Lecture 15 Factor Models - MIT OpenCourseWare

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Factor ModelsFactor ModelsMIT KempthorneFall 2013MIT 15: Factor Models1Factor ModelsLinear Factor ModelMacroeconomic Factor ModelsFundamental Factor ModelsStatistical Factor Models : Factor AnalysisPrincipal Components AnalysisStatistical Factor Models : Principal Factor MethodOutline1Factor ModelsLinear Factor ModelMacroeconomic Factor ModelsFundamental Factor ModelsStatistical Factor Models : Factor AnalysisPrincipal Components AnalysisStatistical Factor Models : Principal Factor MethodMIT Models2Factor ModelsLinear Factor ModelMacroeconomic Factor ModelsFundamental Factor ModelsStatistical Factor Models : Factor AnalysisPrincipal Components AnalysisStatistical Factor Models : Principal Factor MethodLinear Factor ModelData:massets/instruments/indexes:i= 1,2,...,mntime periods:t= 1,2,...,nm-variate random vector for each time period:xt= (x1,t,x2,t.)

45 4 5 (m K); t = 6 6 6 .. 1). 7. m; 7 7 5 (m t and B are the same for all t. ff. t. gis (Kvariate) covariance stationary I(0) with E[f. t] = f. Cov[f. t] = E[(f. t f)(f. t f) 0] = f. f t. gis m-variate white noise with: E[ t] = 0. m. Cov[ t] = E[ t 0t] = Cov[ t; 0] = E[ t 0] = 0. t. 0. 8t 6=t. 0. is the (m 2m) diagonal matrix with entries ...

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