I am working on time series and removing obvious trends. Something
which has me intrigued is that by choosing different times as the origin
I can fit equivalent but different models, but I do not recall seeing
this discussed in my training or in the literature.
For example, my data run from 1960 to 2002. A linear trend will have
the same slope regardless of whether it is regressed on year or
(year-1900) or (year-1960) but will have different intercepts. As
these are economic data, it wsa of interest to note that "solving" the
regression suggested an intercept of zero in the year before the
programme began, so there was a logic in choosing that as the origin
year.
Some of the series, however, require a curved fit, and a quadratic was
used as a first approximation. Fitting year^2 may be equivalent to
fitting (year-z)^2, but the first caused a numerical failure in the
algorithm (tolerance exceeded). I had a pragmatic reason for choosing
a value for z in the centre of the distribution. Different z's give the
same overall fit (of course) but strongly influence the coefficients on
lower powers.
It seems to me therefore that the choice of z ought to be a
consideration in the analysis, maybe using a pragmatic or theory-based
value. If z is considered another parameter, which criterion should be
"optimized" given that all models fit equally? How would you define
the "simplest" model? There may be a connection with fitting orthogonal
polynomials, so adding the kth order does not change the coefficients
on k-1 etc, but this seems to me an extra topic.
Comments or references to existing literature, sent to me, would be
welcomed.
NB. If you have old emails from me "@humus1.ucc..." that address no
longer works. Use the reply address below.
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R Allan Reese Email: [log in to unmask]
Graduate School
University of Hull
Tel +44 1482 466845 Fax: +44 1482 466436
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