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lec10 - 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 . Motivation 1 14.384 Time Series Analysis, Fall 2007 Professor Anna Mikusheva Paul Schrimpf, scribe October 11, 2007 Lecture 10 Factor Models Motivation Last time, we discussed structural VARs. One of our main concerns was that shocks might not be fundamental for the system that we considered. Recall the monetary policy example from last time – in a 2 variable VAR, due to non-fundamentalness, tightening of monetary policy might appear to induce inflation when in reality inflation caused monetary policy to tighten. Another way to state our concern is that the space of structural shocks in not spanned by the residuals in our VAR. A potential solution is to: • Add more variables – this is not a good idea because: – Number of parameters increases too fast with number of variables – Number of shocks = number of variables – how do we interpret them all? – Which variables do we use? – many variables measure similar things Factor-augmented VARs are another approach. Setup Assume : there are a small number of structural shocks explaining co-movements of a large number of time series. Our notation will follow Stock & Watson (2005). • x t is a stationary n × 1 vector time-series. We have observations for t = 1 , ..., T . Both n and T are large. For example in Stock and Watson, n = 132....
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lec10 - MIT OpenCourseWare http://ocw.mit.edu 14.384 Time...

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