Eigenvalue Ratio Test for the Number of Factors

By Seung C. Ahn, Alex R. Horenstein. 2013

834 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Jushan Bai
2. Liangjun Su
3. Serena Ng
4. M. Pesaran
5. Matteo Barigozzi
6. D. Xiu
7. Jianqing Fan
8. George Kapetanios

In Finance

1. Serena Ng
2. Jushan Bai
3. Jianqing Fan
4. Liangjun Su
5. Markus Pelger
6. Marco Lippi
7. Matteo Barigozzi
8. D. Xiu

In Statistics and Probability

1. Jushan Bai
2. Liangjun Su
3. Jianqing Fan
4. Yuan Liao
5. Serena Ng
6. D. Xiu
7. Yacine Aït-Sahalia
8. Lingzhou Xue

Citations in the corpus

• Sufficient Forecasting Using Factor Models (2015, background): “(2012) and Ahn and Horenstein (2013) proposed a ratio-based estimator by maximizing the ratio of two adjacent eigenvalues of XX arranged in descending order, i.”
• Detecting big structural breaks in large factor models (2014, methodology): “For example, Onatski (2009, 2010), and Ahn and Horenstein (2013) show that their methods have better finite sample properties than BN (2002) especially when the errors are cross sectionally correlated.”
• Testing for Factor Loading Structural Change under Common Breaks (2015, methodology): “(13)We also computed power functions of the BE tests using the ER and GR statistics of Ahn and Horenstein (2013) and got similar results. The results based on Onatski (2010) are less sensitive to common breaks.”
• Non-Stationary Dynamic Factor Models for Large Datasets (2016, background): “(2010) and Ahn and Horenstein (2013). In order to determine q and τ , we have instead to study the spectral density matrix of ∆xit, ∆χit and ∆ξit, which are defined by Σ(θ) = Σ(θ) +Σ(θ) = 1 2π ΛC(e−iθ)C′(eiθ)Λ′ +Σ(θ), θ ∈ [−π, π].”
• 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).”
• Exponent of Cross-Sectional Dependence: Estimation and Inference (2016, positive): “We conclude by pointing out some of the implications of our analysis for largeN factor models of the type analysed by Bai and Ng (2002), Bai (2003), and Stock and Watson (2002).”
• Estimating Number of Factors by Adjusted Eigenvalues Thresholding (2019, methodology): “We compare our ACT method with 13 existing methods: “ P C 1 ”, “ P C 2 ”,“ P C 3 ”,“ IC 1 ”, “ IC 2 ” and “ IC 3 ” in Bai and Ng (2002), “ ON 1 ”, “ ON 2 ” and “ ON 3 ” in Onasti (2005), “ NON ” in Onatski (2010), “ ER ” and “ GR ” in Ahn and Horenstein (2013).”
• Identification and estimation of a large factor model with structural instability (2017, background): “To show τ̃ −τ0 = op(1), we need to show that for any > 0 and any η > 0, P (|τ̃ − τ0| > η) < holds for suffi ciently large N and T .”
• A diagnostic criterion for approximate factor structure (2016, background): “As discussed in Ahn and Horenstein (2013) (see also Onatski (2013)), we can rewrite (9) in the balanced case as ξ(k) = SSk − SSk+1 − g(n, T ) where SSk equals the sample mean of the squared residuals from the time-series regressions of individual response variables (ε̂i,t) on the first k principal c”
• State-Varying Factor Models of Large Dimensions (2018, neutral): “For example, the theory could potentially be extended to the eigenvalue difference estimator of (Onatski, 2010), the eigenvalue ratio estimator of (Ahn and Horenstein, 2013) or the perturbed eigenvalue ratio estimator of (Pelger, 2019a).”
• Factor Models with Local Factors — Determining the Number of Relevant Factors (2021, methodology): “This assumption is somewhat restrictive, but still less restrictive than the setup of Ahn and Horenstein (2013), who impose |Ak| n for k = 1, .”
• On factor models with random missing: EM estimation, inference, and cross validation (2020, methodology): “Hallin and Líska (2007), Onatski (2009, 2010, 2012), and Ahn and Horenstein (2013), among others. Nevertheless, all these authors assume a balanced panel in their asymptotic analyses. Empirical data typically contain a variety of irregularities, including occasionally missing observations, unbalance”
• Approximate factor models with weaker loadings (2021, background): “References Ahn, S., and R. Horenstein (2013): “Eigenvalue Ratio Test for the Number of Factors,” Econometrica, 81:3, 1203–1227.”