On Tue, 31 Jan 2023, Olasehinde Timmy wrote:

> Dear profs.,
>
> Please, I would like to know how to perform a grid search in order to find
> an optimal value for a threshold—for example, the threshold value to choose
> for the inflation rate in an asymmetric model.

A grid search is relatively easy to perform via the "for" variant of
the loop command. However, if you want to find the extremum of a
one-variable function in a specified range, the golden ratio method is
generally faster and more accurate. Here's an example script where the
function to be maximised is f(x) = (1-x) * sqrt(x)

<hansl>
function scalar f(scalar x)
     return (1-x) * sqrt(x)
end function

### grid search for a maximum between 0 and 1

mx = -$huge
best = 0
loop for (x = 0; x<=1; x += 0.01)
     y = f(x)
     if y > mx
         mx = y
         best = x
     endif
endloop

print best mx

### golden ratio method

matrix m = {0, 0, 1}
mx = GSSmax(&m, f(m[1]))
best = m[1]
print best mx
</hansl>

-------------------------------------------------------
   Riccardo (Jack) Lucchetti
   Dipartimento di Scienze Economiche e Sociali (DiSES)

   Università Politecnica delle Marche
   (formerly known as Università di Ancona)

   r.lucchetti@univpm.it
   http://www2.econ.univpm.it/servizi/hpp/lucchetti
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