Determining the Number of Factors in Approximate Factor Models
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References
An Introduction to Multivariate Statistical Analysis
The econometrics of financial markets
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The Generalized Dynamic-Factor Model: Identification and Estimation
Related Papers (5)
Frequently Asked Questions (14)
Q2. What future works have the authors mentioned in the paper "Determining the number of factors in approximate factor models" ?
Many issues in factor analysis await further research. But using Theorem 1, it maybe possible to obtain these limiting distributions. It can be shown that ŷT+1|T is not only a consistent but a√ T consistent estimator of yT+1, conditional on the information up to time T ( provided that N is of no smaller order of magnitude than T ). Stock and Watson ( 1998 ) suggest how dynamics can be introduced into factor models when both N and T are large, although their empirical applications assume a static factor structure.
Q3. What is the drawback of the approach?
The drawback of the approach is that, because the number of parameters increases with N ,3 computational difficulties make it necessary to abandoninformation on many series even though they are available.
Q4. What are the two main assumptions that are crucial for the validity of the test?
because their test is based on a comparison of variances over different time periods, covariance stationarity and homoskedasticity are not only technical assumptions, but are crucial for the validity of their test.
Q5. What is the main advantage of these three panel information criteria?
The main advantage of these three panel information criteria (ICp) is that they do not depend on the choice of kmax through σ̂2, which could be desirable in practice.
Q6. What is the test for the number of factors in asset returns?
For large dimensional panels, Connor and Korajczyk (1993) developed a test for the number of factors in asset returns, but their test is derived under sequential limit asymptotics, i.e., N converges to infinity with a fixed T and then T converges to infinity.
Q7. What is the significance of the likelihood ratio test?
A likelihood ratio test can also, in theory, be used to select the number of factors if, in addition, normality of et is assumed.
Q8. How can the forecast mean squared error of a large number of macroeconomic variables be reduced?
More recently, Stock and Watson (1999) showed that the forecast mean squared error of a large number of macroeconomic variables can be reduced by including diffusion indexes, or factors, in structural as well as non-structural forecasting models.
Q9. What is the way to determine the number of factors in a series?
Assuming N, T → ∞ with √ N/T → ∞, Stock and Watson (1998) showed that a modification tothe BIC can be used to select the number of factors optimal for forecasting a single series.
Q10. What is the idiosyncratic component of returns?
In this case, Xit represents the return of asset i at time t, Ft represents the vector of factor returns and eit is the idiosyncratic component of returns.
Q11. What is the implication of the proof of the theorem 2?
However the proof of Theorem 2 mainly uses the fact that ̂Ft satisfies Theorem 1, and does not rely on the principle components per se.
Q12. What is the way to determine the number of factors in a dynamic setting?
Stock and Watson (1998) suggest how dynamics can be introduced into factor models when both N and T are large, although their empirical applications assume a static factor structure.
Q13. What is the simplest way to estimate the rank of a demand system?
when J is large, the theory developed in this paper still provides a consistent estimation of the rank of the demand system and without the need for nonparametric estimation of theG(·) functions.
Q14. What is the simplest way to determine the number of factors?
The shifting interesttowards use of multifactor models inevitably calls for a formal procedure to determine the number of factors.