9252012 p kolm 4 different functional forms how do we

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: © P. KOLM 4 Different Functional Forms How do we incorporate a different functional form? For example: y = b0 + b1 log(x ) + u (assuming x ¹ 0 ) 1 +u (assuming x ¹ 0 ) x log(y ) = b0 + b1x + u (assuming y ¹ 0 ) y = b0 + b1 1 (compared to x + u 1 which would require non-linear regression) Note these parameterizations are linear in x, log(x ) and y = b0 + b1x b2 Many non-linear forms can be given a useful linear representation Interpretation of estimated parameters depends on precise functional form Choice should be based on views of underlying data generation process (statistical tests, convenience) VER. 9/25/2012. © P. KOLM 5 Example: Nonlinear Model of Market Impact Equity market impact model as in Almgren, Thum et al. (2005) Permanent market impact: Find impact parameter g I tperm = g ⋅ st ⋅ nt + etperm Vt (linear regression) Temporary market impact: Find temporary impact parameters (h, b ) I ttemp nt = h ⋅ st ⋅ sign(nt ) ⋅ Vt ⋅ T b + ettemp (non-linear regression) VER. 9/25/2012...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online