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Kernel specification in FAR(1) model

Discussion in 'Education' started by Filippo, Oct 8, 2018.

  1. Filippo

    Filippo Guest

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    I'm trying to simulate from a functional AR(1) model. I read in 'Introduction to Functional Data Analysis' (by Kokoszka and Reimherr) an example of R code to do this, but I dind't understand how they pass from the kernel to the expression I'll specify below. In order not to break copyright I'll write only the 'incriminated' row, but everyone can get more searching FAR in Google books.Specifically, they use kernel $psi(s,t) = alpha * s * t$ with $alpha = 9/4$ and, when they simulate, they write:

    X[,i]<- alpha*((1/m)^2)*sum((1:m)*X[2:(m+1),i-1])*(0:m/m) + epsilon[,i]

    In that expression I can't recognize the kernel. Someone could help me?

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