Determining the Number of Factors from Empirical Distribution of Eigenvalues

By A. Onatski. Review of Economics and Statistics, 2010

658 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4b1ef85b1bad9cf560a08f6f7f5b294bebc180df

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Citations in the corpus

Bi-cross-validation for factor analysis (2015, methodology): “ED: the eigenvalue difference method [42] which estimates the number of factors as k̂ = max{i ≤ kmax : λ(2)i − λ(2)i+1 ≥ δ},”
Shrinkage Estimation of Dynamic Panel Data Models with Interactive Fixed Effects (2016, positive): “…for our agLasso, BC-agLasso and post-agLasso estimators are 4.82, 4.70 and 4.70 respectively, while those for PC1 PC2 IC1 IC2 in Bai and Ng (2002), Onatski (2009), Onatski (2010), ER and GR in Ahn and Horenstein (2013) are 18.05, 17.89, 17.90, 15.25, 15.51, 8.59, 6.60 and 7.13, respectively.”
State-Varying Factor Models of Large Dimensions (2018, positive): “Our data set is the same as in Pelger (2019b) and consists of the daily stock returns for the balanced panel of S&P 500 stocks from January 1st 2004 to December 31st 2016.”
Factor Models with Local Factors — Determining the Number of Relevant Factors (2021, methodology): “8Under more restrictive assumptions on the error terms, Onatski (2010) proposes an appealing way to calibrate the tuning parameter Q, exploiting the shape of the eigenvalue distribution of the idiosyncratic noise at their edge, that unfortunately is no longer valid in the setup of this paper.”
Estimation of random coefficients logit demand models with interactive fixed effects (2012, background): “The mean utility is defined as δ0jt = X ′ jtβ 0 + ξ0jt , (2.2) where Xjt = (X1,jt, . . . ,XK,jt) ′ is a vector of K observed product characteristics (including price), and β0 = ( β01 , . . . , β 0 K )′ is the corresponding vector of coefficients.”
Random matrix theory in statistics: A review (2014, methodology): “RMT has been used to explain the bias of arbitrage pricing models in finite samples (Harding, 2008; Onatski, 2012) and in determining the number of significant factors (Onatski, 2009, 2010).”
Spiked separable covariance matrices and principal components (2019, background): “High-dimensional data obtained at space-time points has been increasingly employed in various scientific fields, such as geophysical and environmental sciences [32, 36], wireless communications [28, 52, 54], medical imaging [49] and financial economics [41, 42, 59].”
Cleaning large correlation matrices: tools from random matrix theory (2016, background): “This approach has been generalized in [145] to the case where the empirical estimator of the Σε is an anisotropic Wishart matrix for which one has several results concerning the spectrum (see Chapter 3).”
Dynamic Factor Models with Infinite-Dimensional Factor Space: Asymptotic Analysis (2017, background): “…rewritten in the so-called static representation xit = λi1F1t + λi2F2t + · · ·+ λirFrt + ξit Ft = (F1t . . . Frt) ′ = N(L)ut. (1.2) Criteria to determine r consistently have been given in Bai and Ng (2002) and, more recently, in Alessi et al. (2010), Onatski (2010), and Ahn and Horenstein (2013).”
Exponent of Cross-Sectional Dependence: Estimation and Inference (2016, positive): “15It is interesting to note that another contribution to this literature (Onatski (2010)) does not assume strong factors and, therefore, the suggested method will be valid in our framework.”
Granger Causality: A Review and Recent Advances (2021, background): “Followup work has further investigated the estimability of the parameters (Belviso and Milani, 2006) and the choice of number of unobserved factors (Ahn and Horenstein, 2013; Onatski, 2010; Amengual and Watson, 2007).”
Approximate factor models with weaker loadings (2021, background): “Onatski (2012) considers the other extreme that requires Λ ′ Λ to have a positive limit and shows that the factor estimates are inconsistent. There are many ways to accommodate weaker factor structures. For example, DeMol, Giannone, and Reichlin (2008) let the eigenvalues of Σe to be large relative ”
Eigenvalue Ratio Test for the Number of Factors (2013, methodology): “Here, ( ) V k equals the sample mean of the squared residuals from the time series regressions of individual response variables on the first k principal components of / ( ) XX TN ′ (see Onatski (2006)).”
Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-Frequency Data (2017, methodology): “Moreover, suppose {ξj , 1 ≤ j ≤ d} are the corresponding eigenvectors of Σ, we have ∥∥∥∥∥∥ r̄∑ j=1 λjξjξ ᵀ j − βEβ ᵀ ∥∥∥∥∥∥ MAX ≤ Kd−1/2md, and ∥∥∥∥∥∥ d∑ j=r̄+1 λjξjξ ᵀ j − Γ ∥∥∥∥∥∥ MAX ≤ Kd−1/2md. 1This unboundedness issue has also been studied by Onatski (2010) in a different setting.”
A Testing Procedure for Determining the Number of Factors in Approximate Factor Models With Large Datasets (2010, background): “In particular, Onatski (2006) assumed that the data are Gaussian and temporally independent.”