  Reconstructions of past climates are based on the calibration of available
proxy data. This calibration is usually achieved by means of linear regression
models. In the recent paleo-climate literature there is an ongoing discussion
on the validity of highly resolved climate reconstructions. The reason for this
is that the proxy data are noisy, i.e. in addition to the variability that is
related to the climate variable of interest, they contain other sources of
variability. Inadequate treatment of such noise leads to a biased estimation of
regression slopes, resulting in a wrong representation of the real amplitude of
past climate variations. Methods to overcome this problem have had a limited
success so far. Here, we present a new approach - SINOMA - for noisy serial
data streams that are characterized by different spectral characteristics of
signal and noise. SINOMA makes use of specific properties of the data streams
temporal or spatial structure and by this is able to deliver a precise estimate
of the true regression slope and, simultaneously, of the ratio of noise
variances present in the predictor and predictand. The paper introduces the
underlying mathematics as well as a general description of the presented
algorithm. The validity of SINOMA is illustrated with two test data-sets.
Finally we address methodological limitations and further potential
applications.
