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on Econometric Time Series |
| By: | Castellanos, Juan (Bank of England) |
| Abstract: | This paper conducts a Monte Carlo study to examine the small sample performance of impulse response (IRF) matching and Indirect Inference estimators that target IRFs that have been estimated with Local Projections (LP) or Vector Autoregressions (VAR). The analysis considers various identification schemes for the shocks and several variants of LP and VAR estimators. Results show that the lower bias from LP responses is a big advantage when it comes to IRF matching, while the lower variance from VAR is desirable for Indirect Inference applications as it is robust to the higher bias of VAR-IRFs. Overall, I recommend the use of Indirect Inference over IRF matching when estimating Dynamic Stochastic General Equilibrium (DSGE) models as the former is robust to potential misspecification coming from invalid identification assumptions, small sample issues or incorrect lag selection. |
| Keywords: | DSGE estimation; impulse responses; Indirect Inference; Local Projection; Vector Autoregression; Monte Carlo analysis |
| JEL: | C13 C15 E00 |
| Date: | 2025–02–14 |
| URL: | https://d.repec.org/n?u=RePEc:boe:boeewp:1116 |
| By: | Jingyi Wei; Steve Yang; Zhenyu Cui |
| Abstract: | In this study, we propose a novel integrated Generalized Autoregressive Conditional Heteroskedasticity-Gated Recurrent Unit (GARCH-GRU) model for financial volatility modeling and forecasting. The model embeds the GARCH(1, 1) formulation directly into the GRU cell architecture, yielding a unified recurrent unit that jointly captures both traditional econometric properties and complex temporal dynamics. This hybrid structure leverages the strengths of GARCH in modeling key stylized facts of financial volatility, such as clustering and persistence, while utilizing the GRU's capacity to learn nonlinear dependencies from sequential data. Compared to the GARCH-LSTM counterpart, the GARCH-GRU model demonstrates superior computational efficiency, requiring significantly less training time, while maintaining and improving forecasting accuracy. Empirical evaluation across multiple financial datasets confirms the model's robust outperformance in terms of mean squared error (MSE) and mean absolute error (MAE) relative to a range of benchmarks, including standard neural networks, alternative hybrid architectures, and classical GARCH-type models. As an application, we compute Value-at-Risk (VaR) using the model's volatility forecasts and observe lower violation ratios, further validating the predictive reliability of the proposed framework in practical risk management settings. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.09380 |
| By: | Matthew Read (Reserve Bank of Australia); Dan Zhu (Department of Econometrics and Business Statistics, Monash University) |
| Abstract: | We propose algorithms for conducting Bayesian inference in structural vector autoregressions identified using sign restrictions. The key feature of our approach is a sampling step based on 'soft' sign restrictions. This step draws from a target density that smoothly penalises parameter values violating the restrictions, facilitating the use of computationally efficient Markov chain Monte Carlo sampling algorithms. An importance-sampling step yields draws from the desired distribution conditional on the 'hard' sign restrictions. Relative to standard accept-reject sampling, the method substantially improves computational efficiency when identification is 'tight'. It can also greatly reduce the computational burden of implementing prior-robust Bayesian methods. We illustrate the broad applicability of the approach in a model of the global oil market identified using a rich set of sign, elasticity and narrative restrictions. |
| Keywords: | Bayesian inference; Markov chain Monte Carlo; oil market; sign restrictions; structural vector autoregression |
| JEL: | C32 Q35 Q43 |
| Date: | 2025–05 |
| URL: | https://d.repec.org/n?u=RePEc:rba:rbardp:rdp2025-03 |
| By: | Jungbin Hwang (University of Connecticut); Gonzalo Valdés (Universidad de Tarapacá) |
| Abstract: | This paper develops robust inference for conditional quantile regression (QR) under unknown forms of weak dependence in time series data. We rst establish xed-smoothing asymptotic theory for QR by showing that the long-run variance (LRV) estimator for the non-smooth QR score process weakly converges to a random matrix scaled by the true LRV. Additionally, QR-Wald statistics based on the kernel LRV estimator converge to non-standard limits, while using orthonormal series LRV estimators yields standard F and t limits. For the practical implementation of our new asymptotic theory for Wald and t inference in QR, we extend heteroskedasticity and autocorrelation robust (HAR) inference for conditional mean regression to QR and apply the optimal smoothing parameter selection rule based on the Neyman-Pearson principle. Monte Carlo simulation results show that our QR-HAR procedure reduces size distortions of the HAR inference based on the conditional mean regression and the QR-HAC inference particularly in scenarios with moderate sample sizes, strong temporal dependence, and multiple parameters in the joint null hypothesis. |
| Keywords: | Quantile regression, heteroskedasticity and autocorrelation robust, long-run variance, alter-native asymptotics, testing-optimal smoothing parameter choice |
| JEL: | C12 C19 C22 C32 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:uct:uconnp:2025-03 |
| By: | Alessandro Morico; Ovidijus Stauskas |
| Abstract: | We present four novel tests of equal predictive accuracy and encompassing for out-of-sample forecasts based on factor-augmented regression. We extend the work of Pitarakis (2023a, b) to develop the inferential theory of predictive regressions with generated regressors which are estimated by using Common Correlated Effects (henceforth CCE) - a technique that utilizes cross-sectional averages of grouped series. It is particularly useful since large datasets of such structure are becoming increasingly popular. Under our framework, CCE-based tests are asymptotically normal and robust to overspecification of the number of factors, which is in stark contrast to existing methodologies in the CCE context. Our tests are highly applicable in practice as they accommodate for different predictor types (e.g., stationary and highly persistent factors), and remain invariant to the location of structural breaks in loadings. Extensive Monte Carlo simulations indicate that our tests exhibit excellent local power properties. Finally, we apply our tests to a novel EA-MD-QD dataset by Barigozzi et al. (2024b), which covers Euro Area as a whole and primary member countries. We demonstrate that CCE factors offer a substantial predictive power even under varying data persistence and structural breaks. |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2504.08455 |
| By: | Uwe Hassler; Marc-Oliver Pohle; Tanja Zahn |
| Abstract: | Sample autocorrelograms typically come with significance bands (non-rejection regions) for the null hypothesis of temporal independence. These bands have two shortcomings. First, they build on pointwise intervals and suffer from joint undercoverage (overrejection) under the null hypothesis. Second, if this null is clearly violated one would rather prefer to see confidence bands to quantify estimation uncertainty. We propose and discuss both simultaneous significance bands and simultaneous confidence bands for time series and series of regression residuals. They are as easy to construct as their pointwise counterparts and at the same time provide an intuitive and visual quantification of sampling uncertainty as well as valid statistical inference. For regression residuals, we show that for static regressions the asymptotic variances underlying the construction of the bands are as for observed time series and for dynamic regressions (with lagged endogenous regressors) we show how they need to be adjusted. We study theoretical properties of simultaneous significance bands and two types of simultaneous confidence bands (sup-t and Bonferroni) and analyse their finite-sample performance in a simulation study. Finally, we illustrate the use of the bands in an application to monthly US inflation and residuals from Phillips curve regressions. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.18560 |
| By: | Monica Billio; Roberto Casarin; Fausto Corradin; Antonio Peruzzi |
| Abstract: | Bayes Factor (BF) is one of the tools used in Bayesian analysis for model selection. The predictive BF finds application in detecting outliers, which are relevant sources of estimation and forecast errors. An efficient framework for outlier detection is provided and purposely designed for large multidimensional datasets. Online detection and analytical tractability guarantee the procedure's efficiency. The proposed sequential Bayesian monitoring extends the univariate setup to a matrix--variate one. Prior perturbation based on power discounting is applied to obtain tractable predictive BFs. This way, computationally intensive procedures used in Bayesian Analysis are not required. The conditions leading to inconclusive responses in outlier identification are derived, and some robust approaches are proposed that exploit the predictive BF's variability to improve the standard discounting method. The effectiveness of the procedure is studied using simulated data. An illustration is provided through applications to relevant benchmark datasets from macroeconomics and finance. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.19515 |
| By: | Masahiro Tanaka |
| Abstract: | While local projections (LPs) are widely used for impulse response analysis, existing Bayesian approaches face fundamental challenges because a set of LPs does not constitute a likelihood function. Prior studies address this issue by constructing a pseudo-likelihood, either by treating LPs as a system of seemingly unrelated regressions with a multivariate normal error structure or by applying a quasi-Bayesian approach with a sandwich estimator. However, these methods lead to posterior distributions that are not "well calibrated, " preventing proper Bayesian belief updates and complicating the interpretation of posterior distributions. To resolve these issues, we propose a novel quasi-Bayesian approach for inferring LPs using the Laplace-type estimator. Specifically, we construct a quasi-likelihood based on a generalized method of moments criterion, which avoids restrictive distributional assumptions and provides well-calibrated inferences. The proposed framework enables the estimation of simultaneous credible bands and naturally extends to LPs with an instrumental variable, offering the first Bayesian treatment of this method. Furthermore, we introduce two posterior simulators capable of handling the high-dimensional parameter space of LPs with the Laplace-type estimator. We demonstrate the effectiveness of our approach through extensive Monte Carlo simulations and an empirical application to U.S. monetary policy. |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2503.20249 |