This research is dedicated to the analysis of firm growth rate correlations, with the primary focus on deciphering signals embedded within the time series data while effectively discerning them from random noise fluctuations. To achieve this, we employ methodologies derived from Random Matrix Theory and non-linear dynamics tools. The study focuses on a meticulous examination of eigenvectors across diverse frequency ranges, aiming to reveal patterns and dependencies within the dataset. Additionally, it employs an unconventional approach known as Hilbert Complex Principal Component Analysis (HPCA) to explore potential lead-lag relationships among these growth rates. The thesis begins by providing a comprehensive literature review, including an overview of Random Matrix Theory and its analytical tools, such as the Marcenko-Pastur distribution.