Study of Relationships Between Time Series by Co-spectral Analysis

In the literature, cross correlation is often used to analyze the relationships between time series. When the objective of the study is to determine the antecedents and consequences between two or more data sets, cross-correlation analysis is a useful but not sufficient tool to provide information. This paper presents an exploratory technique for investigating relationships between time series. The chosen technique can provide information about priority or precedence within a series, which may establish dependency relationships that cross-correlation analysis cannot identify. The proposed solution is based on the transformation of the observed data into Fourier series and the joint analysis of two series by co-spectral analysis. An example is presented to demonstrate the application of time series analysis to the study of financial data. The article emphasizes the usefulness of these techniques for subsequent analysis.