Econometric Time Series http://lists.repec.org/mailman/listinfo/nep-ets Econometric Time Series 2026-03-09 Redesigning the classical automatic selection of X-11 seasonal filters https://d.repec.org/n?u=RePEc:zbw:bubdps:337482&r=&r=ets The classical X-11 seasonal adjustment method for monthly and quarterly time series is equipped with routines for data-driven selections of both Henderson trendcycle filters and 3 × k seasonal moving averages, currently involving up to three candidate filters in either case. Although these routines have a long-standing tradition that can be traced back at least to 1960, they have not been adopted in a recent JDemetra+ implementation of a modified X-11 method tailored to the specifics of infra-monthly time series, such as the coexistence of multiple seasonal patterns with potentially fractional periodicities. Focusing on seasonal moving averages, we seek to fill this gap by suggesting a generic redesign of the legacy selection concept based upon the so-called moving seasonality ratio. This blueprint utilises a broader set of candidate seasonal filters and, unlike the original setting, a set of common approaches for deriving the requisite asymmetric variants. Considering intersections of multiple approach-specific selection rules stabilises the final filter choice and, what is more, naturally provides the warranted thresholds controlling the potential recalculation of the moving seasonality ratio from suitably shortened detrended observations. Our proposed redesign is illustrated using one specific rule based upon threshold quartiles and real-time data for three German macroeconomic time series sampled at quarterly, monthly, and daily intervals. The last example also highlights the need for additional intermediate steps in the calculation of the moving seasonality ratio when the data contain complex seasonal dynamics. Webel, Karsten asymmetric linear filters, concurrent revision policy, JDemetra+, moving seasonality ratio, nonparametric seasonal adjustment, real-time data 2026 A least-squares filter for sequence-space models https://d.repec.org/n?u=RePEc:ecb:ecbwps:20263191&r=&r=ets Sequence-space models are becoming increasingly popular in macroeconomics, especially in the heterogeneous-agent literature. However, the econometric toolkit for users of these models remains less developed than that available for traditional state-space methods. This note introduces an algorithm for efficiently filtering unobserved shocks in linear sequence-space models. The proposed filter solves a least-squares optimization problem in closed form and returns the expectation of unobserved shocks conditional on observed data. It handles heteroskedasticity, missing observations, measurement error, and non- Gaussian shock distributions. To illustrate its properties, I apply it to data simulated from a medium-scale heterogeneous-agent New Keynesian model and show that it accurately recovers the underlying structural shocks. JEL Classification: C32, E27, E32, E37 Rigato, Rodolfo Dinis filtering, least squares, sequence space 2026-02 Gaussian Maximum Likelihood Estimation of Static and Dynamic Factor Models https://d.repec.org/n?u=RePEc:ces:ceswps:_12380&r=&r=ets The paper derives and proves results of Gaussian maximum likelihood estimation of constant unknowns (coefficients, covariances) and time-varying unknowns (factors, disturbances) of static and dynamic factor models and, thereby, extends the statistics and econometrics literatures on estimation and statistical evaluation of estimates of the unknowns. The paper presents a new, general, unified, and one-step-comprehensive method for simultaneously estimating and statistically evaluating all constant and time-varying unknowns of static and dynamic factor models. Peter A. Zadrozny differential matrix, differentiations, vectorized to Hessians 2026 How Well Are State-Dependent Local Projections Capturing Nonlinearities? https://d.repec.org/n?u=RePEc:arx:papers:2602.14455&r=&r=ets We evaluate how well state-dependent local projections recover true impulse responses in nonlinear environments. Using quadratic vector autoregressions as a laboratory, we show that linear local projections fail to capture any nonlinearities when shocks are symmetrically distributed. Popular state-dependent local projections specifications capture distinct aspects of nonlinearity: those interacting shocks with their signs capture higher-order effects, while those interacting shocks with lagged states capture state dependence. However, their gains over linear specifications are concentrated in tail shocks or tail states; and, for lag-based specifications, hinge on how well the chosen observable proxies the latent state. Our proposed specification-which augments the linear specification with a squared shock term and an interaction between the shock and lagged observables-best approximates the true responses across the entire joint distribution of shocks and states. An application to monetary policy reveals economically meaningful state dependence, whereas higher-order effects, though statistically significant, prove economically modest. Zhiheng You 2026-02 A Quadratic Link between Out-of-Sample $R^2$ and Directional Accuracy https://d.repec.org/n?u=RePEc:arx:papers:2602.07841&r=&r=ets This study provides a novel perspective on the metric disconnect phenomenon in financial time series forecasting through an analytical link that reconciles the out-of-sample $R^2$ ($R^2_{OOS}$) and directional accuracy (DA). In particular, using the random walk model as a baseline and assuming that sign correctness is independent of realized magnitude, we show that these two metrics exhibit a quadratic relationship for MSE-optimal point forecasts. For point forecasts with modest DA, the theoretical value of $R^2_{OOS}$ is intrinsically negligible. Thus, a negative empirical $R^2_{OOS}$ is expected if the model is suboptimal or affected by finite sample noise. Cheng Zhang 2026-02 Inference for High-Dimensional Local Projection https://d.repec.org/n?u=RePEc:arx:papers:2602.10415&r=&r=ets This paper rigorously analyzes the properties of the local projection (LP) methodology within a high-dimensional (HD) framework, with a central focus on achieving robust long-horizon inference. We integrate a general dependence structure into h-step ahead forecasting models via a flexible specification of the residual terms. Additionally, we study the corresponding HD covariance matrix estimation, explicitly addressing the complexity arising from the long-horizon setting. Extensive Monte Carlo simulations are conducted to substantiate the derived theoretical findings. In the empirical study, we utilize the proposed HD LP framework to study the impact of business news attention on U.S. industry-level stock volatility. Jiti Gao Fei Liu Bin Peng 2026-02 Initial-Condition-Robust Inference in Autoregressive Models https://d.repec.org/n?u=RePEc:arx:papers:2602.09382&r=&r=ets This paper considers confidence intervals (CIs) for the autoregressive (AR) parameter in an AR model with an AR parameter that may be close or equal to one. Existing CIs rely on the assumption of a stationary or fixed initial condition to obtain correct asymptotic coverage and good finite sample coverage. When this assumption fails, their coverage can be quite poor. In this paper, we introduce a new CI for the AR parameter whose coverage probability is completely robust to the initial condition, both asymptotically and in finite samples. This CI pays only a small price in terms of its length when the initial condition is stationary or fixed. The new CI also is robust to conditional heteroskedasticity of the errors. Donald W. K. Andrews Ming Li Yapeng Zheng 2026-02 The Accuracy Smoothness Dilemma in Prediction: a Novel Multivariate M-SSA Forecast Approach https://d.repec.org/n?u=RePEc:arx:papers:2602.13722&r=&r=ets Forecasting presents a complex estimation challenge, as it involves balancing multiple, often conflicting, priorities and objectives. Conventional forecast optimization methods typically emphasize a single metric--such as minimizing the mean squared error (MSE)--which may neglect other crucial aspects of predictive performance. To address this limitation, the recently developed Smooth Sign Accuracy (SSA) framework extends the traditional MSE approach by simultaneously accounting for sign accuracy, MSE, and the frequency of sign changes in the predictor. This addresses a fundamental trade-off--the so-called accuracy-smoothness (AS) dilemma--in prediction. We extend this approach to the multivariate M-SSA, leveraging the original criterion to incorporate cross-sectional information across multiple time series. As a result, the M-SSA criterion enables the integration of various design objectives related to AS forecasting performance, effectively generalizing conventional MSE-based metrics. To demonstrate its practical applicability and versatility, we explore the application of the M-SSA in three primary domains: forecasting, real-time signal extraction (nowcasting), and smoothing. These case studies illustrate the framework's capacity to adapt to different contexts while effectively managing inherent trade-offs in predictive modelling. Marc Wildi 2026-02 VOLatility Archive for Realized Estimates (VOLARE) https://d.repec.org/n?u=RePEc:arx:papers:2602.19732&r=&r=ets VOLARE (VOLatility Archive for Realized Estimates - https://volare.unime.it) is an open research infrastructure providing standardized realized volatility and covariance measures constructed from ultra-high-frequency financial data. The platform processes tick-level observations across equities, exchange rates, and futures using an asset-specific pipeline that addresses heterogeneous trading calendars, microstructure noise, and timestamp precision. For equities, price series are cleaned using a documented outlier detection procedure and sampled at regular intervals. VOLARE delivers a comprehensive set of realized estimators, including realized variance, range-based measures, bipower variation, semivariances, realized quarticity, realized kernels, and multivariate covariance measures, ensuring methodological consistency and cross-asset comparability. In addition to bulk dataset download, the platform supports interactive visualization and real-time estimation of established volatility models such as HAR and MEM specifications. Fabrizio Cipollini Giulia Cruciani Giampiero M. Gallo Alessandra Insana Edoardo Otranto Fabio Spagnolo 2026-02 Schr\"odinger bridges with jumps for time series generation https://d.repec.org/n?u=RePEc:arx:papers:2602.20011&r=&r=ets We study generative modeling for time series using entropic optimal transport and the Schr\"odinger bridge (SB) framework, with a focus on applications in finance and energy modeling. Extending the diffusion-based approach of Hamdouche, Henry-Labord\`ere, Pham, 2023, we introduce a jump-diffusion Schr\"odinger bridge model that allows for discontinuities in the generative dynamics. Starting from a Schr\"odinger bridge entropy minimization problem, we reformulate the task as a stochastic control problem whose solution characterizes the optimal controlled jump-diffusion process. When sampled on a fixed time grid, this process generates synthetic time series matching the joint distributions of the observed data. The model is fully data-driven, as both the drift and the jump intensity are learned directly from the data. We propose practical algorithms for training, sampling, and hyperparameter calibration. Numerical experiments on simulated and real datasets, including financial and energy time series, show that incorporating jumps substantially improves the realism of the generated data, in particular by capturing abrupt movements, heavy tails, and regime changes that diffusion-only models fail to reproduce. Comparisons with state-of-the-art generative models highlight the benefits and limitations of the proposed approach. Stefano De Marco Huy\^en Pham Davide Zanni 2026-02 Model Selection in High-Dimensional Linear Regression using Boosting with Multiple Testing https://d.repec.org/n?u=RePEc:arx:papers:2602.19705&r=&r=ets High-dimensional regression specification and analysis is a complex and active area of research in statistics, machine learning, and econometrics. This paper proposes a new approach, Boosting with Multiple Testing (BMT), which combines forward stepwise variable selection with the multiple testing framework of Chudik et al (2018). At each stage, the model is updated by adding only the most significant regressor conditional on those already included, while a family-wise multiple testing filter is applied to the remaining candidates. In this way, the method retains the strong screening properties of Chudik et al (2018) while operating in a less greedy manner with respect to proxy and noise variables. Using sharp probability inequalities for heterogeneous strongly mixing processes from Dendramis et al (2022), we show that BMT enjoys oracle type properties relative to an approximating model that includes all true signals and excludes pure noise variables: this model is selected with probability tending to one, and the resulting estimator achieves standard parametric rates for prediction error and coefficient estimation. Additional results establish conditions under which BMT recovers the exact true model and avoids selection of proxy signals. Monte Carlo experiments indicate that BMT performs very well relative to OCMT and Lasso type procedures, delivering higher model selection accuracy and smaller RMSE for the estimated coefficients, especially under strong multicollinearity of the regressors. Two empirical illustrations based on a large set of macro-financial indicators as covariates, show that BMT yields sparse, interpretable specifications with favourable out-of-sample performance. George Kapetanios Vasilis Sarafidis Alexia Ventouri 2026-02 Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data https://d.repec.org/n?u=RePEc:arx:papers:2602.19645&r=&r=ets We show how pre-averaging can be applied to the problem of measuring the ex-post covariance of financial asset returns under microstructure noise and non-synchronous trading. A pre-averaged realised covariance is proposed, and we present an asymptotic theory for this new estimator, which can be configured to possess an optimal convergence rate or to ensure positive semi-definite covariance matrix estimates. We also derive a noise-robust Hayashi-Yoshida estimator that can be implemented on the original data without prior alignment of prices. We uncover the finite sample properties of our estimators with simulations and illustrate their practical use on high-frequency equity data. Kim Christensen Silja Kinnebrock Mark Podolskij 2026-02