R help - Apr 2013 - Parameter Estimation in R with Sums and Lagged Variables

Hi guys,

I am afraid I am stuck with an estimation problem.

I have two variables, X and Y. Y is explained by the weighted sum of n
lagged values of X. My aim is to estimate the two parameters
c(alpha0,alpha1) in:

Yt = Sum from j=1 to n of ( ( alpha0 + alpha1 * j ) * Xt-j )

Where Xt-j denotes the jth lag of X.

I came up with this approach because I thought it would be a good idea to
estimate the slope of the weights rather than estimating one parameter for
each lag of X added (I intent to set n very large). Is that easily doable
in R?

My first try looks like this:

    parameters<-function(alpha,y){
    logl<- for(i in 1:n){
    sum((alpha[1]+alpha[2]*i)*lag(xvar,i))
    }
    return(-logl)
    }
    optim(c(0.001,0.001),parameters,y=yvar)

It is really hard to find any clear sources when it comes to optimization
including lags.

I would really appreciate if someone could help me out on this one!

Kind regards & Happy Easter,

Christian

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Hi: Google for koyck distributed lag. Based on what you wrote, I think
that's what you're looking for or something close to it.

There is tons of literature on that model and if you read enough about it,
you'll see that
through a  transformation, reduces to something that much simpler to
estimate. There are so many papers that I wouldn't know which one to send
you. As far as textbooks, Baltagi's has the best explanation that I've
seen.









There is tons of literature on that model


On Mon, Apr 1, 2013 at 2:37 AM, Christian Satzky <c.satzky@gmail.com>
wrote:
> Hi guys,
>
> I am afraid I am stuck with an estimation problem.
>
> I have two variables, X and Y. Y is explained by the weighted sum of n
> lagged values of X. My aim is to estimate the two parameters
> c(alpha0,alpha1) in:
>
> Yt = Sum from j=1 to n of ( ( alpha0 + alpha1 * j ) * Xt-j )
>
> Where Xt-j denotes the jth lag of X.
>
> I came up with this approach because I thought it would be a good idea to
> estimate the slope of the weights rather than estimating one parameter for
> each lag of X added (I intent to set n very large). Is that easily doable
> in R?
>
> My first try looks like this:
>
>     parameters<-function(alpha,y){
>     logl<- for(i in 1:n){
>     sum((alpha[1]+alpha[2]*i)*lag(xvar,i))
>     }
>     return(-logl)
>     }
>     optim(c(0.001,0.001),parameters,y=yvar)
>
> It is really hard to find any clear sources when it comes to optimization
> including lags.
>
> I would really appreciate if someone could help me out on this one!
>
> Kind regards & Happy Easter,
>
> Christian
>
>         [[alternative HTML version deleted]]
>
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>
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