Anon

240 The Basics of financial economeTrics

Alternatively, we could subtract the mean from the data and write fac-
tor models in terms of de-meaned data xytt=−μμwhere is the mean of y.
In this case, the constant terms ai are all equal to zero.
In terms of de-meaned data xt, the factor model in vector form, equa-
tion (12.3), becomes

(^) xBtt=+ftt,,=ε ...,1 T (12.5)
The vector model written in matrix form, equation (12.4), Y = FB + E
becomes:
X = FB′ + E (12.6)
where

=





     





     

X

xx

xx

xx

N

tNt

TNT

11 1

1

1

is the matrix of demeaned data;

=





      





      

F

ff

ff

ff

q

tqt

TqT

11 1

1

1

is the matrix of factors without a column of ones.

Assumptions and Categorization of Factor Models

As is the case with a linear regression, specific assumptions about factors and
error terms need to be made, otherwise factor models are void of empirical