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on Econometric Time Series |
| By: | Joshua C. C. Chan; Yaling Qi |
| Abstract: | We consider Bayesian tensor vector autoregressions (TVARs) in which the VAR coefficients are arranged as a three-dimensional array or tensor, and this coefficient tensor is parameterized using a low-rank CP decomposition. We develop a family of TVARs using a general stochastic volatility specification, which includes a wide variety of commonly-used multivariate stochastic volatility and COVID-19 outlier-augmented models. In a forecasting exercise involving 40 US quarterly variables, we show that these TVARs outperform the standard Bayesian VAR with the Minnesota prior. The results also suggest that the parsimonious common stochastic volatility model tends to forecast better than the more flexible Cholesky stochastic volatility model. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.16132 |
| By: | Niklas Ahlgren; Alexander Back; Timo Ter\"asvirta |
| Abstract: | It is common for long financial time series to exhibit gradual change in the unconditional volatility. We propose a new model that captures this type of nonstationarity in a parsimonious way. The model augments the volatility equation of a standard GARCH model by a deterministic time-varying intercept. It captures structural change that slowly affects the amplitude of a time series while keeping the short-run dynamics constant. We parameterize the intercept as a linear combination of logistic transition functions. We show that the model can be derived from a multiplicative decomposition of volatility and preserves the financial motivation of variance decomposition. We use the theory of locally stationary processes to show that the quasi maximum likelihood estimator (QMLE) of the parameters of the model is consistent and asymptotically normally distributed. We examine the quality of the asymptotic approximation in a small simulation study. An empirical application to Oracle Corporation stock returns demonstrates the usefulness of the model. We find that the persistence implied by the GARCH parameter estimates is reduced by including a time-varying intercept in the volatility equation. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.03239 |
| By: | Leona Han Chen (Hunan University); Yijie Fei (Hunan University); Jun Yu (University of Macau) |
| Abstract: | Modeling multivariate stochastic volatility (MSV) can pose significant challenges, particularly when both variances and covariances are time-varying. In this study, we tackle these complexities by introducing novel MSV models based on the generalized Fisher transformation (GFT) proposed by Archakov and Hansen (2021). Our model exhibits remarkable flexibility, ensuring the positive-definiteness of the variancecovariance matrix, and disentangling the driving forces of volatilities and correlations. To conduct Bayesian analysis of the models, we employ a Particle Gibbs Ancestor Sampling (PGAS) method, facilitating efficient Bayesian model comparisons. Furthermore, we extend our MSV model to cover leverage effects and incorporate realized measures. Our simulation studies demonstrate that the proposed method performs well for our GFT-based MSV model. Furthermore, empirical studies based on equity returns show that the MSV models outperform alternative specifications in both in-sample and outof-sample performances. |
| Keywords: | Multivariate stochastic volatility; Dynamic correlation; Leverage effect; Particle filter; Markov chain Monte Carlo; Realized measures |
| JEL: | G10 C53 C12 C32 C58 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:boa:wpaper:202419 |
| By: | Zeda Xu; John Liechty; Sebastian Benthall; Nicholas Skar-Gislinge; Christopher McComb |
| Abstract: | Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives extensive attention. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its succeeding variants are well established models for stock volatility forecasting. More recently, deep learning models have gained popularity in volatility prediction as they demonstrated promising accuracy in certain time series prediction tasks. Inspired by Physics-Informed Neural Networks (PINN), we constructed a new, hybrid Deep Learning model that combines the strengths of GARCH with the flexibility of a Long Short-Term Memory (LSTM) Deep Neural Network (DNN), thus capturing and forecasting market volatility more accurately than either class of models are capable of on their own. We refer to this novel model as a GARCH-Informed Neural Network (GINN). When compared to other time series models, GINN showed superior out-of-sample prediction performance in terms of the Coefficient of Determination ($R^2$), Mean Squared Error (MSE), and Mean Absolute Error (MAE). |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.00288 |
| By: | Kurt Graden Lunsford; Kenneth D. West |
| Abstract: | We use long-run annual cross-country data for 10 macroeconomic variables to evaluate the long-horizon forecast distributions of six forecasting models. The variables we use range from ones having little serial correlation to ones having persistence consistent with unit roots. Our forecasting models include simple time series models and frequency domain models developed in Müller and Watson (2016). For plausibly stationary variables, an AR(1) model and a frequency domain model that does not require the user to take a stand on the order of integration appear reasonably well calibrated for forecast horizons of 10 and 25 years. For plausibly non-stationary variables, a random walk model appears reasonably well calibrated for forecast horizons of 10 and 25 years. No model appears well calibrated for forecast horizons of 50 years. |
| Keywords: | fractional integration; forecast interval; low frequency |
| JEL: | C22 C53 E17 |
| Date: | 2024–09–24 |
| URL: | https://d.repec.org/n?u=RePEc:fip:fedcwq:98821 |
| By: | Francesco Fusari (Newcastle University Business School); Joe Marlow (University of Surrey); Alessio Volpicella (University of Surrey) |
| Abstract: | We study the Structural Vector Autoregressions (SVARs) that impose internal and external restrictions to set-identify the Forecast Error Variance Decomposition (FEVD). This object measures the importance of shocks for macroeconomic fluctuations and is therefore of first-order interest in business cycle analysis. We make the following contributions. First, we characterize the endpoints of the FEVD as the extreme eigenvalues of a symmetric reduced-form matrix. A consistent plug-in estimator naturally follows. Second, we use the perturbation theory to prove that the endpoints of the FEVD are differentiable. Third, we construct confidence intervals that are uniformly consistent in level and have asymptotic Bayesian interpretation. We also describe the conditions to derive uniformly consistent confidence intervals for impulse responses. A Monte-Carlo exercise demonstrates the approach properties in finite samples. An unconventional monetary policy application illustrates our toolkit.e of the cost of sovereign default, capturing the FDI activity of small firms better. |
| JEL: | F13 F21 F34 |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:sur:surrec:0424 |
| By: | Eugene Dettaa; Endong Wang |
| Abstract: | This paper presents a Wald test for multi-horizon Granger causality within a high-dimensional sparse Vector Autoregression (VAR) framework. The null hypothesis focuses on the causal coefficients of interest in a local projection (LP) at a given horizon. Nevertheless, the post-double-selection method on LP may not be applicable in this context, as a sparse VAR model does not necessarily imply a sparse LP for horizon h>1. To validate the proposed test, we develop two types of de-biased estimators for the causal coefficients of interest, both relying on first-step machine learning estimators of the VAR slope parameters. The first estimator is derived from the Least Squares method, while the second is obtained through a two-stage approach that offers potential efficiency gains. We further derive heteroskedasticity- and autocorrelation-consistent (HAC) inference for each estimator. Additionally, we propose a robust inference method for the two-stage estimator, eliminating the need to correct for serial correlation in the projection residuals. Monte Carlo simulations show that the two-stage estimator with robust inference outperforms the Least Squares method in terms of the Wald test size, particularly for longer projection horizons. We apply our methodology to analyze the interconnectedness of policy-related economic uncertainty among a large set of countries in both the short and long run. Specifically, we construct a causal network to visualize how economic uncertainty spreads across countries over time. Our empirical findings reveal, among other insights, that in the short run (1 and 3 months), the U.S. influences China, while in the long run (9 and 12 months), China influences the U.S. Identifying these connections can help anticipate a country's potential vulnerabilities and propose proactive solutions to mitigate the transmission of economic uncertainty. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.04330 |
| By: | Yinhao Wu; Ping He |
| Abstract: | This paper explores the continuous-time limit of a class of Quasi Score-Driven (QSD) models that characterize volatility. As the sampling frequency increases and the time interval tends to zero, the model weakly converges to a continuous-time stochastic volatility model where the two Brownian motions are correlated, thereby capturing the leverage effect in the market. Subsequently, we identify that a necessary condition for non-degenerate correlation is that the distribution of driving innovations differs from that of computing score, and at least one being asymmetric. We then illustrate this with two typical examples. As an application, the QSD model is used as an approximation for correlated stochastic volatility diffusions and quasi maximum likelihood estimation is performed. Simulation results confirm the method's effectiveness, particularly in estimating the correlation coefficient. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.14734 |
| By: | Zhe Sun; Yundong Tu |
| Abstract: | The modal factor model represents a new factor model for dimension reduction in high dimensional panel data. Unlike the approximate factor model that targets for the mean factors, it captures factors that influence the conditional mode of the distribution of the observables. Statistical inference is developed with the aid of mode estimation, where the modal factors and the loadings are estimated through maximizing a kernel-type objective function. An easy-to-implement alternating maximization algorithm is designed to obtain the estimators numerically. Two model selection criteria are further proposed to determine the number of factors. The asymptotic properties of the proposed estimators are established under some regularity conditions. Simulations demonstrate the nice finite sample performance of our proposed estimators, even in the presence of heavy-tailed and asymmetric idiosyncratic error distributions. Finally, the application to inflation forecasting illustrates the practical merits of modal factors. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.19287 |
| By: | Roberto Fuentes M.; Irene Crimaldi; Armando Rungi |
| Abstract: | Inspired by Jang et al. (2022), we propose a Granger causality-in-the-mean test for bivariate $k-$Markov stationary processes based on a recently introduced class of non-linear models, i.e., vine copula models. By means of a simulation study, we show that the proposed test improves on the statistical properties of the original test in Jang et al. (2022), constituting an excellent tool for testing Granger causality in the presence of non-linear dependence structures. Finally, we apply our test to study the pairwise relationships between energy consumption, GDP and investment in the U.S. and, notably, we find that Granger-causality runs two ways between GDP and energy consumption. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.15070 |
| By: | Jin Seo Cho (Yonsei University); Peter C.B. Phillips (Yale University) |
| Abstract: | In GMM estimation, it is well known that if the moment dimension grows with the sample size, the asymptotics of GMM differ from the standard finite dimensional case. The present work examines the asymptotic properties of infinite dimensional GMM estimation when the weight matrix is formed by inverting Brownian motion or Brownian bridge covariance kernels. These kernels arise in econometric work such as minimum Cram´er-von Mises distance estimation when testing distributional specification. The properties of GMM estimation are studied under different environments where the moment conditions converge to a smooth Gaussian or non-differentiable Gaussian process. Conditions are also developed for testing the validity of the moment conditions by means of a suitably constructed J-statistic. In case these conditions are invalid we propose another test called the U-test. As an empirical application of these infinite dimensional GMM procedures the evolution of cohort labor income inequality indices is studied using the Continuous Work History Sample database. The findings show that labor income inequality indices are maximized at early career years, implying that economic policies to reduce income inequality should be more effective when designed for workers at an early stage in their career cycles. |
| Keywords: | Infinite-dimensional GMM estimation; Brownian motion kernel; Brownian bridge kernel; Gaussian process; Infinite-dimensional MCMD estimation; Labor income inequality. |
| JEL: | C13 C18 C32 C55 D31 O15 P36 |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:yon:wpaper:2024rwp-232 |
| By: | Luca Margaritella; Ovidijus Stauskas |
| Abstract: | We provide the theoretical foundation for the recently proposed tests of equal forecast accuracy and encompassing by Pitarakis (2023a) and Pitarakis (2023b), when the competing forecast specification is that of a factor-augmented regression model, whose loadings are allowed to be homogeneously/heterogeneously weak. This should be of interest for practitioners, as at the moment there is no theory available to justify the use of these simple and powerful tests in such context. |
| Date: | 2024–09 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2409.20415 |