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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 = λ i ( L ) f t + δ i ( L ) x it- 1 + v it (1) f t =Γ( L ) f t- 1 + η t The space spanned by the factors f t is consistently estimable, i.e. there exists an invertible H such that ˆ p || f t- Hf t || 2 → ˆ We estimate f t in two steps: 1. Estimate static factors F t , which is size τ × 1, with τ ≥ q ( f t is q × 1) by iterations: (a) pick δ i ( L ) (b) let x ˜ it = ( I- δ i ( L ) L ) x it (c) principal components (eigenvectors corresponding to largest eigenvalues) of x ˆ ˜ it give F (d) Regress x ˆ it on its lags and F to get a new δ i ( L ) (e) repeat until convergence 2. Dynamic factors : the static factors evolve as: F t = Φ( L ) F t- 1 + ε t where ε t = Gη t and ε t is τ × 1, G is τ × q , and η t is q × 1, so the variance-covariance matrix of ε t is not full rank. Two ways to estimate space spanned by η t : • Observe x it = λ i Φ( L ) F t + δ i ( L ) x it + ²-...
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lec11 - MIT OpenCourseWare http/ocw.mit.edu 14.384 Time...

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