Non negativity constraints on forecasts

[jacarandas]

Hi,

I am attempting to forecast a few variables (ratios) in a very simple manner - using a time trend and lag value of the variable. In the following code, a b c are groups with the variables in them. There are two requirements:
1. The forecasts of these variables (ratios) are constrained by the identity set out below. Basically, the ratios will sum up to 1. (Actually, I just realised that sum of the identity appears to be imposed, while some aren't. Is there a standard way of making sure the ratios sum up to 1 in the forecasts?)
2. The forecasts of these variables can't be negative. How can I go about setting up this constraint in the following code?
I had a look at this thread: viewtopic.php?t=48. But, I am still not entirely sure how to add in this non-negativity constraint in my case.

Code: Select all

for %g a b c
   model shares_{%g}
   for !i=1 to {%g}.@count
      %1 = {%g}.@seriesname(!i)
      equation eqxr{%1}.ls xr{%1} c @trend xr{%1}(-1)
      shares_{%g}.merge eqxr{%1}
   next
next

shares_a.append @identity asum = a1 + a2 + a3
shares_b.append @identity bsum = b1 + b2 + b3 + b4
shares_c.append @identity csum = c1 + c2 + c3 + c4 + c5

smpl July2014 July2050

for %g a b c
   shares_{%g}.solve
next

Any help would be greatly appreciated. Thanks.

[jacarandas]

Hi,

Just wondering if anyone is able to help? I have a large number of identities in each model. But, I'm not entirely sure how to go about imposing the inequality as follows:

Mixed equality and inequality

A commonly encountered mixed type of restriction is to have all parameters non-negative and sum up to one


ai > 0 and a1 + a2 + ... + ak = 1


A reparameterization that satisfies these constraints is

Code: Select all
ai = exp( bi ) / ( exp( b1 ) + exp( b2 ) + ... + exp( bk ) )


where the bi parameters are unconstrained.


Any help would be great.

Thanks.

[EViews Glenn]

Where are the ai coming from in your original example?

[jacarandas]

Hi,

My ai's in this example are:

shares_a system - a1, a2, a3
shares_b system - b1, b2, b3, b4
shares_c system - c1, c2, c3, c4, c5

So, these are historical ratios I have calculated, and they add up to 1.

But, I wasn't sure how to ensure that when the system is solved, the forecasts of these ratios are all positive and add up to 1. The identities I have imposed appear to add most of them up to 1. But, some of them don't.

Any help would be great.

[EViews Glenn]

Can you post what you've currently done.

[jacarandas]

Hi,

Here's what I have done so far. The identity was one way I thought would ensure that the ratios sum up to 1 in the forecasts. But, I am doubtful now.

Here are the constraints I am hoping to implement:
- Forecast ratios in each group sum up to 1
- None of the forecast ratios are <1

Any help on how I can amend the code would be appreciated.

Code: Select all


'Calculate historical ratios

for %g a b c
   for !i=1 to {%g}.@count
      %1 = {%g}.@seriesname(!i)
      series xr{%1} = {%1}/@rsum({%g})
      series xr{%g}sum =  @rsum({%g})/@rsum({%g})
   next
next

'Create and estimate models to forecast ratios
for %g a b c
   model shares_{%g}
   for !i=1 to {%g}.@count
      %1 = {%g}.@seriesname(!i)
      equation eqxr{%1}.ls xr{%1} c @trend xr{%1}(-1)
      shares_{%g}.merge eqxr{%1}
   next
next

'Create adding up constraints

shares_a.append @identity xrasum = a1 + a2 + a3
shares_b.append @identity xrbsum = b1 + b2 + b3 + b4
shares_c.append @identity xrcsum = c1 + c2 + c3 + c4 + c5

'Solve the model

smpl July2014 July2050

for %g a b c
   shares_{%g}.solve
next