SINOMA - A new approach for estimating linear relationships between noisy serial data streams

TL;DR

SINOMA is a novel method for accurately estimating linear relationships in noisy serial data streams, especially useful for paleoclimate reconstructions, by leveraging spectral properties of signal and noise.

Contribution

It introduces SINOMA, a new approach that effectively estimates true regression slopes and noise ratios in noisy data streams with different spectral characteristics.

Findings

SINOMA accurately estimates regression slopes in simulated data.

It successfully distinguishes signal from noise in real paleoclimate data.

The method outperforms traditional regression techniques in noisy conditions.

Abstract

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.