Development of Cyclical Indicators Based on Multivariate Spectral Analysis
摘要
In this chapter, we review a method proposed by Bustos (Statistical Methodology for leading Indicator, Bulletin of the International Statistical Institute. Contributed papers, Book I. 49th session Florence, Italy, 1993, pp 189–190) to develop sets of optimal weights for constructing cyclical indicators. To achieve this, we employ the canonical analysis of multivariate time series in the frequency domain, as described by Brillinger (Time Series, Data Analysis and Theory, Holden Day, Inc., San Fran-cisco; 1981). For comparative purposes, we use the sets of coincident and leading indicators utilized by the Cyclical Indicators System of the National Institute of Statistics and Geography (SIC-INEGI) from January 2004 to March 2020. The initial application of the proposed procedure to this dataset does not yield optimal results. However, we demonstrate how our approach allows for evaluating candidate indicators for inclusion in the analysis, resulting in refined sets. Following this selection process, a new application of the methodology is conducted. Considering criteria such as cross-correlation at different lags and the ability to forecast the coincident indicator from the leading one, we assess the improvements offered by our proposal. The results obtained through this approach surpass the performance of indicators developed using traditional methods in several aspects.