Efficient Approximation of Statistical Significance in Local Trend Analysis of Dependent Time Series

Abstract

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Biological time series data plays an important role in exploring the dynamic changes of biological systems, while the determinate patterns of association between various biological factors can further deepen the understanding of biological system functions and the interactions between them. At present, local trend analysis (LTA) has been commonly conducted in many biological fields, where the biological time series data can be the sequence at either the level of gene expression or OTU abundance, etc., A local trend score can be obtained by taking the similarity degree of the upward, constant or downward trend of time series data as an indicator of the correlation between different biological factors. However, a major limitation facing local trend analysis is that the permutation test conducted to calculate its statistical significance requires a time-consuming process. Therefore, the problem attracting much attention from bioinformatics scientists is to develop a method of evaluating the statistical significance of local trend scores quickly and effectively. In this paper, a new approach is proposed to evaluate the efficient approximation of statistical significance in the local trend analysis of dependent time series, and the effectiveness of the new method is demonstrated through simulation and real data set analysis.

Keywords

• local trend analysis
• dependent time series
• statistical significance
• Markov chain model
• spectral decomposition theory