Wow! How many data points? How many parameters?
How much collinearity?
The correct name is Fourier, as already
pointed out. Apart from that pedantic
correction, I regret that this is too
complex a question for me in the time available.
Nick
[email protected]
Dev Vencappa
> Nick, thanks for the solution you provided. I have tried it
> but got stuck and on second thoughts I realised it may be
> better to explain more clearly what I want exactly.
>
> Suppose I have the following equation to estimate:
>
> to=f(clli, clnl, ca, te, re)
>
> We want to estimate a flexible fourier representation of the
> above. The final equation will have the first five terms,
> translog terms and trigonometric terms, as follows:
>
> to= clli + clnl + ca + te + re + Translog terms + Fourier terms
> where Translog terms are: (0.5*clli^2)+(0.5*clnl^2) +
> (0.5*ca^2)+(0.5*te^2)+(0.5*ro^2)+ (clli * clnl) + (clli *
> ca)+ (clli * te) + (clli * ro) + (clnl * ca)+ (clnl * te) +
> (clnl * ro)+ (ca*te) + (ca*ro) + (te*ro)
>
> where Fourier terms are
>
> sin(clli) + cos (clli)+ sin (clnl) + cos (clnl) + sin(ca) +
> cos (ca) + sin (te) + cos (te) + sin (ro) + cos (ro)
>
> By flexible fourrier I mean that one can have more layers of
> trigonometric terms that combine these variables in different
> ways, eg. combining two variables as follows:
>
> sin(clli+ clnl) + cos (clli+clnl)+ sin (clli+ca) + cos
> (cli+ca) + sin (clli+te) + cos (clli+te) + sin (clli+ro) +
> cos (clli+ro) + sin (clnl+ca) + cos (clnl+ca) + sin (clnl+te)
> + cos (clnl +te) + sin(clnl+ro) + cos (clnl + ro) + sin
> (ca+te) + cos (ca+te) + sin (ca+ro) + cos (ca+ro) + sin
> (te+ro) + cos (te+ro)
>
> Another layer of this function would be combining three
> variables in the same way, four variables and five variables
> (five would be the highest combination of variables one can
> create because there are only five right hand side variables)
>
> Now, each of these right hand side variables is rescaled
> using a particular formulae (e.g. see paper by A. Kasnan
> (2002) Central Bank Review 1, pp. 1-20). I have copied below
> how I created the variables and the rescaling used.
>
> gen to=lntoen
> gen pro=lnprof
> gen clli=lnclli
> gen clnl=lnclnl
> gen ca=lnca
> gen te=lntech
> gen ro=lnroin
> gen pril=lnpril
> gen prinl=lnprinl
>
> local var "to pro clli clnl ca te ro"
> foreach j of local var{
> sum `j'
> gen x=(1.6*_pi)/(r(max)-r(min))
> gen z=(0.2*_pi)-(x*r(min))+(x*`j')
> *z is the rescaling to be applied to each variable
> gen R`j'=z
> *create trigonometric terms for these rescaled variables
> gen sin`j'=sin(R`j')
> gen cos`j'=cos(R`j')
> *create squared terms of the rescaled variable
> gen `j'sqr=0.5*R`j'^2
> drop x z
> }
>
> local z "clnl ca te ro"
> foreach x of local z{
> gen clli`x'=Rclli*R`x'
> gen sinclli`x'=sin(Rclli+R`x')
> gen cosclli`x'=cos(Rclli+R`x')
> }
>
> local z "ca te ro"
> foreach x of local z{
> gen clnl`x'=Rclnl*R`x'
> }
>
> gen cate=Rca*Rte
> gen caro=Rca*Rro
> gen tero=Rte*Rro
>
> local z "prinl ca te ro"
> foreach x of local z{
> gen pril`x'=Rpril*R`x'
> gen sinpril`x'=sin(Rpril+R`x')
> gen cospril`x'=cos(Rpril+R`x')
> }
>
> local z "ca te ro"
> foreach x of local z{
> gen prinl`x'=Rprinl*R`x'
> gen sinprinl`x'=sin(Rprinl+R`x')
> gen cosprinl`x'=cos(Rprinl+R`x')
> }
>
> *create third layer of FF function
> local z "sin cos"
> foreach x of local z{
> gen `x'clliclnlca=`x'(Rclli+Rclnl+Rca)
> gen `x'clliclnlte=`x'(Rclli+Rclnl+Rte)
> gen `x'clliclnlro=`x'(Rclli+Rclnl+Rro)
> gen `x'cllicate=`x'(Rclli+Rca+Rte)
> gen `x'cllicaro=`x'(Rclli+Rca+Rro)
> gen `x'clnlcate=`x'(Rclnl+Rca+Rte)
> gen `x'clnlcaro=`x'(Rclnl+Rca+Rro)
> gen `x'clnltero=`x'(Rclnl+Rte+Rro)
> gen `x'catero=`x'(Rca+Rte+Rro)
> gen `x'prilprinlca=`x'(Rpril+Rprinl+Rca)
> gen `x'prilprinlte=`x'(Rpril+Rprinl+Rte)
> gen `x'prilprinlro=`x'(Rpril+Rprinl+Rro)
> gen `x'prilcate=`x'(Rpril+Rca+Rte)
> gen `x'prilcaro=`x'(Rpril+Rca+Rro)
> gen `x'prinlcate=`x'(Rprinl+Rca+Rte)
> gen `x'prinlcaro=`x'(Rprinl+Rca+Rro)
> gen `x'prinltero=`x'(Rprinl+Rte+Rro)
> *create fourth layer of FF function
> gen `x'clliclnlcate=`x'(Rclli+Rclnl+Rca+Rte)
> gen `x'clliclnlcaro=`x'(Rclli+Rclnl+Rca+Rro)
> gen `x'clliclnltero=`x'(Rclli+Rclnl+Rte+Rro)
> gen `x'cllicatero=`x'(Rclli+Rca+Rte+Rro)
> gen `x'clnlcatero=`x'(Rclnl+Rca+Rte+Rro)
> *fifth layer
> gen `x'clliclnlcatero=`x'(Rclli+Rclnl+Rca+Rte+Rro)
> }
>
> To make it easier for estimation, I store the Translog terms
> in a global macro, and same for each of the layers of the
> fourier terms (i.e. first layer, second layer, etc)
>
> My first question is how I find a shortcut way of creating
> these different combinations of fourier terms?
> Clearly, somehow, Stata will need to be told that if two
> variables are combined once through a sine and cosine of
> their additions, then they cannot be combined a second time.
>
> Second, suppose I have estimated an equation. Suppose I want
> to differentiate the above with respect to all variables that
> have clli in their names and add all these partial
> derivatives. This would be the addition of all these terms
> retrieved from the estimated coefficients. When there are
> interaction of terms,I am not too sure how to handle this in
> an automated function in Stata.
>
> Suppose I have a translog term cllica which is the product of
> clli and ca. differentiating lntoen with respect to clli will
> be the coefficient of cllica multiplied by ca (I will
> evaluate this at mean values of the variables). Any thoughts
> on how I would go about doing this automatically please?
>
> It gets a little bit more complicated for me when I try with
> the fourrier terms. Suppose my variable is
>
> sincllica =sin (Rclli+Rca). The derivative with respect to
> clli is _b[sincllica]*cos(clli+ca)
>
> or if
>
> coscllica =cos (Rclli+Rca). The derivative with respect to
> clli is _b[coscllica]* - sin(Rclli+Rca)
>
> How would I tell Stata to automatically deal with that (i.e
> recognise where there are sin and cosine variables (I guess
> wildcards will provide the solution here but I can't figure
> out how to write this)? The solution to this will be the
> solution for the third layers, fourth layers and fifth layers as well.
>
> Apologies for this long email, but I would really be grateful
> if a shortcut solution to this problem were available as I am
> finding myself writing a very long do file to work this out.
> Many thanks in advance.
>
> Dev
>
> >>> [email protected] 11/21/05 11:14 am >>>
> I don't see that you need a function here.
>
> The set of variables with "clli" as part of
> their names is given by the wildcard *clli*
> and so can be put into a macro by
>
> unab clli : *clli*
>
> Presumably you know what variables appear
> on the RHS of your regression and can manufacture
> a local macro containing them, say rhs.
>
> The intersection is then
>
> local cllirhs : list clli & rhs
>
> and you can cycle over these with
>
> foreach v of local cllirhs {
> ... = ... + _b[`v']
> }
>
> Assuming that by Fourrier you mean Fourier, I don't see why
> handling a set of Fourier terms need be messy. The utility
> -fourier- from -circular- on SSC provides one way of getting
> a bunch of them.
>
> Alternatively, in one recent program I needed to generate a bunch
> of them on the fly. Here is the code generalised mildly:
>
> // regression in terms of sin j theta, cos j theta
> local sc
> local terms = <plug in your own>
>
> forval j = 1/`terms' {
> tempvar S C
> gen `S' = sin(`j' * `theta')
> gen `C' = cos(`j' * `theta')
> local sc `sc' `S' `C'
> }
>
> // regression will fail if data points too few
> // or response missing
> // assumes a `touse' marking observations to be used
>
> capture regress <response to be plugged in> `sc' if `touse'
> if _rc gen `sm' = . if `touse'
> else predict `sm' if `touse'
>
> drop `sc'
>
> On the other hand, quite what a "Flexible" Fourier analysis
> is I don't know.
>
> Nick
> [email protected]
>
> Dev Vencappa
>
> > I have the following problem and would be grateful if you
> > could provide some help:
> >
> > Suppose I have a regression equation with lntoen as my
> > dependent variable and a lot of right hand side variables
> > called lncllisqr lncllica lncllite lncaclli (and there are
> > more variables like these which contain the word "clli" in
> > their name as well as other variables named differently).
> > After estimation, I am trying to add the coefficients of all
> > variables in an estimation that have "clli" in their names.
> > While I can do this manually by using _b[variablename], I am
> > faced with a problem as I am estimating a Flexible Fourrier
> > function, which tends to be very messy in terms of the
> > addition of trigonometric terms.
> >
> > I am trying to differentiate lntoen with respect to all
> > variables that contain "clli" in their names. I am trying to
> > automate this process by asking stata to add the coefficients
> > of all variables that contain "clli" in their names.
> >
> > Does anybody know if there is an equivalent to one of the
> > list of string functions (such as e.g. substr) that can allow
> > me to write some condition to check if the variable contains
> > the characters "clli" in its name and then add their
> > coefficients please?
> >
> > Apologies if a similar posting has been up on the list before
> > and escaped my attention.
>
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