings indicate infinite-mean durations for all the five cryptocurrencies examined, with the integrated ACD hypothesis rejected -- against alternatives with tail index less than one -- for four out of the five cryptocurrencies considered. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.06190 |
| By: | Haoyuan Wang; Chen Liu; Minh-Ngoc Tran; Chao Wang |
| Abstract: | This paper introduces a novel multivariate volatility modeling framework, named Long Short-Term Memory enhanced BEKK (LSTM-BEKK), that integrates deep learning into multivariate GARCH processes. By combining the flexibility of recurrent neural networks with the econometric structure of BEKK models, our approach is designed to better capture nonlinear, dynamic, and high-dimensional dependence structures in financial return data. The proposed model addresses key limitations of traditional multivariate GARCH-based methods, particularly in capturing persistent volatility clustering and asymmetric co-movement across assets. Leveraging the data-driven nature of LSTMs, the framework adapts effectively to time-varying market conditions, offering improved robustness and forecasting performance. Empirical results across multiple equity markets confirm that the LSTM-BEKK model achieves superior performance in terms of out-of-sample portfolio risk forecast, while maintaining the interpretability from the BEKK models. These findings highlight the potential of hybrid econometric-deep learning models in advancing financial risk management and multivariate volatility forecasting. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.02796 |
| By: | De Graeve, Ferre (KU Leuven); Westermark, Andreas (Research Department, Central Bank of Sweden) |
| Abstract: | Macroeconomic research often relies on structural vector autoregressions, (S)VARs, to uncover empirical regularities. Critics argue the method goes awry due to lag truncation: short lag-lengths imply a poor approximation to important data-generating processes (e.g. DSGE-models). Empirically, short lag-length is deemed necessary as increased parametrization induces excessive uncertainty. The paper shows that this argument is incomplete. Longer lag-length simultaneously reduces misspecification, which in turn reduces variance. For data generated by frontier DSGE-models long-lag VARs are feasible, reduce bias and variance, and have better coverage. Long-lag VARs are also viable in common macroeconomic data and applications. Thus, contrary to conventional wisdom, the trivial solution to the critique actually works. |
| Keywords: | VAR; SVAR; Lag-length; Lag truncation |
| JEL: | C18 E37 |
| Date: | 2025–05–01 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:rbnkwp:0451 |
| By: | Jarek Duda |
| Abstract: | Nonstationarity of real-life time series requires model adaptation. In classical approaches like ARMA-ARCH there is assumed some arbitrarily chosen dependence type. To avoid their bias, we will focus on novel more agnostic approach: moving estimator, which estimates parameters separately for every time $t$: optimizing $F_t=\sum_{\tau |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.05354 |
| By: | Bańbura, Marta; Bobeica, Elena; Giammaria, Alessandro; Porqueddu, Mario; van Spronsen, Josha |
| Abstract: | Energy inflation is a major source of headline inflation volatility and forecast errors, therefore it is critical to model it accurately. This paper introduces a novel suite of Bayesian VAR models for euro area HICP energy inflation, which adopts a granular, bottom-up approach – disaggregating energy into subcomponents, such as fuels, gas, and electricity. The suite incorporates key features for energy prices: stochastic volatility, outlier correction, high-frequency indicators, and pre-tax price modelling. These characteristics enhance both in-sample explanatory power and forecast accuracy. Compared to standard benchmarks and official projections, our BVARs achieve better forecasting performance, particularly beyond the very short term. The suite also captures a sizable variation in the impact of commodity price shocks, pointing to higher elasticities at higher levels of commodity prices. Beyond forecasting, our framework is also useful for scenario and sensitivity analysis as an effective tool to gauge risks, which is especially relevant amid ongoing energy market transformations. JEL Classification: C32, C53, E31, E37 |
| Keywords: | Bayesian VAR, gas prices, HICP, oil prices |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:ecb:ecbwps:20253062 |
| By: | Jiang Hu; Jiahui Xie; Yangchun Zhang; Wang Zhou |
| Abstract: | Factor models are essential tools for analyzing high-dimensional data, particularly in economics and finance. However, standard methods for determining the number of factors often overestimate the true number when data exhibit heavy-tailed randomness, misinterpreting noise-induced outliers as genuine factors. This paper addresses this challenge within the framework of Elliptical Factor Models (EFM), which accommodate both heavy tails and potential non-linear dependencies common in real-world data. We demonstrate theoretically and empirically that heavy-tailed noise generates spurious eigenvalues that mimic true factor signals. To distinguish these, we propose a novel methodology based on a fluctuation magnification algorithm. We show that under magnifying perturbations, the eigenvalues associated with real factors exhibit significantly less fluctuation (stabilizing asymptotically) compared to spurious eigenvalues arising from heavy-tailed effects. This differential behavior allows the identification and detection of the true and spurious factors. We develop a formal testing procedure based on this principle and apply it to the problem of accurately selecting the number of common factors in heavy-tailed EFMs. Simulation studies and real data analysis confirm the effectiveness of our approach compared to existing methods, particularly in scenarios with pronounced heavy-tailedness. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.05116 |
| By: | Tom Boot; Bart Keijsers |
| Abstract: | We study the accuracy of forecasts in the diffusion index forecast model with possibly weak loadings. The default option to construct forecasts is to estimate the factors through principal component analysis (PCA) on the available predictor matrix, and use the estimated factors to forecast the outcome variable. Alternatively, we can directly relate the outcome variable to the predictors through either ridge regression or random projections. We establish that forecasts based on PCA, ridge regression and random projections are consistent for the conditional mean under the same assumptions on the strength of the loadings. However, under weaker loadings the convergence rate is lower for ridge and random projections if the time dimension is small relative to the cross-section dimension. We assess the relevance of these findings in an empirical setting by comparing relative forecast accuracy for monthly macroeconomic and financial variables using different window sizes. The findings support the theoretical results, and at the same time show that regularization-based procedures may be more robust in settings not covered by the developed theory. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.09575 |
| By: | Qian Hui; Sidney I. Resnick; Tiandong Wang |
| Abstract: | Accurately identifying the extremal dependence structure in multivariate heavy-tailed data is a fundamental yet challenging task, particularly in financial applications. Following a recently proposed bootstrap-based testing procedure, we apply the methodology to absolute log returns of U.S. S&P 500 and Chinese A-share stocks over a time period well before the U.S. election in 2024. The procedure reveals more isolated clustering of dependent assets in the U.S. economy compared with China which exhibits different characteristics and a more interconnected pattern of extremal dependence. Cross-market analysis identifies strong extremal linkages in sectors such as materials, consumer staples and consumer discretionary, highlighting the effectiveness of the testing procedure for large-scale empirical applications. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.04656 |
| By: | Jan-Lukas Wermuth |
| Abstract: | develop an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale that is attainable for all marginal distributions and propose a set of dependence measures that are 1 if and only if this perfect dependence is satisfied. The advantages of these dependence measures relative to classical dependence measures like contingency coefficients, Goodman-Kruskal’s lambda and tau and the so-called uncertainty coefficient are twofold. Firstly, they are defined if one of the variables is real-valued and exhibits continuities. Secondly, they satisfy the property of attainability. That is, they can take all values in the interval [0, 1] irrespective of the marginals involved. Both properties are not shared by the classical dependence measures which need two discrete marginal distributions and can in some situations yield values close to 0 even though the dependence is strong or even perfect. Additionally, I provide a consistent estimator for one of the new dependence measures together with its asymptotic distribution under independence as well as in the general case. This allows to construct confidence intervals and an independence test, whose finite sample performance I subsequently examine in a simulation study. Finally, I illustrate the use of the new dependence measure in two applications on the dependence between the variables country and income or country and religion, respectively. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:lis:liswps:897 |
| By: | Peter K. Friz; Benjamin Jourdain; Thomas Wagenhofer; Alexandre Zhou |
| Abstract: | Local stochastic volatility refers to a popular model class in applied mathematical finance that allows for "calibration-on-the-fly", typically via a particle method, derived from a formal McKean-Vlasov equation. Well-posedness of this limit is a well-known problem in the field; the general case is largely open, despite recent progress in Markovian situations. Our take is to start with a well-defined Euler approximation to the formal McKean-Vlasov equation, followed by a newly established half-step-scheme, allowing for good approximations of conditional expectations. In a sense, we do Euler first, particle second in contrast to previous works that start with the particle approximation. We show weak order one for the Euler discretization, plus error terms that account for the said approximation. The case of particle approximation is discussed in detail and the error rate is given in dependence of all parameters used. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.10817 |
| By: | Cui Rui; Li Yuhao; Song Xiaojun |
| Abstract: | We propose power-boosting strategies for kernel-based specification tests in conditional moment models, with a focus on the Kernel Conditional Moment (KCM) test. By decomposing the KCM statistic into spectral components, we demonstrate that truncating poorly estimated directions and selecting kernels based on a non-asymptotic signal-to-noise ratio significantly improves both test power and size control. Our theoretical and simulation results demonstrate that, while divergent component weights may offer higher asymptotic power, convergent component weights perform better in finite samples. The methods outperform existing tests across various settings and are illustrated in an empirical application. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.04900 |
| By: | Gupta, Abhijit |
| Abstract: | Commodity futures price volatility creates significant economic challenges, necessitating accurate multi-horizon forecasting. Predicting these prices is complicated by diverse interacting factors (macroeconomic, supply/demand, geopolitical). Current models often lack transparency, limiting strategic use. This paper presents a Regularized Sparse Autoencoder (RSAE), a deep learning framework for simultaneous multi-horizon commodity futures prediction and discovery of interpretable latent market drivers. The RSAE forecasts prices at multiple horizons (e.g., 1-day, 1-week, 1-month) using multivariate time series. A key L1 regularization on its latent vector enforces sparsity, promoting parsimonious explanations of market dynamics through learned factors representing underlying drivers (e.g., demand shifts, supply shocks). Drawing from energy-based models and sparse coding, the RSAE optimizes predictive accuracy while learning sparse representations. Evaluated on historical Copper and Crude Oil futures data with numerous indicators, our findings suggest the RSAE offers competitive multi-horizon forecasting accuracy and data-driven insights into price dynamics via its interpretable latent space, a notable advantage over traditional black-box approaches. |
| Date: | 2025–05–10 |
| URL: | https://d.repec.org/n?u=RePEc:osf:osfxxx:4rzky_v1 |
| By: | Ziyang Xiong; Zhao Chen; Christina Dan Wang |
| Abstract: | Estimating the leverage effect from high-frequency data is vital but challenged by complex, dependent microstructure noise, often exhibiting non-Gaussian higher-order moments. This paper introduces a novel multi-scale framework for efficient and robust leverage effect estimation under such flexible noise structures. We develop two new estimators, the Subsampling-and-Averaging Leverage Effect (SALE) and the Multi-Scale Leverage Effect (MSLE), which adapt subsampling and multi-scale approaches holistically using a unique shifted window technique. This design simplifies the multi-scale estimation procedure and enhances noise robustness without requiring the pre-averaging approach. We establish central limit theorems and stable convergence, with MSLE achieving convergence rates of an optimal $n^{-1/4}$ and a near-optimal $n^{-1/9}$ for the noise-free and noisy settings, respectively. A cornerstone of our framework's efficiency is a specifically designed MSLE weighting strategy that leverages covariance structures across scales. This significantly reduces asymptotic variance and, critically, yields substantially smaller finite-sample errors than existing methods under both noise-free and realistic noisy settings. Extensive simulations and empirical analyses confirm the superior efficiency, robustness, and practical advantages of our approach. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.08654 |
| By: | Michal Franta; Jan Vlcek |
| Abstract: | Inflation at Risk provides a coherent description of the risks associated with an inflation outlook. This paper explores the practical applicability of this approach in central banks. The method is applied to Czech inflation to highlight issues related to short data sample. A set of quantile regressions with a non-crossing quantiles constraint is estimated using monthly data from the year 2000 onwards, and the model's in-sample fit and out-of-sample forecasting performance are then assessed. Furthermore, we discuss the Inflation at Risk estimates in the context of several historical events and demonstrate how the approach can inform monetary policy. The estimation results suggest the presence of nonlinearities in the Czech inflation process, which are related to supply-side pressures. In addition, it appears that regime changes have occurred recently. |
| Keywords: | Inflation dynamics, inflation risk, quantile regressions |
| JEL: | E31 E37 E52 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:cnb:wpaper:2025/8 |
| By: | Daniil Bargman |
| Abstract: | This paper introduces a new least squares regression methodology called (C)LARX: a (constrained) latent variable autoregressive model with exogenous inputs. Two additional contributions are made as a side effect: First, a new matrix operator is introduced for matrices and vectors with blocks along one dimension; Second, a new latent variable regression (LVR) framework is proposed for economics and finance. The empirical section examines how well the stock market predicts real economic activity in the United States. (C)LARX models outperform the baseline OLS specification in out-of-sample forecasts and offer novel analytical insights about the underlying functional relationship. |
| Date: | 2025–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2506.04488 |
| By: | Jutta G. Kurth; Adam A. Majewski; Jean-Philippe Bouchaud |
| Abstract: | We amend and extend the Chiarella model of financial markets to deal with arbitrary long-term value drifts in a consistent way. This allows us to improve upon existing calibration schemes, opening the possibility of calibrating individual monthly time series instead of classes of time series. The technique is employed on spot prices of four asset classes from ca. 1800 onward (stock indices, bonds, commodities, currencies). The so-called fundamental value is a direct output of the calibration, which allows us to (a) quantify the amount of excess volatility in these markets, which we find to be large (e.g. a factor $\approx$ 4 for stock indices) and consistent with previous estimates; and (b) determine the distribution of mispricings (i.e. the difference between market price and value), which we find in many cases to be bimodal. Both findings are strongly at odds with the Efficient Market Hypothesis. We also study in detail the 'sloppiness' of the calibration, that is, the directions in parameter space that are weakly constrained by data. The main conclusions of our study are remarkably consistent across different asset classes, and reinforce the hypothesis that the medium-term fate of financial markets is determined by a tug-of-war between trend followers and fundamentalists. |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2505.07820 |
| By: | Thomas B. Marvell |
| Abstract: | Textbook theory predicts that t-ratios decline towards zero in regressions when there is increasing collinearity between two independent variables. This article shows that this rarely happens if the two variables are endogenous, and coefficients increase greatly with more collinearity. The purposes of this article are 1) to illustrate this bias and explain why it occurs, and 2) to use the phenomenon to develop a test for endogeneity. For the test, one creates a variable that is highly collinear with the independent variable of interest, and endogeneity is indicated if t-ratios do not decline with increasing collinearity. False negatives are possible, but not likely. The test is confirmed with algebraic examples and simulations. I give many empirical examples of the bias and the test, including testing exogeneity assumptions behind instrumental variables and Granger causality. |
| Keywords: | Endogeneity, collinearity, simultaneity, omitted variable bias, instrumental variables. |
| JEL: | C12 C13 C26 |
| Date: | 2025–05–05 |
| URL: | https://d.repec.org/n?u=RePEc:eei:rpaper:eeri_rp_2025_05 |
| By: | Wen, Kaiyue; Wang, Tengyao; Wang, Yuhao |
| Abstract: | We consider the problem of testing whether a single coefficient is equal to zero in linear models when the dimension of covariates p can be up to a constant fraction of sample size n. In this regime, an important topic is to propose tests with finite-population valid size control without requiring the noise to follow strong distributional assumptions. In this paper, we propose a new method, called residual permutation test (RPT), which is constructed by projecting the regression residuals onto the space orthogonal to the union of the column spaces of the original and permuted design matrices. RPT can be proved to achieve finite-population size validity under fixed design with just exchangeable noises, whenever p |
| Keywords: | distribution-free test; permutation test; finite-population validity; heavy tail distribution; high-dimensional data |
| JEL: | C1 |
| Date: | 2025–04–30 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:126275 |
| By: | Ally Manengu Manengu (UNIKIN - Département des Sciences économiques, Université de Kinshasa) |
| Abstract: | This study takes part in the debate about nature of the relationship between exchange rate fluctuations and inflation. The goal is to demonstrate that the exchange rate evolves in a volatile manner, and that its effects on inflation are positive and non-linear for the case of the Democratic Republic of Congo (DRC), with annual data for the period from 1970 to 2022. Two econometric models are fitted for this purpose : (i) the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, which was developed by Robert Engle, F., (1986); (ii) the Nonlinear Staggered Lag Autoregressive (NARDL) model, which was developed by Shin, Y.; Yu, B. C., and Greenwood-Nimmo, M. (2014). The results obtained from the estimations attest to the following : (i) the exchange rate in the DRC evolves in a volatile manner ; (ii) in the short term, the effects of exchange rate volatility on inflation are positive and non-linear, while they are linear in the long term. Positive shocks have an inflationary effect ; while negative shocks have a negative and statistically insignificant effect (prices are rigid to exchange rate depreciation in the DRC). |
| Abstract: | Cette étude participe au débat sur la nature de la relation entre les fluctuations du taux de change et l'inflation. L'objectif est de démontrer que le taux de change évolue de manière volatile, et que ses effets sur l'inflation sont positifs et non-linéaires pour le cas de la République Démocratique du Congo (RDC), avec les données annuelles pour la période allant de 1970 à 2022. A cet effet, deux modèles économétriques ont été construits : (i) le modèle d'Hétéroscédasticité Conditionnelle Autorégressive Généralisée (GARCH), qui a été développé par Robert Engle, F., (1986) ; (ii) le modèle autorégressif à retard échelonné non-linéaire (NARDL), qui a été développé par Shin, Y. ; Yu, B. C., et Greenwood-Nimmo, M. ( 2014). Les résultats obtenus des estimations attestent ce qui suit : (i) le taux de change en RDC évolue de manière volatile ; (ii) à court terme, les effets de la volatilité du taux de change sur l'inflation sont positifs et non-linéaires, tandis qu'ils sont linéaires à long terme. Les chocs positifs ont un effet inflationniste, alors que les chocs négatifs ont un effet négatif et statistiquement non significatif (les prix sont rigides à la baisse du taux de change en RDC). |
| Keywords: | Taux de change Inflation volatilité et GARCH effets non-linéaires et NARDL. Classification JEL : E31 F41 E44 et C52 C53 C22 Exchange rate Inflation volatility and GARCH non-linear effects and NARDL. JEL code : E31 F41 E44 and C52 C53 C22, Taux de change, Inflation, volatilité et GARCH, effets non-linéaires et NARDL. Classification JEL : E31, F41, E44 et C52, C53, C22 Exchange rate, volatility and GARCH, non-linear effects and NARDL. JEL code : E31, E44 and C52, C22 |
| Date: | 2025–05–25 |
| URL: | https://d.repec.org/n?u=RePEc:hal:journl:hal-05083768 |