Dear all,
Note, that X13 allows for trend extrraction
using modified Hodric-Prescott filter
It would be nice if gretl interface
swithed from x12 default options (even if
one use x13 binary to have the possibility
easy output not only trend+cycle but
trend and cycle separately, now it is
possible only via detailed x13 file

Oleh


14 жовтня 2016, 16:17:23, від "Ignacio Diaz-Emparanza" <ignacio.diaz-emparanza@ehu.eus>:

I see that gretl uses by default the value lambda=1600 for quarterly 
data, lambda = 100 for annual data and lambda=14400 for monthly data.

For the quarterly case this was studied in the HP article and this value 
has been adopted almost as a "convention" for obtaining a trend/cycle 
decomposition.

The values for annual and monthly data has been during some time subject 
to controversy. In particular, some papers consider the above values 
inappropiate because the agregation(from monthly to quarterly or 
quarterly to annual) of the trend gives very different results. But now, 
based on this requirement of equivalence on agregation, it seems that 
finally an agreement has been reached. It implies lambda(annual)=6.25 
and lambda(monthly)=129600 or more generally

lambda(S)=6.25*S^4

being S the seasonal periodicity.

I suggest that gretl adopts these defaults.

In these papers we have different justifications for such a formula:


Maravall, A. y del Rı̀o, A. (2001), Time aggregation and the Hodrick-
Prescott filter, Working paper 0108, Banco de España.

Ravn, M. O. y Uhlig, H. (2002), ‘On adjusting the Hodrick-Prescott 
filter for
the frequency of observations’, The Review of Economics and Statistics
84(2), 371–380.

de Jong, R. M. y Sakarya, N. (2016), ‘The econometrics of the Hodrick-
Prescott filter’, The Review of Economics and Statistics 98(2), 310–317.

-- 
Ignacio Díaz-Emparanza
Departamento de Economía Aplicada III (Econometría y Estadística)
Universidad del País Vasco - Euskalherriko Unibertsitatea, UPV/EHU
Tfno: (+34) 94 601 3732
http://www.ehu.eus/ea3

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