Estimation of Factor Models by Realization-based and Approximation Methods PDF Download

Author: Wolfgang Scherrer
Publisher:
ISBN:
Category :
Languages : en
Pages : 9

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Author: Jushan Bai
Publisher: Now Publishers Inc
ISBN: 1601981449
Category : Business & Economics
Languages : en
Pages : 90

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Book Description
Large Dimensional Factor Analysis provides a survey of the main theoretical results for large dimensional factor models, emphasizing results that have implications for empirical work. The authors focus on the development of the static factor models and on the use of estimated factors in subsequent estimation and inference. Large Dimensional Factor Analysis discusses how to determine the number of factors, how to conduct inference when estimated factors are used in regressions, how to assess the adequacy pf observed variables as proxies for latent factors, how to exploit the estimated factors to test unit root tests and common trends, and how to estimate panel cointegration models.

Author: Jushan Bai
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the factor loadings or common factors because it essentially treats the idiosyncratic error to be homoskedastic and cross sectionally uncorrelated. For the efficient estimation, it is essential to estimate a large error covariance matrix. We assume the model to be conditionally sparse, and propose two approaches to estimating the common factors and factor loadings; both are based on maximizing a Gaussian quasi-likelihood and involve regularizing a large covariance sparse matrix. In the first approach the factor loadings and the error covariance are estimated separately while in the second approach they are estimated jointly. Extensive asymptotic analysis has been carried out. In particular, we develop the inferential theory for the two-step estimation. Because the proposed approaches take into account the large error covariance matrix, they produce more efficient estimators than the classical PCA methods or methods based on a strict factor model.

Author: Wayne A. Woodward
Publisher: CRC Press
ISBN: 1498734316
Category : Mathematics
Languages : en
Pages : 460

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Book Description
Virtually any random process developing chronologically can be viewed as a time series. In economics closing prices of stocks, the cost of money, the jobless rate, and retail sales are just a few examples of many. Developed from course notes and extensively classroom-tested, Applied Time Series Analysis with R, Second Edition includes examples across a variety of fields, develops theory, and provides an R-based software package to aid in addressing time series problems in a broad spectrum of fields. The material is organized in an optimal format for graduate students in statistics as well as in the natural and social sciences to learn to use and understand the tools of applied time series analysis. Features Gives readers the ability to actually solve significant real-world problems Addresses many types of nonstationary time series and cutting-edge methodologies Promotes understanding of the data and associated models rather than viewing it as the output of a "black box" Provides the R package tswge available on CRAN which contains functions and over 100 real and simulated data sets to accompany the book. Extensive help regarding the use of tswge functions is provided in appendices and on an associated website. Over 150 exercises and extensive support for instructors The second edition includes additional real-data examples, uses R-based code that helps students easily analyze data, generate realizations from models, and explore the associated characteristics. It also adds discussion of new advances in the analysis of long memory data and data with time-varying frequencies (TVF).

Author: Jared R. Studyvin
Publisher:
ISBN: 9781321918243
Category : Factor analysis
Languages : en
Pages : 93

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Book Description
Factor analytic models use a variance-covariance matrix to estimate underlying factors through the equation Sigma = Lambda Phi Lambda' + Psi . In order to provide estimates for the matrices Lambda, Phi, and Psi, some of the parameters need to be restricted and at least k2 restrictions are required to provide a unique estimate (Joreskog, 1969). The most commonly specified models place restrictions on Phi or Lambda. The estimation of the specified models, which make restrictions on Lambda or Phi, was compared and evaluated. Several different Lambda and Phi conditions were used to assess whether the specified models can reproduce these target Lambda and Phi conditions. The estimation results indicated that when the Lambda and Phi conditions matched the restrictions imposed by the specified models, the models performed well in reproducing the target values. However, when the conditions did not match the imposed restrictions the specified models performed poorly. In practice, a researcher must assume "a priori" knowledge of the restrictions to be imposed on Lambda and Phi, and hence, would not really know if the estimation results are correct or not. Several measures of fit (fit statistics) are commonly used to assess factor analytic models and were evaluated using a simulation. The simulation results indicated in general that fit statistics have no consistent relationship with the estimation quality of the specified models. In particular, the fit statistics could not identify when the estimated correlation between the factors was incorrect. In an attempt to provide better estimation of factor analytic models, a new model was developed which places no restrictions on Lambda or Phi. This was accomplished by expanding Lambda by a set of known constants which then could be appropriately restricted, thus satisfying Joreskog's requirement. The estimation based on this model performed better than the other methods considered and appears to be capable of estimating Lambda and Phi of any possible form.

Author: Jennie Si
Publisher: John Wiley & Sons
ISBN: 9780471660545
Category : Technology & Engineering
Languages : en
Pages : 670

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A complete resource to Approximate Dynamic Programming (ADP), including on-line simulation code Provides a tutorial that readers can use to start implementing the learning algorithms provided in the book Includes ideas, directions, and recent results on current research issues and addresses applications where ADP has been successfully implemented The contributors are leading researchers in the field

Author: J. Grasman
Publisher: Springer Science & Business Media
ISBN: 9401109621
Category : Mathematics
Languages : en
Pages : 662

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Researchers in the natural sciences are faced with problems that require a novel approach to improve the quality of forecasts of processes that are sensitive to environmental conditions. Nonlinearity of a system may significantly complicate the predictability of future states: a small variation of parameters can dramatically change the dynamics, while sensitive dependence of the initial state may severely limit the predictability horizon. Uncertainties also play a role. This volume addresses such problems by using tools from chaos theory and systems theory, adapted for the analysis of problems in the environmental sciences. Sensitive dependence on the initial state (chaos) and the parameters are analyzed using methods such as Lyapunov exponents and Monte Carlo simulation. Uncertainty in the structure and the values of parameters of a model is studied in relation to processes that depend on the environmental conditions. These methods also apply to biology and economics. For research workers at universities and (semi)governmental institutes for the environment, agriculture, ecology, meteorology and water management, and theoretical economists.

Author:
Publisher:
ISBN: 9789155491994
Category :
Languages : en
Pages : 29

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Author: Chris Heaton
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 31

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Abstract : The use of principal component techniques to estimate approximate factor models with large cross-sectional dimension is now well established. However, recent work ... has cast some doubt on the importance of a large cross-sectional dimension for the precision of the estimates. This paper presents some new theory for approximate factor model estimation. Consistency is proved and rates of convergence are derived under conditions that allow for a greater degree of cross-correlation in the model disturbances than previously published results. The rates of convergence depend on the rate at which the cross-sectional correlation of the model disturbances grows as the cross-sectional dimension grows. The consequences for applied economic analysis are discussed. Keywords: factor analysis, time series models, principal components.

Author: D. N. Lawley
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 174

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Book Description
The scope of factor analysis; Parameters in factor models; Principal component analysis; Estimation in the unrestricted model; Sampling formulae for the unrestricted model; Factor transformation and interpretation; Estimation in restricted factor models; The estimation of factor scores; Identifying factors in different populations.