The Experts below are selected from a list of 157083 Experts worldwide ranked by ideXlab platform
Paolo Zaffaroni - One of the best experts on this subject based on the ideXlab platform.
-
dynamic Factor models with infinite Dimensional Factor space asymptotic analysis
Journal of Econometrics, 2017Co-Authors: Mario Forni, Marc Hallin, Marco Lippi, Paolo ZaffaroniAbstract:Abstract Factor models, all particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni et al., (2000), have become extremely popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni et al. (2004) . Those estimators, however, rely on Brillinger’s concept of dynamic principal components, and thus involve two-sided filters, which leads to rather poor forecasting performances. No such problem arises with estimators based on standard ( static ) principal components, which have been dominant in this literature. On the other hand, the consistency of those static estimators requires the assumption that the space spanned by the Factors has finite dimension, which severely restricts their generality—prohibiting, for instance, autoregressive Factor loadings. This paper derives the asymptotic properties of a semiparametric estimator of the loadings and common shocks based on one-sided filters recently proposed by Forni et al., (2015). Consistency and exact rates of convergence are obtained for this estimator, under a general class of GDFMs that does not require a finite-Dimensional Factor space. A Monte Carlo experiment and an empirical exercise on US macroeconomic data corroborate those theoretical results and demonstrate the excellent performance of those estimators in out-of-sample forecasting.
-
dynamic Factor models with infinite Dimensional Factor space asymptotic analysis
Research Papers in Economics, 2015Co-Authors: Mario Forni, Marc Hallin, Marco Lippi, Paolo ZaffaroniAbstract:Factor models, all particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni, Hallin, Lippi and Reichlin (2000), have become extremely popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni, Hallin, Lippi and Reichlin (2004). Those estimators, however, rely on Brillinger's dynamic principal components, and thus involve two-sided filters, which leads to rather poor forecasting performances. No such problem arises with estimators based on standard (static) principal components, which have been dominant in this literature. On the other hand, the consistency of those static estimators requires the assumption that the space spanned by the Factors has finite dimension, which severely restricts the generality afforded by the GDFM. This paper derives the asymptotic properties of a semiparametric estimator of the loadings and common shocks based on one-sided filters recently proposed by Forni, Hallin, Lippi and Zaffaroni (2015). Consistency and exact rates of convergence are obtained for this estimator, under a general class of GDFMs that does not require a finite-Dimensional Factor space. A Monte Carlo experiment and an empirical exercise on US macroeconomic data corroborate those theoretical results and demonstrate the excellent performance of those estimators in out-of-sample forecasting.
-
dynamic Factor models with infinite Dimensional Factor space asymptotic analysis
Social Science Research Network, 2015Co-Authors: Mario Forni, Marc Hallin, Marco Lippi, Paolo ZaffaroniAbstract:Factor models, all particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni, Hallin, Lippi and Reichlin (2000), have become extremely popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni, Hallin, Lippi and Reichlin (2004). Those estimators, however, rely on Brillinger's dynamic principal components, and thus involve two-sided filters, which leads to rather poor forecasting performances. No such problem arises with estimators based on standard (static) principal components, which have been dominant in this literature. On the other hand, the consistency of those static estimators requires the assumption that the space spanned by the Factors has finite dimension, which severely restricts the generality afforded by the GDFM. This paper derives the asymptotic properties of a semiparametric estimator of the loadings and common shocks based on one-sided filters recently proposed by Forni, Hallin, Lippi and Zaffaroni (2015). Consistency and exact rates of convergence are obtained for this estimator, under a general class of GDFMs that does not require a finite-Dimensional Factor space. A Monte Carlo experiment corroborates those theoretical results and demonstrates the excellent performance of those estimators in out-of-sample forecasting.
-
dynamic Factor models with infinite Dimensional Factor spaces one sided representations
Journal of Econometrics, 2015Co-Authors: Mario Forni, Marc Hallin, Marco Lippi, Paolo ZaffaroniAbstract:Abstract Factor model methods recently have become extremely popular in the theory and practice of large panels of time series data. Those methods rely on various Factor models which all are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forniet al. (2000). That paper, however, rests on Brillinger’s dynamic principal components . The corresponding estimators are two-sided filters whose performance at the end of the observation period or for forecasting purposes is rather poor. No such problem arises with estimators based on standard principal components, which have been dominant in this literature. On the other hand, those estimators require the assumption that the space spanned by the Factors has finite dimension. In the present paper, we argue that such an assumption is extremely restrictive and potentially quite harmful. Elaborating upon recent results by Anderson and Deistler (2008a, b) on singular stationary processes with rational spectrum, we obtain one-sided representations for the GDFM without assuming finite dimension of the Factor space. Construction of the corresponding estimators is also briefly outlined. In a companion paper, we establish consistency and rates for such estimators, and provide Monte Carlo results further motivating our approach.
Jianqing Fan - One of the best experts on this subject based on the ideXlab platform.
-
robust high Dimensional Factor models with applications to statistical machine learning
Statistical Science, 2021Co-Authors: Jianqing Fan, Kaizheng Wang, Yiqiao Zhong, Ziwei ZhuAbstract:Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are collected at an ever-growing scale, statistical machine learning faces some new challenges: high Dimensionality, strong dependence among observed variables, heavy-tailed variables and heterogeneity. High-Dimensional robust Factor analysis serves as a powerful toolkit to conquer these challenges. This paper gives a selective overview on recent advance on high-Dimensional Factor models and their applications to statistics including Factor-Adjusted Robust Model selection (FarmSelect) and Factor-Adjusted Robust Multiple testing (FarmTest). We show that classical methods, especially principal component analysis (PCA), can be tailored to many new problems and provide powerful tools for statistical estimation and inference. We highlight PCA and its connections to matrix perturbation theory, robust statistics, random projection, false discovery rate, etc., and illustrate through several applications how insights from these fields yield solutions to modern challenges. We also present far-reaching connections between Factor models and popular statistical learning problems, including network analysis and low-rank matrix recovery.
-
high Dimensional covariance matrix estimation in approximate Factor models
2011Co-Authors: Jianqing Fan, Yuan Liao, Martina MinchevaAbstract:The variance covariance matrix plays a central role in the inferential theories of high Dimensional Factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict Factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow for the presence of the cross-sectional correlation even after taking out common Factors, and it enables us to combine the merits of both sparsity and Factor structures. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high Dimensionality on the covariance matrix estimation based on the Factor structure is then studied.
-
high Dimensional covariance matrix estimation in approximate Factor models
Annals of Statistics, 2011Co-Authors: Jianqing Fan, Yuan Liao, Martina MinchevaAbstract:The variance–covariance matrix plays a central role in the inferential theories of high-Dimensional Factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict Factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common Factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu [J. Amer. Statist. Assoc. 106 (2011) 672–684], taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high Dimensionality on the covariance matrix estimation based on the Factor structure is then studied.
A A Kobtsev - One of the best experts on this subject based on the ideXlab platform.
-
stable exponential cosmological solutions with 3 and l Dimensional Factor spaces in the einstein gauss bonnet model with a lambda term
arXiv: General Relativity and Quantum Cosmology, 2017Co-Authors: V D Ivashchuk, A A KobtsevAbstract:A $D$-Dimensional gravitational model with a Gauss-Bonnet term and the cosmological term $\Lambda$ is studied. We assume the metrics to be diagonal cosmological ones. For certain fine-tuned $\Lambda $, we find a class of solutions with exponential time dependence of two scale Factors, governed by two Hubble-like parameters $H >0$ and $h$, corresponding to Factor spaces of dimensions $3$ and $l > 2$, respectively and $D = 1 + 3 + l$. The fine-tuned $\Lambda = \Lambda (x, l, \alpha)$ depends upon the ratio $h/H = x$, $l$ and the ratio $\alpha = \alpha_2/\alpha_1$ of two constants ($\alpha_2$ and $\alpha_1$) of the model. For fixed $\Lambda, \alpha$ and $l > 2$ the equation $\Lambda(x,l,\alpha) = \Lambda$ is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals (the example $l =3$ is presented). For certain restrictions on $x$ we prove the stability of the solutions in a class of cosmological solutions with diagonal metrics. A subclass of solutions with small enough variation of the effective gravitational constant $G$ is considered. It is shown that all solutions from this subclass are stable.
-
on exponential cosmological type solutions in the model with gauss bonnet term and variation of gravitational constant
European Physical Journal C, 2015Co-Authors: V D Ivashchuk, A A KobtsevAbstract:A \(D\)-Dimensional gravitational model with Gauss–Bonnet term is considered. When an ansatz with diagonal cosmological type metrics is adopted, we find solutions with an exponential dependence of the scale Factors (with respect to a “synchronous-like” variable) which describe an exponential expansion of “our” 3-Dimensional Factor space and obey the observational constraints on the temporal variation of effective gravitational constant \(G\). Among them there are two exact solutions in dimensions \(D = 22, 28\) with constant \(G\) and also an infinite series of solutions in dimensions \(D \ge 2690\) with the variation of \(G\) obeying the observational data.
-
on exponential cosmological type solutions in the model with gauss bonnet term and variation of gravitational constant
arXiv: General Relativity and Quantum Cosmology, 2015Co-Authors: V D Ivashchuk, A A KobtsevAbstract:A D-Dimensional gravitational model with Gauss-Bonnet term is considered. When ansatz with diagonal cosmological type metrics is adopted, we find solutions with exponential dependence of scale Factors (with respect to "synchronous-like" variable) which describe an exponential expansion of "our" 3-Dimensional Factor-space and obey the observational constraints on the temporal variation of effective gravitational constant G. Among them there are two exact solutions in dimensions D = 22, 28 with constant G and also an infinite series of solutions in dimensions D \ge 2690 with the variation of G obeying the observational data.
Martina Mincheva - One of the best experts on this subject based on the ideXlab platform.
-
high Dimensional covariance matrix estimation in approximate Factor models
2011Co-Authors: Jianqing Fan, Yuan Liao, Martina MinchevaAbstract:The variance covariance matrix plays a central role in the inferential theories of high Dimensional Factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict Factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow for the presence of the cross-sectional correlation even after taking out common Factors, and it enables us to combine the merits of both sparsity and Factor structures. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu (2011), taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high Dimensionality on the covariance matrix estimation based on the Factor structure is then studied.
-
high Dimensional covariance matrix estimation in approximate Factor models
Annals of Statistics, 2011Co-Authors: Jianqing Fan, Yuan Liao, Martina MinchevaAbstract:The variance–covariance matrix plays a central role in the inferential theories of high-Dimensional Factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many financial problems. Classical methods of estimating the covariance matrices are based on the strict Factor models, assuming independent idiosyncratic components. This assumption, however, is restrictive in practical applications. By assuming sparse error covariance matrix, we allow the presence of the cross-sectional correlation even after taking out common Factors, and it enables us to combine the merits of both methods. We estimate the sparse covariance using the adaptive thresholding technique as in Cai and Liu [J. Amer. Statist. Assoc. 106 (2011) 672–684], taking into account the fact that direct observations of the idiosyncratic components are unavailable. The impact of high Dimensionality on the covariance matrix estimation based on the Factor structure is then studied.
Badi H Baltagi - One of the best experts on this subject based on the ideXlab platform.
-
estimating and testing high Dimensional Factor models with multiple structural changes
Social Science Research Network, 2019Co-Authors: Badi H Baltagi, Chihwa Kao, Fa WangAbstract:This paper considers multiple changes in the Factor loadings of a high Dimensional Factor model occurring at dates that are unknown but common to all subjects. Since the Factors are unobservable, the problem is converted to estimating and testing structural changes in the second moments of the pseudo Factors. We consider both joint and sequential estimation of the change points and show that the distance between the estimated and the true change points is Op(1). We find that the estimation error contained in the estimated pseudo Factors has no effect on the asymptotic properties of the estimated change points as the cross-sectional dimension N and the time dimension T go to infinity jointly. No N-T ratio condition is needed. We also propose (i) tests for the null of no change versus the alternative of l changes (ii) tests for the null of l changes versus the alternative of l + 1 changes, and show that using estimated Factors asymptotically has no effect on their limit distributions if √T/N→0. These tests allow us to make inference on the presence and number of structural changes. Simulation results show good performance of the proposed procedure. In an application to US quarterly macroeconomic data we detect two possible breaks.
-
identification and estimation of a large Factor model with structural instability
Journal of Econometrics, 2017Co-Authors: Badi H Baltagi, Chihwa Kao, Fa WangAbstract:This paper tackles the identification and estimation of a high Dimensional Factor model with unknown number of latent Factors and a single break in the number of Factors and/or Factor loadings occurring at unknown common date. First, we propose a least squares estimator of the change point based on the second moments of estimated pseudo Factors and show that the estimation error of the proposed estimator is Op(1). We also show that the proposed estimator has some degree of robustness to misspecification of the number of pseudo Factors. With the estimated change point plugged in, consistency of the estimated number of pre and post-break Factors and convergence rate of the estimated pre and post-break Factor space are then established under fairly general assumptions. The finite sample performance of our estimators is investigated using Monte Carlo experiments.
-
identification and estimation of a large Factor model with structural instability
Research Papers in Economics, 2016Co-Authors: Badi H Baltagi, Chihwa Kao, Fa WangAbstract:This paper tackles the identi cation and estimation of a high Dimensional Factor model with unknown number of latent Factors and a single break in the number of Factors and/or Factor loadings occurring at unknown common date. First, we propose a least squares estimator of the change point based on the second moments of estimated pseudo Factors and show that the estimation error of the proposed estimator is Op(1). We also show that the proposed estimator has some degree of robustness to misspeci cation of the number of pseudo fac-tors. With the estimated change point plugged in, consistency of the estimated number of pre and post-break Factors and convergence rate of the estimated pre and post-break Factor space are then established under fairly general assump-tions. The nite sample performance of our estimators is investigated using Monte Carlo experiments. JEL Classification: C13; C33 Key words: high Dimensional Factor model, structural change, rate of con-vergence, number of Factors, model selection, Factor space, panel data