1:05 p.m.
Hi there,
it's been a while since my last post...how was the gretl conference in
Berlin?)
Today I'm concerned with an optimization problem.
I have the following goal:
Find a linear combination of input series in such a way that
- the resulting series is used to calculate the difference to another
exogenous series
- the variance of the 'difference-series' shall be minimized
- the coefficients are weights for the input series
- there are 2 groups of weights and in each group the weights sum up to 1
and are all positive
(In a next step I also restrict the coeffs so that the weights of the two
groups are identical).
I manged to use gretls numerical methods, somehow. Code see below.
However the results are not as good as the Excel Solver solutions: gretl
gives a small but not the minimal variance.
I want to use gretl since stability analysis is much easier (and I prefer
gretl for such tasks at any rate :-).
Is it a necessary to use analytical derivatives?
At the moment I'm not sure how to implement them in the optimization
procedure...
I also tried to use the simann helping step, but this function ignores all
restrictions already implemented and did not produce valuable results.
I'd be happy to receive some advice.
Cheers
Leon
<hansl>
function scalar fn_Dif_min_Vola_sharesTo100_2gr (matrix *x, list lXlist, \
scalar nGr1, series sComp , series *sProg, series *sDiff)
scalar nParams = rows(x)
x[nGr1] = 1-sumc(x[1:nGr1-1])
if nParams-nGr1<>1
x[nParams] = 1-sumc(x[nGr1+1:nParams-1])
endif
x = (x.<0)? 0 : x
x = (x.>1)? 1: x
series sProg = lincomb(lXlist, x)
series sDiff = sProg-sComp
scalar ret = -sd(sDiff)
return ret
end function
function scalar fn_Dif_min_Vola_equal_2gr (matrix *x, list lXlist,\
scalar nGr1, series sComp , series *sProg, series *sDiff)
scalar nParams = rows(x)
x[nGr1] = 1-sumc(x[1:nGr1-1])
# shares of 1st group to use for 2nd
x[nGr1+1:nParams] = x[1:nGr1]
x = (x.<0)? 0: x
x = (x.>1)? 1: x
series sProg = lincomb(lXlist, x)
series sDiff = sProg-sComp
scalar ret = -sd(sDiff)
return ret
end function
# not run
list xList1 = Input1 Input2 Input3 Input4
list xList2 = Input5 Input6 Input7 Input8
list lData = xList1 xList2
matrix mParams = {0.25; 0.25; 0.25; 0.25; 0.25; 0.25; 0.25; 0.25} # nx1
matrix
x = mParams
series y = lincomb(lData, mParams)
series sDiff = y- sExo
# simann produced incorrect values, since the 0<=x<=1 of the function is
ignored
#u = simann(&x, fn_Dif_min_Vola_sharesTo100_2gr(&x, lData, 4,sExo, &y,
&sDiff), 100)
#print x
u = BFGSmax(&x, fn_Dif_min_Vola_sharesTo100_2gr(&x, lData, 4, sExo, &y,
&sDiff))
print x
<hansl>
5:14 p.m.
On Mon, 5 Oct 2015, Pindar Os wrote:
Hi there,
it's been a while since my last post...how was the gretl conference in
Berlin?)
Both productive and fun (thanks, Sven!).
Today I'm concerned with an optimization problem.
I have the following goal:
Find a linear combination of input series in such a way that
- the resulting series is used to calculate the difference to another
exogenous series
- the variance of the 'difference-series' shall be minimized
- the coefficients are weights for the input series
- there are 2 groups of weights and in each group the weights sum up to 1
and are all positive
(In a next step I also restrict the coeffs so that the weights of the two
groups are identical).
I manged to use gretls numerical methods, somehow. Code see below.
However the results are not as good as the Excel Solver solutions: gretl
gives a small but not the minimal variance.
I want to use gretl since stability analysis is much easier (and I prefer
gretl for such tasks at any rate :-).
Is it a necessary to use analytical derivatives?
I think BFGS ought to be able to do a decent job without that. Not
sure, but I think that rather than just truncating your parameters
that are supposed to be in the range 0 to 1, as in
x = (x.<0)? 0 : x
x = (x.>1)? 1: x
you might do better to use a transformation such as cnorm() which
"naturally" enforces the constraint. That is, let the x's be
unconstrained but apply weights of w[i] = cnorm(x[i]). (You'd then
have to use critical(), the inverse CDF function, to set the nth
parameter such that the weights sum to 1.0. However, if the implied
nth weight was negative, I guess you'd want your function to return
NA).
Allin Cottrell
5:33 p.m.
On Mon, 5 Oct 2015, Allin Cottrell wrote:
I think BFGS ought to be able to do a decent job without that. Not
sure, but I think that rather than just truncating your parameters that are
supposed to be in the range 0 to 1, as in
> x = (x.<0)? 0 : x
> x = (x.>1)? 1: x
you might do better to use a transformation such as cnorm() which "naturally"
enforces the constraint. That is, let the x's be unconstrained but apply
weights of w[i] = cnorm(x[i]). (You'd then have to use critical(), the
inverse CDF function, to set the nth parameter such that the weights sum to
1.0. However, if the implied nth weight was negative, I guess you'd want your
function to return NA).
The problem with that approach is that you cannot have boundary values.
Numerical optimisation of function with inequality constraints is in fact
a very tricky and difficult task. AFAIK, most numerical methods in use
for this are variants of the so-called Sequential Quadratic Programming
approach. See for example here:
http://optimalisatie-project.googlecode.com/svn/trunk/actaSqp.pdf
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
5:59 a.m.
Hi there,
thanks for the quick response!
I gonna try the 'functional approach' and see how it performs.
I also gonna have a look at the paper concerning quadratic programming, but that will be
for some rainy WE in autumn.
In the meantime a write a VBA script.
Have a nice day
Leon
Am 05.10.2015 um 23:14 schrieb Allin Cottrell
<cottrell(a)wfu.edu>:
> On Mon, 5 Oct 2015, Pindar Os wrote:
>
> Hi there,
>
> it's been a while since my last post...how was the gretl conference in
> Berlin?)
Both productive and fun (thanks, Sven!).
> Today I'm concerned with an optimization problem.
> I have the following goal:
> Find a linear combination of input series in such a way that
> - the resulting series is used to calculate the difference to another
> exogenous series
> - the variance of the 'difference-series' shall be minimized
> - the coefficients are weights for the input series
> - there are 2 groups of weights and in each group the weights sum up to 1
> and are all positive
>
> (In a next step I also restrict the coeffs so that the weights of the two
> groups are identical).
>
> I manged to use gretls numerical methods, somehow. Code see below.
> However the results are not as good as the Excel Solver solutions: gretl
> gives a small but not the minimal variance.
> I want to use gretl since stability analysis is much easier (and I prefer
> gretl for such tasks at any rate :-).
>
> Is it a necessary to use analytical derivatives?
I think BFGS ought to be able to do a decent job without that. Not
sure, but I think that rather than just truncating your parameters that are supposed to
be in the range 0 to 1, as in
> x = (x.<0)? 0 : x
> x = (x.>1)? 1: x
you might do better to use a transformation such as cnorm() which "naturally"
enforces the constraint. That is, let the x's be unconstrained but apply weights of
w[i] = cnorm(x[i]). (You'd then have to use critical(), the inverse CDF function, to
set the nth parameter such that the weights sum to 1.0. However, if the implied nth weight
was negative, I guess you'd want your function to return NA).
Allin Cottrell
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3 comments
4 participants
participants (4)
-
Allin Cottrell -
Pindar -
Pindar Os
-
Riccardo (Jack) Lucchetti