A1046
Title: Frequency singular spectrum analysis
Authors: Pilar Poncela - Universidad Autonoma de Madrid (Spain) [presenting]
Gabriel Martos - Fundacion Universidad Torcuato Di Tella (Argentina)
Diego Fresoli - Universidad Autonoma de Madrid (Spain)
Abstract: Singular spectrum analysis (SSA) is a nonparametric method for time series modeling and forecasting. Via the singular value decomposition on the so-called trajectory matrix, or equivalently, by diagonalizing the second moment matrix of the dataSSA decomposes a time series into quasi-orthogonal components that aim to maximize variance. The resulting trendlines provide natural estimates of the underlying unobserved trend, cycles, and noise. However, these trendlines are not directly associated with specific oscillation frequencies. A novel extension of SSA that reconciles frequency identification with variance-based decomposition is introduced. The aim is to propose a consistent estimator of the spectral density embedded within the method and offer guidance on selecting appropriate decomposition parameters. Additionally, inferential tools are developed to address the grouping problem, enabling the identification of statistically significant components related to specific oscillation frequencies. The performance of the proposed methodology is demonstrated through simulation studies. The method is further applied to analyze US temperature dynamics, identifying a steady increase of 5F in average temperature over the past century.
