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on Econometric Time Series |
| By: | Leo Krippner |
| Abstract: | The eigenvalue/eigenvector structure underlying a standard N-variable P -lag vector autoregression (VAR) may be transformed into a system of NP scalar AR1 processes, each with an eigenvalue as its coefficient. This perspective allows a VAR to be assessed, analyzed, and manipulated using the mathematical and statistical convenience of elementary AR1 processes. Illustrative empirical applications demonstrate the inherent benefits: (1) the persistence of a VAR’s dynamics is interpreted from its AR1 processes; (2) closed-form VAR forecasts are obtained from AR1 forecasts; (3) equality or zero constraints on selected AR1 coefficients are tested and imposed for VAR parsimony; (4) a median-unbiased estimate of the largest AR1 coefficient is generated and imposed to produce a more persistent VAR; (5) a unit root for the largest AR1 coefficient is tested and imposed to produce a cointegrated VAR, which also produces an estimate of the associated cointegrating vector. |
| Keywords: | vector autoregression, VAR, companion matrix, eigenvalues, eigenvectors |
| JEL: | C13 C32 C53 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:een:camaaa:2024-71 |
| By: | Mohammad R. Jahan-Parvar; Charles Knipp; Pawel J. Szerszen |
| Abstract: | We propose a generalized multivariate unobserved components model to decompose macroeconomic data into trend and cyclical components. We then forecast the series using Bayesian methods. We document that a fully Bayesian estimation, that accounts for state and parameter uncertainty, consistently dominates out-of-sample forecasts produced by alternative multivariate and univariate models. In addition, allowing for stochastic volatility components in variables improves forecasts. To address data limitations, we exploit cross-sectional information, use the commonalities across variables, and account for both parameter and state uncertainty. Finally, we find that an optimally pooled univariate model outperforms individual univariate specifications, andperforms generally closer to the benchmark model. |
| Keywords: | Bayesian estimation; Maximum likelihood estimation; Online forecasting; Out-of-sample forecasting; Parameter uncertainty; Sequential Monte Carlo methods; Trend-cycle decomposition |
| JEL: | C11 C22 C32 C53 |
| Date: | 2024–12–30 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedgfe:2024-100 |
| By: | Silvia Goncalves; Ana María Herrera; Lutz Kilian; Elena Pesavento |
| Abstract: | Nonlinearities play an increasingly important role in applied work when studying the responses of macroeconomic aggregates to policy shocks. Seemingly natural adaptations of the popular local linear projection estimator to nonlinear settings may fail to recover the population responses of interest. In this paper we study the properties of an alternative nonparametric local projection estimator of the conditional and unconditional responses of an outcome variable to an observed identified shock. We discuss alternative ways of implementing this estimator and how to allow for data-dependent tuning parameters. Our results are based on data generating processes that involve, respectively, nonlinearly transformed regressors, state-dependent coefficients and nonlinear interactions between shocks and state variables. Monte Carlo simulations show that a local-linear specification of the estimator tends to work well in reasonably large samples and is robust to nonlinearities of unknown form. |
| Keywords: | impulse response; Local Projection; nonparametric estimation; nonlinear structural model; potential outcomes |
| JEL: | C14 C32 E52 |
| Date: | 2024–11–20 |
| URL: | https://d.repec.org/n?u=RePEc:fip:feddwp:99177 |
| By: | Matias Quiroz (University of Technology Sydney, Australia); Laleh Tafakori (RMIT University, Australia); Hans Manner (University of Graz, Austria) |
| Abstract: | We investigate methods for forecasting multivariate realized covariances matrices applied to a set of 30 assets that were included in the DJ30 index at some point, including two novel methods that use existing (univariate) log of realized variance models that account for attenuation bias and time-varying parameters. We consider the implications of some modeling choices within the class of heterogeneous autoregressive models. The following are our key findings. First, modeling the logs of the marginal volatilities is strongly preferred over direct modeling of marginal volatility. Thus, our proposed model that accounts for attenuation bias (for the log-response) provides superior one-step-ahead forecasts over existing multivariate realized covariance approaches. Second, accounting for measurement errors in marginal realized variances generally improves multivariate forecasting performance, but to a lesser degree than previously found in the literature. Third, time-varying parameter models based on state-space models perform almost equally well. Fourth, statistical and economic criteria for comparing the forecasting performance lead to some differences in the model's rankings, which can partially be explained by the turbulent post-pandemic data in our out-of-sample validation dataset using sub-sample analyses. |
| Keywords: | State space model, Heterogeneous autoregressive, Realized measures, Volatility forecasting. |
| JEL: | C51 C53 G17 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:grz:wpaper:2024-20 |
| By: | Faria, Gonçalo; Verona, Fabio |
| Abstract: | This paper explores the out-of-sample forecasting performance of 25 equity premium predictors over a sample period from 1973 to 2023. While conventional time-series methods reveal that only one predictor demonstrates significant out-of-sample predictive power, frequency-domain analysis uncovers additional predictive information hidden in the time series. Nearly half of the predictors exhibit statistically and economically meaningful predictive performance when decomposed into frequency components. The findings suggest that frequency-domain techniques can extract valuable insights that are often missed by traditional methods, enhancing the accuracy of equity premium forecasts. |
| Keywords: | equity premium, predictability, frequency domain |
| JEL: | C58 G11 G17 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:bofrdp:306348 |
| By: | Aßmann, Christian; Boysen-Hogrefe, Jens; Pape, Markus |
| Abstract: | Orthonormality constraints are common in reduced rank models. They imply that matrix-variate parameters are given as orthonormal column vectors. However, these orthonormality restrictions do not provide identification for all parameters. For this setup, we show how the remaining identification issue can be handled in a Bayesian analysis via post-processing the sampling output according to an appropriately specified loss function. This extends the possibilities for Bayesian inference in reduced rank regression models with a part of the parameter space restricted to the Stiefel manifold. Besides inference, we also discuss model selection in terms of posterior predictive assessment. We illustrate the proposed approach with a simulation study and an empirical application. |
| Keywords: | Bayesian estimation, Post-processing, Reduced rank regression, Orthogonal transformation, Model selection, Stiefel manifold, Posterior predictive assessment |
| JEL: | C11 C31 C51 C52 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:ifwkie:306605 |
| By: | Xu, Yongdeng (Cardiff Business School) |
| Abstract: | This paper introduces an extended multivariate EGARCH model that overcomes the zero-return problem and allows for negative news and volatility spillover effects, making it an attractive tool for multivariate volatility modeling. Despite limitations, such as noninvertibility and unclear asymptotic properties of the QML estimator, our Monte Carlo simulations indicate that the standard QML estimator is consistent and asymptotically normal for larger sample sizes (i.e., T ≥ 2500). Two empirical examples demonstrate the model’s superior performance compared to multivariate GJR-GARCH and Log-GARCH models in volatility modeling. The first example analyzes the daily returns of three stocks from the DJ30 index, while the second example investigates volatility spillover effects among the bond, stock, crude oil, and gold markets. Overall, this extended multivariate EGARCH model offers a flexible and comprehensive framework for analyzing multivariate volatility and spillover effects in empirical finance research. |
| Keywords: | Multivariate EGARCH, QML Estimator, Volatility Spillovers, Zero Return |
| JEL: | C32 C58 G17 |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:cdf:wpaper:2024/24 |
| By: | Faria, Gonçalo; Verona, Fabio |
| Abstract: | We introduce a frequency-domain forecast combination method that leverages time- and frequencydependent predictability to enhance forecast accuracy. By decomposing both the target variables (equity premium and real GDP growth) and predictor variables into distinct frequency components, this method aligns forecasts with frequency-specific predictive relationships. This approach yields significantly higher accuracy than traditional time-domain methods, as evidenced by both statistical and economic out-of-sample metrics. Gains are particularly pronounced during recessions, where excluding low-frequency components further enhances forecast precision. Overall, these findings highlight the value of frequency-domain forecasting in capturing complex, time-varying patterns across varied macro-financial contexts. |
| Keywords: | forecast combination, frequency domain, equity premium, GDP growth, Haar filter |
| JEL: | C58 G11 G17 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:bofrdp:307140 |
| By: | Jean-Jacques Forneron; Zhongjun Qu |
| Abstract: | This paper considers filtering, parameter estimation, and testing for potentially dynamically misspecified state-space models. When dynamics are misspecified, filtered values of state variables often do not satisfy model restrictions, making them hard to interpret, and parameter estimates may fail to characterize the dynamics of filtered variables. To address this, a sequential optimal transportation approach is used to generate a model-consistent sample by mapping observations from a flexible reduced-form to the structural conditional distribution iteratively. Filtered series from the generated sample are model-consistent. Specializing to linear processes, a closed-form Optimal Transport Filtering algorithm is derived. Minimizing the discrepancy between generated and actual observations defines an Optimal Transport Estimator. Its large sample properties are derived. A specification test determines if the model can reproduce the sample path, or if the discrepancy is statistically significant. Empirical applications to trend-cycle decomposition, DSGE models, and affine term structure models illustrate the methodology and the results. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.20204 |
| By: | Andrade, Philippe (Federal Reserve Bank of Boston); Ferroni, Filippo (Federal Reserve Bank of Chicago); Melosi, Leonardo (University of Warwick, EUI, DNB & CEPR) |
| Abstract: | We introduce a method that exploits some non-gaussian features of structural shocks to identify structural vector autoregressive models. More specifically, we propose to combine inequality restrictions on the higher-order moments of the structural shocks of interest with other set-identifying constraints, typically sign restrictions. We illustrate how, both in large or small sample settings, higher-moment restrictions considerably narrows the identification of monetary policy shocks compared to what is obtained with minimal sign restrictions typically used in the SVAR literature. The proposed methodology also delivers new insights on the macroeconomic effects of sovereign risk in the Euro Area, and on the transmission of geopolitical risk to the US economy. |
| Keywords: | Shock identification ; skewness ; kurtosis ; sign restrictions ; monetary policy ; sovereign risk ; geopolitical risk. JEL Codes: C32 ; E27 ; E32 |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1537 |
| By: | António Rua; Junho Lee; Miguel de Carvalho; Julio Avila |
| Abstract: | We propose a Bayesian time-varying model that learns about the dynamics governing joint extreme values over time. Our model relies on dual measures of time-varying extremal dependence, that are modelled via a suitable class of generalized linear models conditional on a large threshold. The simulation study indicates that the proposed methods perform well in a variety of scenarios. The application of the proposed methods to some of the world’s most important stock markets reveals complex patterns of extremal dependence over the last 30 years, including passages from asymptotic dependence to asymptotic independence. |
| JEL: | C11 C40 C58 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ptu:wpaper:w202406 |
| By: | Raffaella Giacomini; Jason Lu; Katja Smetanina |
| Abstract: | This paper develops a novel approach that leverages the information contained in expectations datasets to derive empirical measures of beliefs regarding economic shocks and their dynamic effects. Utilizing a panel of expectation revisions for a single variable across multiple horizons, we implement a time-varying factor model to nonparametrically estimate the latent shocks and their associated impulse responses at every point in time. The method is designed to accommodate small sample sizes and relies on weak assumptions, requiring no explicit modeling of expectations or assumptions about agents’ forecasting models, information sets, or rationality. Our empirical application to consensus inflation expectations identifies a single perceived shock that closely aligns with observed inflation surprises. The time-varying impulse responses indicate a significant decline in the perceived persistence of this shock, suggesting that inflation expectations have become more “anchored” over time. |
| Date: | 2024–11–25 |
| URL: | https://d.repec.org/n?u=RePEc:azt:cemmap:21/24 |
| By: | Frederik Krabbe |
| Abstract: | A Markov-switching observation-driven model is a stochastic process $((S_t, Y_t))_{t \in \mathbb{Z}}$ where (i) $(S_t)_{t \in \mathbb{Z}}$ is an unobserved Markov process taking values in a finite set and (ii) $(Y_t)_{t \in \mathbb{Z}}$ is an observed process such that the conditional distribution of $Y_t$ given all past $Y$'s and the current and all past $S$'s depends only on all past $Y$'s and $S_t$. In this paper, we prove the consistency and asymptotic normality of the maximum likelihood estimator for such model. As a special case hereof, we give conditions under which the maximum likelihood estimator for the widely applied Markov-switching generalised autoregressive conditional heteroscedasticity model introduced by Haas et al. (2004b) is consistent and asymptotic normal. |
| Date: | 2024–12 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2412.19555 |