Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 1996
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996aj....111..555f&link_type=abstract
Astronomical Journal v.111, p.555
Astronomy and Astrophysics
Astronomy
16
Methods: Analytical
Scientific paper
An impressive array of time series analysis methods are equivalent to treating the data as a vector in function space, then projecting the data vector onto a subspace of low dimension. A geometric approach isolates and exposes many of the important features of time series techniques, directly adapts to irregular time spacing, and easily accommodates variable statistical weights. Tensor notation provides an ideal formalism for these techniques. It is quite convenient for distinguishing a variety of different vector spaces, and is the most compact notation for all the sums which arise in the analysis. Statistics of projections are derived under a number of different null hypotheses. In particular, it is shown that if the data are independent random variables, then projections have simple statistical behavior as the number of data N grows large. The notation is directly applied to the statistics of Fourier analysis methods. When the trial functions depend on variable parameters, a nonlinear least-squares fit is equivalent to a nonlinear projection.
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