Price stability remains a pillar in monetary policy practices and carries a special importance within monetary unions. Mainstream economics tried to leverage price stability using price indices and several metrics to shed light on specific dynamics and optimal macroeconomic levels. The wide availability of data led researchers to consider the study of systems using Random Matrix Theory, based on inner correlation patterns. This aims to enhance the multivariate analysis by removing noisy patterns from the signal and improve data quality for further inferences. This work considers the collection of monthly inflation indices in the Eurozone as a \textit{system} of prices to analyze its eigenvalues' statistical and asymptotic properties and uncover inner country-level insights. Results confirm the system cannot assumed to be randomly generated, and the data exhibit noise-dominated patterns, due to small and persistent variations at the country-level. The latter make the inter-country correlations more dynamic and the separation of the signal from the noise quiet difficult. Findings identified two countries as distorting inflation dynamics besides three other distinct, regional-based groups of countries. Variability sources might stem from economic episodes fueling inflation spikes in some countries, as well as methodological aspects used to ensure data quality and representativeness in the European Union. Despite being complex, the system demonstrates a certain stability, in terms of self-organization; while large monthly fluctuations cannot be considered as rare events, but part of the data-generating process.
Figures & tables
Figure 1: Log-Log Empirical Spectral Density and the Power-law fit for Eurozone prices, yielding α=1.82 on the basis of λ−=37.21
Figure 2: Difference between the Log-Log Empirical Spectral Density of its theoretical (randomly generated) values (max rand ( λ+rand ) is the theoretical largest eigenvalue).
Figure 3: Variations of α values following different thresholds of λ− . The selected λ−=37.21 achieves the lowest Kolmogorov-Smirnov Distance ( DKS ) when computing the Power-law fit.
Figure 4: Plot of the iterative condition number during the period (2019-2026).
Figure 5: Plot of empirical negative log-likelihood distances to Wigner and Exponential distributions, following selected thresholds. The cutoff, or turning point, appears at the value of 0.356 .
Figure 6: Communities reconstructed from the denoised country correlation matrix using leading eigenvector community detection ( Newman, 2006 ) .