  The common methods of spectral analysis for multivariate ($n$-dimensional)
time series, like discrete Frourier transform (FT) or Wavelet transform, are
based on Fourier series to decompose discrete data into a set of trigonometric
model components, e. g. amplitude and phase. Applied to discrete data with a
finite range several limitations of (time discrete) FT can be observed which
are caused by the orthogonality mismatch of the trigonometric basis functions
on a finite interval. However, in the general situation of non-equidistant or
fragmented sampling FT based methods will cause significant errors in the
parameter estimation. Therefore, the classical Lomb-Scargle method (LSM), which
is not based on Fourier series, was developed as a statistical tool for one
dimensional data to circumvent the inconsistent and erroneous parameter
estimation of FT. The present work deduces LSM for $n$-dimensional data sets by
a redefinition of the shifting parameter $\tau$, to maintain orthogonality of
the trigonometric basis. An analytical derivation shows, that $n$-D LSM extents
the traditional 1D case preserving all the statistical benefits, such as the
improved noise rejection. Here, we derive the parameter confidence intervals
for LSM and compare it with FT. Applications with ideal test data and
experimental data will illustrate and support the proposed method.
