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on Econometric Time Series |
| By: | Ruofan Yu; Rong Chen; Han Xiao; Yuefeng Han |
| Abstract: | Matrix time series, which consist of matrix-valued data observed over time, are prevalent in various fields such as economics, finance, and engineering. Such matrix time series data are often observed in high dimensions. Matrix factor models are employed to reduce the dimensionality of such data, but they lack the capability to make predictions without specified dynamics in the latent factor process. To address this issue, we propose a two-component dynamic matrix factor model that extends the standard matrix factor model by incorporating a matrix autoregressive structure for the low-dimensional latent factor process. This two-component model injects prediction capability to the matrix factor model and provides deeper insights into the dynamics of high-dimensional matrix time series. We present the estimation procedures of the model and their theoretical properties, as well as empirical analysis of the estimation procedures via simulations, and a case study of New York city taxi data, demonstrating the performance and usefulness of the model. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.05624 |
| By: | Andrei Renatovich Batyrov |
| Abstract: | There are several approaches to modeling and forecasting time series as applied to prices of commodities and financial assets. One of the approaches is to model the price as a non-stationary time series process with heteroscedastic volatility (variance of price). The goal of the research is to generate probabilistic forecasts of day-ahead electricity prices in a spot marker employing stochastic volatility models. A typical stochastic volatility model - that treats the volatility as a latent stochastic process in discrete time - is explored first. Then the research focuses on enriching the baseline model by introducing several exogenous regressors. A better fitting model - as compared to the baseline model - is derived as a result of the research. Out-of-sample forecasts confirm the applicability and robustness of the enriched model. This model may be used in financial derivative instruments for hedging the risk associated with electricity trading. Keywords: Electricity spot prices forecasting, Stochastic volatility, Exogenous regressors, Autoregression, Bayesian inference, Stan |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.19405 |
| By: | Atsushi Inoue; Lutz Kilian |
| Abstract: | Several recent studies have expressed concern that the Haar prior typically employed in estimating sign-identified VAR models is driving the prior about the structural impulse responses and hence their posterior. In this paper, we provide evidence that the quantitative importance of the Haar prior for posterior inference has been overstated. How sensitive posterior inference is to the Haar prior depends on the width of the identified set of a given impulse response. We demonstrate that this width depends not only on how much the identified set is narrowed by the identifying restrictions imposed on the model, but also depends on the data through the reduced-form model parameters. Hence, the role of the Haar prior can only be assessed on a case-by-case basis. We show by example that, when the identification is sufficiently tight, posterior inference based on a Gaussian-inverse Wishart-Haar prior provides a reasonably accurate approximation. |
| Keywords: | Bayesian VAR; impulse response; sign restrictions; set-identification; Haar prior |
| JEL: | C22 C32 C52 E31 |
| Date: | 2024–07–09 |
| URL: | https://d.repec.org/n?u=RePEc:fip:feddwp:98532 |
| By: | Benjamin Poignard; Manabu Asai |
| Abstract: | Building upon the pertinence of the factor decomposition to break the curse of dimensionality inherent to multivariate volatility processes, we develop a factor model-based multivariate stochastic volatility (fMSV) framework that relies on two viewpoints: sparse approximate factor model and sparse factor loading matrix. We propose a two-stage estimation procedure for the fMSV model: the first stage obtains the estimators of the factor model, and the second stage estimates the MSV part using the estimated common factor variables. We derive the asymptotic properties of the estimators. Simulated experiments are performed to assess the forecasting performances of the covariance matrices. The empirical analysis based on vectors of asset returns illustrates that the forecasting performances of the fMSV models outperforms competing conditional covariance models. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.19033 |
| By: | Marie-Christine D\"uker; David S. Matteson; Ruey S. Tsay; Ines Wilms |
| Abstract: | Vector AutoRegressive Moving Average (VARMA) models form a powerful and general model class for analyzing dynamics among multiple time series. While VARMA models encompass the Vector AutoRegressive (VAR) models, their popularity in empirical applications is dominated by the latter. Can this phenomenon be explained fully by the simplicity of VAR models? Perhaps many users of VAR models have not fully appreciated what VARMA models can provide. The goal of this review is to provide a comprehensive resource for researchers and practitioners seeking insights into the advantages and capabilities of VARMA models. We start by reviewing the identification challenges inherent to VARMA models thereby encompassing classical and modern identification schemes and we continue along the same lines regarding estimation, specification and diagnosis of VARMA models. We then highlight the practical utility of VARMA models in terms of Granger Causality analysis, forecasting and structural analysis as well as recent advances and extensions of VARMA models to further facilitate their adoption in practice. Finally, we discuss some interesting future research directions where VARMA models can fulfill their potentials in applications as compared to their subclass of VAR models. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.19702 |
| By: | Bertille Antoine; Otilia Boldea; Niccolo Zaccaria |
| Abstract: | We consider estimation and inference in a linear model with endogenous regressors where the parameters of interest change across two samples. If the first-stage is common, we show how to use this information to obtain more efficient two-sample GMM estimators than the standard split-sample GMM, even in the presence of near-weak instruments. We also propose two tests to detect change points in the parameters of interest, depending on whether the first-stage is common or not. We derive the limiting distribution of these tests and show that they have non-trivial power even under weaker and possibly time-varying identification patterns. The finite sample properties of our proposed estimators and testing procedures are illustrated in a series of Monte-Carlo experiments, and in an application to the open-economy New Keynesian Phillips curve. Our empirical analysis using US data provides strong support for a New Keynesian Phillips curve with incomplete pass-through and reveals important time variation in the relationship between inflation and exchange rate pass-through. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.17056 |
| By: | Joshua C. C. Chan; Davide Pettenuzzo; Aubrey Poon; Dan Zhu |
| Abstract: | Conditional forecasts, i.e. projections of a set of variables of interest on the future paths of some other variables, are used routinely by empirical macroeconomists in a number of applied settings. In spite of this, the existing algorithms used to generate conditional forecasts tend to be very computationally intensive, especially when working with large Vector Autoregressions or when multiple linear equality and inequality constraints are imposed at once. We introduce a novel precision-based sampler that is fast, scales well, and yields conditional forecasts from linear equality and inequality constraints. We show in a simulation study that the proposed method produces forecasts that are identical to those from the existing algorithms but in a fraction of the time. We then illustrate the performance of our method in a large Bayesian Vector Autoregression where we simultaneously impose a mix of linear equality and inequality constraints on the future trajectories of key US macroeconomic indicators over the 2020--2022 period. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.02262 |
| By: | Bin Chen; Yuefeng Han; Qiyang Yu |
| Abstract: | High-dimensional tensor-valued data have recently gained attention from researchers in economics and finance. We consider the estimation and inference of high-dimensional tensor factor models, where each dimension of the tensor diverges. Our focus is on a factor model that admits CP-type tensor decomposition, which allows for non-orthogonal loading vectors. Based on the contemporary covariance matrix, we propose an iterative simultaneous projection estimation method. Our estimator is robust to weak dependence among factors and weak correlation across different dimensions in the idiosyncratic shocks. We establish an inferential theory, demonstrating both consistency and asymptotic normality under relaxed assumptions. Within a unified framework, we consider two eigenvalue ratio-based estimators for the number of factors in a tensor factor model and justify their consistency. Through a simulation study and two empirical applications featuring sorted portfolios and international trade flows, we illustrate the advantages of our proposed estimator over existing methodologies in the literature. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.17278 |
| By: | Borko Stosic; Tatijana Stosic |
| Abstract: | In this work we address the question of the Multifractal detrended cross-correlation analysis method that has been subject to some controversies since its inception almost two decades ago. To this end we propose several new options to deal with negative cross-covariance among two time series, that may serve to construct a more robust view of the multifractal spectrum among the series. We compare these novel options with the proposals already existing in the literature, and we provide fast code in C, R and Python for both new and the already existing proposals. We test different algorithms on synthetic series with an exact analytical solution, as well as on daily price series of ethanol and sugar in Brazil from 2010 to 2023. |
| Date: | 2024–06 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2406.19406 |
| By: | Anita Behme |
| Abstract: | We introduce generalizations of the COGARCH model of Kl\"uppelberg et al. from 2004 and the volatility and price model of Barndorff-Nielsen and Shephard from 2001 to a Markov-switching environment. These generalizations allow for exogeneous jumps of the volatility at times of a regime switch. Both models are studied within the framework of Markov-modulated generalized Ornstein-Uhlenbeck processes which allows to derive conditions for stationarity, formulas for moments, as well as the autocovariance structure of volatility and price process. It turns out that both models inherit various properties of the original models and therefore are able to capture basic stylized facts of financial time-series such as uncorrelated log-returns, correlated squared log-returns and non-existence of higher moments in the COGARCH case. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.05866 |
| By: | Elnura Baiaman kyzy (HIAS, Hitotsubashi University, Japan); Roberto Leon-Gonzalez (National Graduate Institute for Policy Studies, GRIPS, Japan; Rimini Centre for Economic Analysis) |
| Abstract: | This paper proposes a novel Laplace based solution to nonlinear DSGE models that has a closed form likelihood. We implicitly use a nonlinear approximation to the policy function that is invertible with respect to the shocks, implying that in the approximation the shocks can be recovered uniquely from some of the control variables. Using perturbation methods and a Lagrange inversion formula we are able to calculate the derivatives of the likelihood and construct the Laplace based solution. In contrast with previous likelihood-based approaches, the method used here requires neither the introduction of linear shocks nor simulation to evaluate the likelihood. Using US data we estimate linear and nonlinear variants of a well-known neoclassical growth model with and without time-varying variances. We find that a nonlinear heteroscedastic model has a much better empirical performance. Furthermore, our models allow us to ascertain that the monetary policy shock causes 95% of the time changes in economic uncertainty. |
| Keywords: | Economic Uncertainty, Time-Varying Volatility, Risk-Premium, Higher-Order Approximation |
| JEL: | E0 C63 |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:rim:rimwps:24-11 |
| By: | Diego Fresoli; Pilar Poncela; Esther Ruiz |
| Abstract: | In this paper, we propose a computationally simple estimator of the asymptotic covariance matrix of the Principal Components (PC) factors valid in the presence of cross-correlated idiosyncratic components. The proposed estimator of the asymptotic Mean Square Error (MSE) of PC factors is based on adaptive thresholding the sample covariances of the id iosyncratic residuals with the threshold based on their individual variances. We compare the nite sample performance of condence regions for the PC factors obtained using the proposed asymptotic MSE with those of available extant asymptotic and bootstrap regions and show that the former beats all alternative procedures for a wide variety of idiosyncratic cross-correlation structures. |
| Date: | 2024–07 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2407.06883 |
| By: | Thorsten Drautzburg (Federal Reserve Bank of Philadelphia); Jesus Fernandez-Villaverde (University of Pennsylvania, NBER, and CEPR); Pablo Guerron-Quintana (Boston College and ESPOL); Dick Oosthuizen (University of Pennsylvania) |
| 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. |
| Keywords: | filtering, limited information, non-linear model, dynamic equilibrium model, sudden stops |
| JEL: | C32 C53 E37 E44 O11 |
| Date: | 2024–07–19 |
| URL: | https://d.repec.org/n?u=RePEc:pen:papers:24-016 |