|
on Econometric Time Series |
|
Issue of 2026–09–07
sixteen papers chosen by Simon Sosvilla-Rivero, Instituto Complutense de Análisis Económico |
| By: | Fei Shang; Xiaolei Wang; Tomasz Wo\'zniak |
| Abstract: | We present a suite of R packages for macroeconomic forecasting that leverages advanced Bayesian, structural, multivariate, dynamic, hierarchical, non-linear, and non-Gaussian models. The suite enables both structural and predictive analyses, and is adapted to time series data across various types, dimensions, and sampling frequencies. Each additional feature increases computational complexity. To address this challenge, our software design incorporates a carefully curated selection of models, efficient algorithms implemented in C++, advanced econometric and numerical methods, robust handling of complex input and output objects, and standardised workflows. This approach combines the computational efficiency of C++ with the convenience of working with data in R. We demonstrate that our packages facilitate original research contributions in forecasting, as illustrated by our example in which vector autoregressions with non-centred stochastic volatility enhance density and point predictions relative to models with centred stochastic volatility. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.28087 |
| By: | Justus Holman (Vrije Universiteit Amsterdam); Andre Lucas (Vrije Universiteit Amsterdam); Anne Opschoor (Vrije Universiteit Amsterdam) |
| Abstract: | We propose a new model for realized covariance matrix dynamics using a composite of univariate time series models for its realized eigenvalues, linked by a copula function. The dynamics of each eigenvalue are based on a conditional F distribution, thus allowing for fat-tailedness and outliers in the realized covariance matrices. Given its composition from univariate elements, the static parameters of the new model can be estimated efficiently by maximum likelihood. In an empirical application, we show that the new model outperforms relevant recent benchmarks in an extensive portfolio (Conditional) Volatility-at-Risk (VolaR) application. |
| JEL: | C22 C32 C58 |
| Date: | 2026–08–28 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260061 |
| By: | Niko Hauzenberger; Michael Pfarrhofer |
| Abstract: | We develop fast methods for conditional forecasting and structural scenario analysis with high-dimensional Bayesian vector autoregressions (VARs). Our general framework features a factor structure on the reduced-form errors, which enables fast and order-invariant equation-by-equation estimation; suitably identified factors admit a structural interpretation. The scenarios are defined through separate distributional restrictions on observables, structural shocks and idiosyncratic components. The computational cost of our proposed algorithm is cubic only in the number of restrictions, while the dimension of the forecasted system enters linearly. In our application with $33$ macroeconomic and financial variables and ten set-identified structural shocks for the US, we compute counterfactual predictions for oil price scenarios in the context of the 2026 closure of the Strait of Hormuz. The same oil price path is consistent with outcomes ranging from a mostly benign episode to pronounced stagflation, depending on which structural and idiosyncratic shocks are allowed to deliver it. |
| Date: | 2026–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2607.29215 |
| By: | Pedro Isaac Chavez-Lopez (Bank of Mexico); Tae-Hwy Lee (Department of Economics, University of California Riverside) |
| Abstract: | We develop the Quantile-Covariance Three-Pass Regression Filter (Qcov3PRF), a supervised factor model for quantile regression that exploits quantile-covariance (qcov). This method extracts latent factors from a high-dimensional set of predictors to forecast conditional quantiles of a response variable. Unlike Partial Quantile Regression (PQR), Qcov3PRF identifies multiple relevant factors for the target conditional quantiles by qcov. We establish that the resulting forecasts are consistent and asymptotically normal as both the time-series and cross-sectional dimensions diverge. Monte Carlo evidence supports the theoretical results and indicates favorable finite-sample performance. An empirical application to Growth-at-Risk forecasting further demonstrates the advantages of Qcov3PRF over competing alternatives. |
| Keywords: | Factor models; quantile-covariance; quantile regression; Qcov3PRF; PQR; Growth-at-Risk |
| JEL: | C13 C22 C53 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:ucr:wpaper:202605 |
| By: | Justus Holman (Vrije Universiteit Amsterdam); Yicong Lin (Vrije Universiteit Amsterdam); Andre Lucas (Vrije Universiteit Amsterdam); Anne Opschoor (Vrije Universiteit Amsterdam) |
| Abstract: | We introduce the Dynamic Spectral Rotation (DSR) model, allowing for dynamics in both eigenvalues and eigenvectors of time-varying conditional covariance matrices. The construction preserves orthonormality of the entire eigenvector matrix at every point in time. We study the model’s asymptotic properties and establish unique identification of all static parameters governing the joint dynamics of eigenvalues and eigenvectors. Notably, the parameters that determine the dynamic rotation angles remain uniquely identified under mild conditions even when the rotation angles are allowed to evolve over ranges far beyond intervals of length π. In an empirical application to US equity returns, we show that allowing the leading eigendirection of the covariance matrix to vary over time significantly improves the predicted portfolio covariance structure compared to a model in which all eigendirections are held fixed. |
| JEL: | C32 C53 C58 |
| Date: | 2026–08–28 |
| URL: | https://d.repec.org/n?u=RePEc:tin:wpaper:20260060 |
| By: | Drautzburg, Thorsten; Fernández-Villaverde, Jesús; Guerron, Pablo; Oosthuizen, Dick |
| Abstract: | We propose a new tool to filter non-linear dynamic models that does not require the researcher to specify the model fully and can be implemented without solving the model. If two conditions are satisfied, we can use a flexible statistical model and a known measurement equation to back out the hidden states of the dynamic model. The first condition is that the state is sufficiently volatile or persistent to be recoverable. The second condition requires the possibly non-linear measurement to be sufficiently smooth and to map uniquely to the state absent measurement error. We illustrate the method through various simulation studies and an empirical application to a sudden stops model applied to Mexican data. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:cpr:ceprdp:19270 |
| By: | Savi Virolainen |
| Abstract: | We develop a fully nonlinear structural vector autoregressive framework in which the contemporaneous structural mapping may be nonlinear and non-additive. Identification is achieved by exploiting variation in the conditional distributions of the mutually independent structural shocks induced by an observed exogenous variable. Specifically, a general contrastive learning framework that makes use of this variation together with the assumed exponential-family structure is employed to recover the shocks. Existing independent innovation analysis results identify such shocks only up to arbitrary componentwise invertible transformations, which is generally insufficient for structural econometric analysis. We strengthen this result by imposing a structured exponential-family specification for the conditional shock distributions. With the imposed sufficient statistics, the remaining ambiguity is reduced to a one-parameter transformed-scale map for each shock. We then show that, under a logistic specification used for the natural parameters, the identification is further strengthened up to permutation and componentwise sign changes. Once the shocks have been recovered, the fully nonlinear structural vector autoregression can be estimated using feed-forward neural networks, motivated by their universal approximation capabilities. The empirical application studies asymmetries in the responses of U.S. industrial production to the real oil price shock. We find modest asymmetries with respect to the sign of the shock and state of the economy. The accompanying R package iiasvar implements the introduced methods. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.03486 |
| By: | Joshua Elias Fred A. Suero (Bangko Sentral ng Pilipinas) |
| Abstract: | The pursuit of accurate forecasting and the rise of machine learning have led to the development of various forecasting models, making model selection increasingly difficult. This paper aims to address this challenge by developing a standard strategy for time series forecasting using a meta-model approach. A meta-model is constructed by combining individual forecasts from leading statistical and machine learning models, with Philippine external debt as the target variable. The baseline meta-model combines the following individual forecasts using ordinary least squares (OLS): (a) random walk with drift, (b) autoregressive integrated moving average (ARIMA), (c) exponential smoothing with error, trend, and seasonal components (ETS), (d) Holt-Winters, (e) multiple aggregation prediction algorithm (MAPA), (f) temporal hierarchical forecasting (THieF), (g) theta model, (h) Prophet, (i) neural network autoregression (NNAR), (j) long short-term memory (LSTM), (k) gradient boosting machine (GBM), (l) extreme gradient boosting (XGBoost), (m) random forest, (n) support vector regression (SVR), and (o) dynamic linear models (DLM). Alternative meta-models were also evaluated. The best-performing meta-model, which employs the Least Absolute Shrinkage and Selection Operator (LASSO), performs remarkably well, achieving a mean absolute percentage error (MAPE) of 3.0 percent in the validation set. The proposed standard strategy is versatile, with the potential to forecast other financial and economic variables. Additionally, forecasts generated by the meta-model can serve as a valuable benchmark, whether compared to current forecasting practices or in cases where no forecasting methodology exists. |
| JEL: | C22 C53 C61 F34 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:bhd:dpaper:202503 |
| By: | Frederik Bjerg Krabbe |
| Abstract: | In this paper, we study causal non-causal state space models to model time series characterised by a local explosive increase followed by a sharp decrease such as stock prices. To motivate the use of causal non-causal state space models, we show that the causal non-causal convolution autoregressive model introduced by Gourieroux and Zakoian (2017) can be consistent with the rational expectations stock price model. As in a causal state space model, a central question is how to perform state and parameter inference in the causal non-causal state space model, which we discuss in the paper. We also study the causal non-causal convolution autoregressive model in more detail, providing some new results for the model. To illustrate the usefulness of causal non-causal state space models, we use the causal non-causal convolution autoregressive model to estimate the size of the dot-com bubble in both real time and a posteriori with the stable non-causal autoregressive model considered also by Gourieroux and Zakoian (2017) as a benchmark. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.28115 |
| By: | Davide Brignone (Bank of England); Michele Piffer (Bank of England) |
| Abstract: | This paper shows how the structural representation of a vector autoregressive (VAR) model can support forecast analysis. We offer a unified framework that formalises how the structural form of the model can help form a narrative for two key statistics in real-time VAR forecasting: the forecast errors relative to the outturn of the data, and the consequent revisions of the forecast. To illustrate the method developed, we conduct a stylised real-time exercise on the UK, focusing on the inflation surge that followed the pandemic. We show that the inflation forecast produced by a four-variable VAR model was revised upwards not only due to contractionary supply-side shocks, but also due to a mix of expansionary demand-side shocks, and a revision in the past shocks. |
| Keywords: | VAR modelling;forecasting;structural shocks;decomposition |
| JEL: | C32 E52 |
| Date: | 2026–01–09 |
| URL: | https://d.repec.org/n?u=RePEc:boe:boeewp:023287 |
| By: | Eoghan O'Neill (University College Dublin); Sofia Velasco (Banco de España) |
| Abstract: | The question of how oil supply news shocks transmit to real activity, financial conditions and regional labor markets is back at the center of the macroeconomic research agenda. To answer this question, we introduce the Factor Bayesian Additive Regression Tree (FABART) model, a nonlinear factor-augmented vector autoregression model, and apply it to a large U.S. macro-financial dataset with externally identified oil supply news shocks. The framework incorporates a flexible nonparametric measurement equation that allows nonlinear transmission to emerge from the data without imposing a specific functional form on the asymmetry. We find that adverse oil supply news shocks generate stronger and more persistent contractions in real activity than the expansions associated with favorable shocks of comparable magnitude, with especially pronounced differences in industrial production, interest rates and equity prices. Employment responses are highly heterogeneous across U.S. states, with substantially stronger contractions in manufacturing-intensive regions than in energy-producing states. Across shock magnitudes, nonlinearities arise mainly between very small and moderate oil-price movements: small shocks generate weak and imprecisely estimated responses, while even moderate shocks produce economically meaningful effects on industrial production and regional employment. Larger shocks, however, do not systematically generate proportionally stronger responses across variables and shock signs. |
| Keywords: | Bayesian FAVAR, nonlinear models, non-parametric techniques, oil price shocks, factor models |
| JEL: | C11 C32 E32 Q43 |
| Date: | 2026–09 |
| URL: | https://d.repec.org/n?u=RePEc:bde:wpaper:2627 |
| By: | Guilherme Vianna |
| Abstract: | Recursive nonlinear impulse responses require an estimated innovation law whenever the impact shock is normalized by innovation ranks and future innovations are integrated out. The closest semiparametric recursive construction in the literature estimates the relevant innovation quantile functions smoothly and discusses a direct empirical-residual implementation without developing its complete first-order inference theory. We tackle this gap in a finite-dimensional nonlinear structural autoregression with unrestricted continuous marginal innovation distributions and a fixed normal-rank shock. Our estimator replaces each innovation quantile function with the empirical quantile of generated structural residuals and iterates the same structural transition. For any fixed collection of responses, we establish a joint \sqrt{T} asymptotic linear representation with four components: direct transition estimation, the effect of transition estimation on residual order statistics, ordinary innovation-quantile estimation, and the shifted impact quantile. After projection through the recursion, the quantile terms admit a residual-rank-and-spacing representation, yielding feasible inference without innovation-density estimation or quantile smoothing. We then characterize the propagated bias from smoothing, establish validity of a full recursive residual bootstrap, and derive the additional covariance contribution from a finite number of simulated paths, providing bandwidth-free inference for the empirical-residual version of the same normal-rank response used in the smooth recursive construction. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.02943 |
| By: | Joshua C. C. Chan |
| Abstract: | Rejection sampling requires a proposal that dominates the target by a known constant, generally unavailable for non-Gaussian state space models. We construct such a proposal for the latent state path, yielding independent exact smoothing draws and an unbiased likelihood estimator whose relative variance is at most $1/p-1$ per draw at acceptance probability $p$. The method covers scalar states with affine Gaussian dynamics and log-concave observation densities, including multivariate observations. Transition twisting makes the log target-to-proposal ratio separable, and tangent-line twists make each term nonpositive, producing an attained, sharp dominating constant. With a companding node placement, the accumulated envelope error is $O(T/G^2)$ for a sample of length $T$ with $G$ nodes per date, so $G\propto\sqrt{T}$ keeps acceptance bounded away from zero; for stochastic volatility, the required conditions hold almost surely. A simpler mode-centered grid shows the same scaling empirically. At $T=2{, }000$, acceptance is $75\%$, versus roughly $10^{-16}$ for the Gaussian envelope. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.21619 |
| By: | Marko Mlikota |
| Abstract: | I consider an AR($p$) process that is observed every $q$ periods, either as a snapshot (stock variable) or as a sum over the sampling interval (flow variable). Under fairly mild assumptions, I derive the identified set for general lag lengths $p \in \mathbb{N}$ and sampling frequencies $q \in \mathbb{N}$, I bound its cardinality, and I provide a recipe to compute all candidate points and determine their membership in the identified set. My analysis supports the following conjecture: (i) the error term-variance is point-identified, (ii) under temporal aggregation, the autoregressive parameters are point-identified, and (iii) under discrete sampling they are point-identified for odd sampling frequencies and identified up to alternating sign for even sampling frequencies. I prove this conjecture in some settings and verify it numerically more broadly. |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2608.13224 |
| By: | Michael Dueker; Inés Kishkill; Martín Sola |
| Abstract: | We study the extraction of a common European business cycle from quarterly GDP growth when countries need not provide equally informative signals about the contemporaneous common regime. We show that the usual signal-extraction argument for enlarging a cross section can fail when country-specific regime behavior is imperfectly aligned: additional observations may then weaken rather than strengthen common-state identification. Motivated by this result, we develop a Markov-switching Seemingly Unrelated Regressions (MS–SUR) model with an endogenous positive-definite crosssectional weighting structure. The model distinguishes the informational influence of each economy in identifying the common regime from the strength of its cross-sectional commonality. A separate Markov process governs the innovation covariance matrix, allowing changes in the volatility environment to be separated from the weighting mechanism. Empirically, alternative treatments of the cross section generate materially different common-cycle signals, with the largest differences arising during periods of pronounced cross-country heterogeneity. The endogenous specification assigns approximately 95 percent of the posterior informational weight to Germany and the Netherlands, while the estimated commonality loadings produce a substantially different cross-country ranking. These results show that common-regime inference depends not only on the amount of cross-sectional information available, but also on which observations are most informative about the latent state. |
| Keywords: | EuropeanBusiness Cycle, Markov switching, Endogenous weighting, Bayesian estimation. |
| JEL: | C11 C32 E32 |
| Date: | 2026–08 |
| URL: | https://d.repec.org/n?u=RePEc:udt:wpecon:2026_05 |
| By: | Jeremy Bejarano; Viren Desai; Kausthub Keshava; Arsh Kumar; Zixiao Wang; Vincent Hanyang Xu; Yangge Xu |
| Abstract: | An open benchmark that holds financial data fixed across forecasting methods, revealing where machine learning sharpens forecasts of financial stress (Working Paper no. 26-05). |
| Date: | 2026–08–25 |
| URL: | https://d.repec.org/n?u=RePEc:ofr:wpaper:26-05 |