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206
Determining the Number of Factors in Approximate Factor Models
 Econometrica
, 2002
"... In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors c ..."
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Cited by 335 (21 self)
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In this paper we develop some statistical theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose a panel Cp criterion and show that the number of factors can be consistently estimated using the criterion. The theory is developed under the framework of large crosssections (N) and large time dimensions (T). No restriction is imposed on the relation between N and T. Simulations show that the proposed criterion yields almost precise estimates of the number of factors for configurations of the panel data encountered in practice. The idea that variations in a large number of economic variables can be modelled bya small number of reference variables is appealing and is used in manyeconomic analysis. In the finance literature, the arbitrage pricing theory(APT) of Ross (1976) assumes that a small number of factors can be used to explain a large number of asset returns. 1
Macroeconomic Forecasting Using Diffusion Indexes
 Journal of Business and Economic Statistics
, 2002
"... This article studies forecasting a macroeconomic time series variable using a large number of predictors. The predictors are summarized using a small number of indexes constructed by principal component analysis. An approximate dynamic factor model serves as the statistical framework for the estimat ..."
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Cited by 194 (3 self)
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This article studies forecasting a macroeconomic time series variable using a large number of predictors. The predictors are summarized using a small number of indexes constructed by principal component analysis. An approximate dynamic factor model serves as the statistical framework for the estimation of the indexes and construction of the forecasts. The method is used to construct 6, 12, and 24monthahead forecasts for eight monthly U.S. macroeconomic time series using 215 predictors in simulated real time from 1970 through 1998. During this sample period these new forecasts outperformed univariate autoregressions, small vector autoregressions, and leading indicator models.
Data snooping biases in tests of financial asset pricing models
 Review of Financial Studies
, 1990
"... authors not those of the National Bureau of Economic Research. NBER Working Paper #3001 ..."
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Cited by 169 (6 self)
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authors not those of the National Bureau of Economic Research. NBER Working Paper #3001
Asset pricing with a factor ARCH covariance structure: Empirical estimates for Treasury bills, Revised manuscript
 Journal of Political Economy LXXXI
, 1989
"... In this paper we suggest using the FACTORARCH model as a parsimonious structure for the conditional covariance matrix of asset excess returns. This structure allows us to study the dynamic relationship between asset risk premia and volatilities in a multivariate system. One and two FACTORARCH mode ..."
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Cited by 145 (8 self)
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In this paper we suggest using the FACTORARCH model as a parsimonious structure for the conditional covariance matrix of asset excess returns. This structure allows us to study the dynamic relationship between asset risk premia and volatilities in a multivariate system. One and two FACTORARCH models are succussfully applied to pricing of Treasury bills. The results show stability over time, pass a variety of diagnostic tests, and compare favorably with previous empirical findings. 1.
The Generalized Dynamic Factor Model: Identification and Estimation
 Review of Economics and Statistics
, 2000
"... This paper proposes a factor model with infinite dynamics and nonorthogonal idiosyncratic components. The model, which we call the generalized dynamic factor model, isnovel to the literature, and generalizes the static approximate factor model of Chamberlain and Rothschild (1983), as well as the ex ..."
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Cited by 130 (21 self)
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This paper proposes a factor model with infinite dynamics and nonorthogonal idiosyncratic components. The model, which we call the generalized dynamic factor model, isnovel to the literature, and generalizes the static approximate factor model of Chamberlain and Rothschild (1983), as well as the exact factor model àlaSargent and Sims (1977). We provide identification conditions, propose an estimator of the common components, prove convergence as both time and crosssectional size go to infinity at appropriate rates and present simulation results. We use our model to construct a coincident index for the European Union. Such index is defined as the common component of real GDP within a model including several macroeconomic variables for each European country.
Are more data always better for factor analysis
 Journal of Econometrics
, 2006
"... Factors estimated from large macroeconomic panels are being used in an increasing number of applications. However, little is known about how the size and composition of the data affect the factor estimates. In this paper, we question whether it is possible to use more series to extract the factors a ..."
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Cited by 90 (0 self)
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Factors estimated from large macroeconomic panels are being used in an increasing number of applications. However, little is known about how the size and composition of the data affect the factor estimates. In this paper, we question whether it is possible to use more series to extract the factors and that yet the resulting factors are less useful for forecasting, and the answer is yes. Such a problem tends to arise when the idiosyncratic errors are crosscorrelated. It can also arise if forecasting power is provided by a factor that is dominant in a small dataset but is a dominated factor in a larger dataset. In a real time forecasting exercise, we find that factors extracted from as few as 40 prescreened series often yield satisfactory or even better results than using all 147 series. Our simulation analysis is unique in that special attention is paid to crosscorrelated idiosyncratic errors, and we also allow the factors to have weak loadings on groups of series. It thus allows us to better understand the properties of the principal components estimator in empirical applications.
A PANIC Attack on Unit Roots and Cointegration
, 2003
"... This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC – a ‘Panel Analysis of Nonstationarity in Idiosyncratic and Common components’. PANIC consists of univariate and ..."
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Cited by 80 (3 self)
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This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC – a ‘Panel Analysis of Nonstationarity in Idiosyncratic and Common components’. PANIC consists of univariate and panel tests with a number of novel features. It can detect whether the nonstationarity is pervasive, or variablespecific, or both. It tests the components of the data instead of the observed series. Inference is therefore more accurate when the components have different orders of integration. PANIC also permits the construction of valid panel tests even when crosssection correlation invalidates pooling of statistics constructed using the observed data. The key to PANIC is consistent estimation of the components even when the regressions are individually spurious. We provide a rigorous theory for estimation and inference. In Monte Carlo simulations, the tests have very good size and power. PANIC is applied to a panel of inflation series.
Implications of dynamic factor models for VAR analysis
 NBER, WORKING PAPER
, 2005
"... This paper considers VAR models incorporating many time series that interact through a few dynamic factors. Several econometric issues are addressed including estimation of the number of dynamic factors and tests for the factor restrictions imposed on the VAR. Structural VAR identification based on ..."
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Cited by 75 (5 self)
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This paper considers VAR models incorporating many time series that interact through a few dynamic factors. Several econometric issues are addressed including estimation of the number of dynamic factors and tests for the factor restrictions imposed on the VAR. Structural VAR identification based on timing restrictions, long run restrictions, and restrictions on factor loadings are discussed and practical computational methods suggested. Empirical analysis using U.S. data suggest several (7) dynamic factors, rejection of the exact dynamic factor model but support for an approximate factor model, and sensible results for a SVAR that identifies money policy shocks using timing restrictions.
Confidence intervals for diffusion index forecasts and inference for factoraugmented regressions
, 2003
"... We consider the situation when there is a large number of series, N,eachwithTob servations, and each series has some predictive ability for some variable of interest. A methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components an ..."
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Cited by 75 (12 self)
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We consider the situation when there is a large number of series, N,eachwithTob servations, and each series has some predictive ability for some variable of interest. A methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components and then to augment an otherwise standard regression with the estimated factors. In this paper, we show that the least squares estimates obtained from these factoraugmented regressions are √ T consistent and asymptotically normal if √ T/N → 0. The conditional mean predicted by the estimated factors is min [ √ T � √ N] consistent and asymptotically normal. Except when T/N goes to zero, inference should take into account the effect of “estimated regressors ” on the estimated conditional mean. We present analytical formulas for prediction intervals that are valid regardless of the magnitude of N/T and that can also be used when the factors are nonstationary.