Reducing approximation error in the fourier flexible functional form - Tristan D. Skolrud (Econometrics, 2017)
The Fourier Flexible form provides a global approximation to an unknown data generating process. In terms of limiting function specification error, this form is preferable to functional forms based on second-order Taylor series expansions. The Fourier Flexible form is a truncated Fourier series expansion appended to a second-order expansion in logarithms. By replacing the logarithmic expansion with a Box-Cox transformation, we show that the Fourier Flexible form can reduce approximation error by 25% on average in the tails of the data distribution. The new functional form allows for nested testing of a larger set of commonly implemented functional forms.
Keywords: C51; D24; Q12; 330; Fourier series; Box-Cox; functional form selection; specification bias