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on Econometric Time Series |
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Issue of 2026–09–21
eighteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Michael Stanley Smith; Lin Deng |
| Abstract: | Multivariate longitudinal data may exhibit non-Gaussian margins, nonlinear dynamics, and response vectors with composition that varies across waves. To account for these features, we introduce a vector drawable vine (VD-vine) copula that extends conventional drawable vine copulas from scalar to vector-valued nodes. Here, the response vector at each wave forms a multivariate marginal, and serial dependence is captured through a sequence of linking vector copulas. We establish that the VD-vine is itself a vector copula and reduces to a conventional drawable vine for scalar nodes. Recursive forward and backward conditional transports are derived that enable efficient likelihood evaluation and predictive simulation, with parsimonious reductions under finite-order Markov and stationary restrictions. Unconstrained parameterizations for Gaussian and FGM linking vector copulas, flexible multivariate marginals, and Bayesian variational inference provide a practical implementation. Simulations show improved predictive accuracy when the marginals are asymmetric and serial dependence is multivariate, with little loss under a correctly specified Gaussian panel vector autoregression. In an eight-wave Australian panel of 1, 093 individuals with varying response vectors, the full VD-vine delivers the best cross-validated distributional forecasts among the models considered, establishing the benefit of capturing asymmetry and nonlinear dependence. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.19547 |
| By: | Dezhbakhsh, Hashem; Levy, Daniel |
| Abstract: | It is well established that the U.S. prewar output was more volatile and less shock-persistent than the postwar output. This is often attributed to the data interpolation employed to construct the prewar series, rather than the postwar stabilization policies and institutional changes. Our analytical results, however, indicate that commonly used linear interpolation has the opposite effect on shock persistence and volatility of a series—it reduces short-run volatility and raises shock persistence. Therefore, interpolation does not seem to explain away the observed gaps between the volatility and shock persistence of the prewar and postwar series. If anything, it may hide part of the true gap. Consequently, our results strengthen the case that the prewar-postwar difference reflects real economic changes rather than interpolation, leaving stabilization policies and institutional changes as possible explanations. Our results hold for parsimonious stationary and nonstationary time series commonly used to model macroeconomic data. Our theoretical finding is also supported by a counterfactual empirical exercise we conduct using U.S. postwar series |
| Keywords: | Business Cycles, Output Volatility, Shock Persistence, Prewar vs Poswar Time Series, Linear Interpolation, Variance Ratio, Stationary Series, Nonstationary Series, Periodic Nonstationarity, Missing Observations, Macroeconomic Stabilization, Economic Policy |
| JEL: | E32 E01 N10 C02 C18 C22 C82 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:esprep:343604 |
| By: | Luca A. Pennacchio (Johannes Gutenberg University, Germany) |
| Abstract: | Many empirical macroeconomic questions rely on filtering non-stationary data to extract a stationary, business-cycle-like component. Common practice is to apply a linear filter with a standard passband, although economically relevant cycles may lie outside this passband. The resulting signal-extraction error likely affects subsequent regression estimates. This paper proposes a Continuous Wavelet Transform-informed filter that uses the CWT scalogram to identify statistically significant passbands in raw, non-stationary data relative to a researcher-specified null model. These passbands are supplied to a flexible Butterworth bandpass filter to extract a denoised, stationary cycle. Simulations show that the method improves signal extraction for periodic cycles and recovers statistically informative variation in stochastic-cycle settings missed by commonly used BK, HP, and Hamilton filters, while performing comparably or better in terms of correlation and RMSE. Applications demonstrate its use for cycle extraction, seasonal adjustment, and frequency-dependent regression analysis. |
| Keywords: | Business cycles, Signal extraction, Continuous Wavelet Transform, Bandpass filtering, Spectral analysis |
| Date: | 2026–08–31 |
| URL: | https://d.repec.org/n?u=RePEc:jgu:wpaper:2607 |
| By: | Dou, Baojun; He, Jing; Tiwari, Sudhir; Yao, Qiwei |
| Abstract: | Motivated by predicting intraday trading volume curves, we consider two spatio-temporal autoregressive models for matrix time series, in which each column may represent daily trading volume curve of one asset, and each row captures synchronized 5-minute volume intervals across multiple assets. While traditional matrix time series focus mainly on temporal evolution, our approach incorporates both spatial and temporal dynamics, enabling simultaneous analysis of interactions across multiple dimensions. The inherent endogeneity in spatio-temporal autoregressive models renders ordinary least squares estimation inconsistent. To overcome this difficulty while simultaneously estimating two distinct weight matrices with banded structure, we develop an iterated generalized Yule-Walker estimator by adapting a generalized method of moments framework based on Yule-Walker equations. Moreover, unlike conventional models that employ a single bandwidth parameter, the dual-bandwidth specification in our framework requires a new two-step, ratio-based sequential estimation procedure. |
| Keywords: | bandedcoefficient matrices;iterative least squares estimation;Yule-Walker equation;intraday volume curve;percentage of volume (POV) execution strategy |
| JEL: | C1 |
| Date: | 2026–11–30 |
| URL: | https://d.repec.org/n?u=RePEc:ehl:lserod:140645 |
| By: | Simon Donker van Heel (Erasmus University Rotterdam); Neil Shephard (Harvard University) |
| Abstract: | We develop a filter for time series, defined at each time t as the minimizer of a discounted convex combination of observed and expected losses. The filter can be estimated by simulation to an arbitrary level of accuracy in O(1) flops at each time point t and can be run for all values t=1, ..., T in parallel. These methods are applied to robustly compute a preaveraged price process from the more than 1.5 million trades made on a single financial asset in a single day where the noise's variance is infinite. It yields a flat ''volatility signature'' plot, down to the 1 second level, so the microstructure noise no longer biases the volatility estimate. This is not true when linear methods are employed. |
| Keywords: | Filtering; High frequency finance; Loss function; M-estimator; Volatility |
| Date: | 2026–09–13 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260068 |
| By: | Florian Huber; Gary Koop; Christian Matthes |
| Abstract: | Heterogeneous-agent New Keynesian (HANK) models characterize how entire cross-sectional distributions respond to structural shocks. Traditional representative-agent models are routinely disciplined by impulse responses from aggregate vector autoregressions (VARs). HANK models have no comparable established empirical benchmark because they make predictions not only about aggregates, but also about distributions of micro-level data. We propose a Bayesian benchmark that jointly models macroeconomic aggregates and several marginal distributions from repeated cross sections, including distributions observed in different surveys. Our approach can use both standard structural VAR identification approaches on macroeconomic aggregates and identification restrictions imposed on micro-level data. The model delivers a joint posterior of the distributional effects of shocks, without the need for household panel data or a separate first-stage density estimate. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.06827 |
| By: | Joel M. David; Raffaella Giacomini; Xiya Jiao; Weining Wang |
| Abstract: | State-dependent local projections (LPs) are widely used to study how causal effects vary as a function of economic states, but shock exogeneity alone does not identify this response function. We show that identification follows when the underlying conditional mean is linear in the shock with a state-dependent coefficient, a condition satisfied in canonical micro-macro environments, including first-order perturbation solutions of heterogeneous-agent and macro-finance models. Even then, standard linear-interaction LPs generally recover only a projection of the response function, motivating LPs with nonparametric state dependence. We develop a sieve estimator and establish pointwise and uniform inference for micro-macro panels, where a distinctive challenge is that the estimator can converge at different rates across the state space. Applied to firm investment, the method uncovers a hump-shaped response to monetary policy shocks and shows that standard linear-interaction LPs substantially understate the aggregate role of financial heterogeneity. |
| Date: | 2026–09–09 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:16/26 |
| By: | Frédérqiue Bec; Heino Bohn Nielsen (CY Cergy Paris Université, THEMA) |
| Abstract: | Forecast error variance decompositions (FEVDs) are widely used to assess the contribution of structural shocks in vector autoregressions. However, many variables of interest are nonlinear functions of underlying variables, rendering the standard linear FEVD incomplete. We develop a framework for variance decomposition of nonlinear forecast targets in terms of the Shapley value decomposition and compare it with more conventional approaches based on Taylor expansions. We illustrate that nonlinear interaction effects can account for components of forecast uncertainty that are not fully captured by Taylor approximations. As a result, approximation-based FEVD may substantially distort the picture of forecast uncertainty and the attribution of variance across shocks. |
| Keywords: | Vector Autoregression; Nonlinear Forecast Error Variance Decomposition; Shapley Shares; Generalized Shapley Shares; Interaction Terms. |
| JEL: | C32 C13 E44 |
| Date: | 2026 |
| URL: | https://d.repec.org/n?u=RePEc:ema:worpap:2026-09 |
| By: | Luke Hartigan |
| Abstract: | I develop a statistical measure of Australia's common output cycle by combining frequency-domain filtering of industry-level output to isolate its cyclical component with a dynamic factor model featuring stochastic cycle dynamics. The common cycle has an estimated period of around six years and reveals substantial heterogeneity in the timing and strength with which industries participate in the common cycle. Manufacturing and wholesale trade are closely synchronised, while agriculture and mining are mostly driven by their own idiosyncratic cycles. I evaluate the common output cycle's ability to forecast inflation and find that its predictive performance is statistically indistinguishable from that of an AR(1) benchmark over the forecast horizons considered. I also find evidence of potential endpoint issues when estimating the common output cycle in real time. Overall, these findings suggest that the common output cycle is best viewed as a descriptive measure of the historical features of the Australian output cycle that are shared across industries. |
| Keywords: | business cycle measurement, Butterworth filters, dynamic factor model, inflation forecasting, Kalman filter, signal extraction, stochastic cycle |
| JEL: | C32 C38 C53 E32 E37 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2026-78 |
| By: | Kennedy Titus Kayaki; Kyungsub Lee |
| Abstract: | We introduce ALM-GARCH, an asymmetric long-memory GARCH model in which positive and negative innovations enter conditional variance with different injection amplitudes and kernel offsets. These departures define testable level and memory channels relative to a nested symmetric benchmark. Positive Harris recurrence holds for interior configurations under a Foster-Lyapunov condition. Across five equity indices and Bitcoin, joint symmetry is rejected throughout, driven primarily by the level channel. The memory channel is supported for the Nikkei 225, KOSPI, and Bitcoin but is weakly identified when the positive branch is nearly inactive. Out-of-sample performance is broadly comparable to standard benchmarks. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.06422 |
| By: | Elie Tamer; Christopher D. Walker |
| Abstract: | This paper proposes a nonparametric Bayesian inference framework for partially identified discrete response models. The key observation is that these models map a reduced-form conditional choice probability to an identified set. Consequently, nonparametric Bayesian inference for the conditional probability mass function leads to Bayesian inference for the identified set. The inference framework nests conditional moment inequalities and linear systems with unknown coefficients as special cases. Importantly, our proposal does not require converting conditional moments into unconditional moments or discretizing covariates. We show that the posterior is consistent for the true identified set when the model is correctly specified, show that the posterior can consistently detect model misspecification, and show posterior consistency for a pseudo-identified set that is valid under misspecification. We also verify the assumptions for a class of priors based on Gaussian processes that we use to implement our proposal. These priors offer similar flexibility to frequentist partial identification methods, and are computationally attractive because posterior sampling can be performed in closed-form. We also show that many of the ideas in this paper extend to continuous responses and aggregated discrete responses (e.g., market shares). |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.25814 |
| By: | Ayla Jungbluth (Ruhr-University Bochum); Johannes Lederer (University of Hamburg); Simon Trimborn (University of Amsterdam) |
| Abstract: | Modeling the joint distribution of extreme values in high-dimensional financial time series is challenging because extremes are sparse and locally extreme observations are not necessarily extreme relative to their full marginal distribution. To address this, we introduce a time-dependent network Hüsler-Reiss model in which market-informed adjacency matrices determine how strongly observations contribute to the estimation. We propose binary and weighted specifications, including the Joint Extremes Adjacency Matrix (JEAM) which combines information about individual extremeness with historical patterns of joint extreme movements. In the forecasting evaluation part, covering one-minute stock returns from three sectors of the S&P 100, JEAM achieves the best out-of-sample log scores for both tail directions; improving scores by 12.5-13.6% in the lower tail and 11.4-14.9% in the upper tail. The results show that incorporating market-informed network structures in the estimation, improves forecast evaluation of extremes across time series. |
| JEL: | C53 C58 G17 |
| Date: | 2026–09–13 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260070 |
| By: | Kaicheng Chen; Antonio F. Galvao; Seunghwa Rho; Timothy J. Vogelsang; Jungmo Yoon |
| Abstract: | This paper develops fixed-smoothing (fixed-b, fixed-K) inference methods for time-series quantile regression that are robust to heteroskedasticity and autocorrelation. Our approach is uniformly valid over quantile levels and accounts for dependence both over time and across quantiles. It enables the construction of uniform confidence bands, Wald, and Sup-t tests for joint hypotheses, and tests of shape restrictions, providing a unified framework for assessing heterogeneity in quantile effects. A key challenge is that, under weak dependence, uniform inference for quantile regression processes is generally non-pivotal because the limiting distributions depend on the long-run covariance structure across quantiles. To address this issue, we develop two complementary approaches. The uniform-in-$\tau$ method estimates the covariance structure and simulates the non-pivotal limiting distribution. For certain tests involving a finite collection of quantile levels, the stack-Wald method delivers pivotal fixed-smoothing inference. We establish the asymptotic validity of both approaches. Simulation results show that the proposed methods substantially improve size control relative to existing HAC-based procedures while maintaining good power. An application to predictive quantile regressions for stock returns reveals substantial heterogeneity in predictive effects across both quantiles and forecast horizons. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.05883 |
| By: | Alex Bernstein; Lisa R. Goldberg; Nicholas Gunther; Alec N. Kercheval; Tian Lan; Yian Lin; Dayi Yao |
| Abstract: | In a statistical factor model, principal components (or eigenvectors) of a sample covariance matrix serve as estimates of {\it principal directions}, the true drivers of co-movement of a collection of observed variables. We write the often substantial error in these estimates as a sum of two interpretable terms, which we show have almost sure asymptotic limits as the number of variables grows with sample size bounded. This scenario is commonplace in financial economics, genomics, machine learning and signal processing. {\it Out-of-subspace error} measures the distance from an estimate to the subspace spanned by population factor exposures. It can be expressed in terms of data, providing an estimable floor for error. {\it In-subspace error} arises from the fixed sample size of the latent factor returns and cannot be estimated from data alone. We illustrate our error analysis with a three-factor simulation of the US public equity market, showing the dependence of the magnitude of the error and its components on dimension and sample size. In that simulation, out-of-subspace error dominates. Researchers who rely on principal component analysis to estimate factor models can use our results to quantify errors in model-based predictions and attributions. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.20550 |
| By: | Othmane Zarhali; Emmanuel Bacry; Jean-Fran\c{c}ois Muzy |
| Abstract: | The Log S-fBM model, introduced by Wu et al., is a stochastic volatility model whose log volatility is a stationary fractional Brownian motion (S-fBM): a stationary Gaussian process with power-decaying autocovariance driven by the Hurst exponent $H$, and variance scaled by an intermittency coefficient. A key property is that it reconciles rough volatility, where $H$ is typically near $0.1$ (see Gatheral et al.), with multifractal volatility, where $H$ is close to $0$ as in Bacry, Muzy et al.: the model's volatility measure converges to a multifractal random measure as $H\to0$. Numerical findings in Wu et al. show intermittency of order $0.02$ across financial assets, motivating a small intermittency approximation of log volatility moments for calibration via the general method of moments (GMM). In this work, we conduct a statistical analysis of the Log S-fBM model. We derive scaling properties of the S-fBM process and the Log S-fBM integrated volatility measure, present deviation inequalities with tail distributions sensitive to $H$ and intermittency, and develop a hypothesis test for the null Hurst exponent, i.e.\ rough versus multifractal dynamics. Finally, we revisit scale invariance of the log volatility increment process via explicit small-intermittency formulas, reproducing analogous properties in both regimes. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.09405 |
| By: | Kit Baum (Boston College); Jesus Otero (Universidad del Rosario) |
| Abstract: | We present the community-contributed blockboot command to bootstrap time-dependent stationary processes using four schemes that preserve the processes' dependence structure by resampling blocks of observations. These schemes include the nonoverlapping block bootstrap of Carlstein (1986, Annals of Statistics, 14: 1171–1179); the moving block bootstrap of Kunsch (1989, Annals of Statistics, 17: 1217–1241) and Liu and Singh (1992, Exploring the Limits of Bootstrap, ed. LePage and Billard: Wiley); the circular block bootstrap of Politis and Romano (1992, Exploring the Limits of Bootstrap); and the stationary block bootstrap of Politis and Romano (1994, Journal of the American Statistical Association, 89: 1303–1313). An illustration of these four block bootstrap schemes for time-series data in the context of computing the size of unit-root tests extends and updates the findings of Schwert, ”Tests for Unit Roots: A Monte Carlo Investigation“ (1989, Journal of Business and Economic Statistics, 7: 147–159). We find that the results are most sensitive to the choice of block length, which can be specified in the command or computed automatically. |
| Date: | 2026–09–05 |
| URL: | https://d.repec.org/n?u=RePEc:boc:lsug26:02 |
| By: | Matthew Read |
| Abstract: | Sign restrictions on the slopes of supply and demand curves are often used to identify historical decompositions in structural vector autoregressions. I show that the identifying power of these restrictions depends on both reduced-form parameters and realised forecast errors. Consequently, unlike many other structural objects, the strength of identification cannot be assessed from reduced-form parameters alone. Empirically, identified sets for historical decompositions of US inflation are typically largely uninformative, both in aggregate and in most expenditure categories. Existing inflation decompositions are therefore sensitive to auxiliary assumptions used to select among observationally equivalent models. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.06907 |
| By: | Ramzi Jebali |
| Abstract: | Financial markets alternate between periods of relative stability and instability, with structural breaks marking the transitions between these regimes. Identifying such breaks in real time is a central requirement for any trading or risk system operating at high frequency. This report studies Bayesian Online Changepoint Detection (BOCPD) and two extensions proposed in the literature, and applies them to the signed order flow of NASDAQ-listed equities. |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2609.07989 |