Spectral approach for time series analysis

Abstract

The first appearance of spectral analysis in the study of macroeconomic time series dates motivated by the requirement of a more insightful knowledge of the series structure and supported by the contemporaneous progress in spectral estimation and computation. The first works focused on the problem of seasonal adjustment procedures and on the general spectral structure of economic data. Cross spectral methods were pointed out from the outset as being important in discovering and interpreting the relationships between economic variables. After the early years, the range of application of such analysis was extended to the study of other econometric issues, among which the controversial trend-cycle separation, the related problem of business cycles extraction and the analysis of co-movements among series, usefiil in the study of international business cycles. In particular, cross spectral analysis allows a detailed study of the correlation among series. An empirical investigation about the possibility that the market is in a self-organized critical state (SOC) show a power law behaviour in the avalanche size, duration and laminar times during high activity period (Bartolozzi, Leinweber and Thomas, 2005).