lec11 - MIT OpenCourseWare http://ocw.mit.edu 14.384 Time...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 14.384 Time Series Analysis Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Identification in FAVAR 1 14.384 Time Series Analysis, Fall 2007 Professor Anna Mikusheva Paul Schrimpf, scribe October 16, 2007 Lecture 11 Factor Models Part 2 Identification in FAVAR Take the same model as last time: x it = i ( L ) f t + i ( L ) x it- 1 + v it (1) f t =( L ) f t- 1 + t The space spanned by the factors f t is consistently estimable, i.e. there exists an invertible H such that p || f t- Hf t || 2 We estimate f t in two steps: 1. Estimate static factors F t , which is size 1, with q ( f t is q 1) by iterations: (a) pick i ( L ) (b) let x it = ( I- i ( L ) L ) x it (c) principal components (eigenvectors corresponding to largest eigenvalues) of x it give F (d) Regress x it on its lags and F to get a new i ( L ) (e) repeat until convergence 2. Dynamic factors : the static factors evolve as: F t = ( L ) F t- 1 + t where t = G t and t is 1, G is q , and t is q 1, so the variance-covariance matrix of t is not full rank. Two ways to estimate space spanned by t : Observe x it = i ( L ) F t + i ( L ) x it + -...
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lec11 - MIT OpenCourseWare http://ocw.mit.edu 14.384 Time...

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