Modeling of Climate Data in Terms of AR(1) Process Contaminated with Noise
It is widely recognized that teleconnections (correlations between climates at remote places) such as El Niño play a crucial role in understanding abnormal weather phenomena. To extract such correlations in multivariate climate data, the random matrix theory (RMT) combined with the principal component analysis (PCA) can be successfully used; the RMT has power to distinguish between statistically meaningful correlations and noises. Here we demonstrate that sea level pressure (SLP), which is one of basic meteorological measurements for teleconnections, have characteristic autocorrelations. Unfortunately the standard RMT is not able to distinguish between autocorrelations and cross-correlations. We show that an AR(1) process contaminated with noise reproduces the autocorrelations of the SLP quite well. Then we estimate autocorrelation effects on the eigenvalue distribution of the SLP correlation matrix, which makes the extraction procedure of genuine cross-correlations more reliable.
KeywordsTime Series Data Maximal Eigenvalue Random Matrix Theory Eigenvalue Distribution Multivariate Time Series
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