Hi all,
I hope you are well, got a simple one for you...
Can anoyone please tell me what numerical algorithm is internally used in EViews for least squares estimation (the most ordinary one "LS  Least Squares (NLS & ARMA)")? Is it one of the decomposition algorithms like QR or SVD? Or is it the naive direct inverse formula? Can this be altered somewhere in the options?
Great thanks for your answers, have a nice day
Igor
LS regression in EViews
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Re: LS regression in EViews
I'm not sure exactly what you have in mind when you say 'naieve direct inverse'.
In general, EViews uses Cholesky decomposition of moment matrices to solve least squares problems. There's no inversion involved, because you solve the triangular systems directly by forward and back substitution.
The decomposition algorithm used doesn't really matter much here (Cholesky vs QR vs SVD). The real issue is whether we factorize the original data matrix (X) or the moment matrix (X'X).
We generally work with moment matrices because the calculations are faster and require less memory. The downside is that we may report singularity errors on severely colinear data in cases where a QR or SVD decomposition of the original data matrix may have produced results.
There's some subtle issues going on here, but for most real world statistical problems, it's unlikely that you would see much of a difference in results.
There are currently no options provided to change the method for least squares, although it would be possible to write an EViews program that did simple least squares calculations using the SVD of the data matrix.
In general, EViews uses Cholesky decomposition of moment matrices to solve least squares problems. There's no inversion involved, because you solve the triangular systems directly by forward and back substitution.
The decomposition algorithm used doesn't really matter much here (Cholesky vs QR vs SVD). The real issue is whether we factorize the original data matrix (X) or the moment matrix (X'X).
We generally work with moment matrices because the calculations are faster and require less memory. The downside is that we may report singularity errors on severely colinear data in cases where a QR or SVD decomposition of the original data matrix may have produced results.
There's some subtle issues going on here, but for most real world statistical problems, it's unlikely that you would see much of a difference in results.
There are currently no options provided to change the method for least squares, although it would be possible to write an EViews program that did simple least squares calculations using the SVD of the data matrix.
Re: LS regression in EViews
Thanks Chris, your answer is great and enough. I needed to include it somewhere and was struggling to find this piece of information anywhere on the web / manual. Just for your reference by naive "direct inverse formula", I meant the algebraic solution to normal equations, b = (X'X)^1 X'y (which I was hoping is not used). Thanks again, much appreciated.
Igor
Igor
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