cissa(): A MATLAB Function for Signal Extraction

TL;DR

cissa() is a MATLAB tool that automates signal extraction from various time series types using Circulant Singular Spectrum Analysis, with novel grouping and technical solutions demonstrated on synthetic, speech, and economic data.

Contribution

It introduces a MATLAB implementation of Circulant SSA with new criteria for signal grouping and technical improvements for data edges, applicable to diverse time series.

Findings

Effective extraction of signals from synthetic, speech, and economic data.

Automated grouping enhances signal reconstruction accuracy.

Versatile application potential in de-noising, de-seasonalizing, and cycle extraction.

Abstract

cissa() is a MATLAB function for signal extraction by Circulant Singular Spectrum Analysis, a procedure proposed in Bogalo et al (2021). cissa() extracts the underlying signals in a time series identifying their frequency of oscillation in an automated way, by just introducing the data and the window length. This solution can be applied to stationary as well as to non-stationary and non-linear time series. Additionally, in this paper, we solve some technical issues regarding the beginning and end of sample data points. We also introduce novel criteria in order to reconstruct the underlying signals grouping some of the extracted components. The output of cissa() is the input of the function group() to reconstruct the desired signals by further grouping the extracted components. group() allows a novel user to create standard signals by automated grouping options while an expert user can decide on the number of groups and their composition. To illustrate its versatility and performance in several fields we include 3 examples: an AM-FM synthetic signal, an example of the physical world given by a voiced speech signal and an economic time series. Possible applications include de-noising, de-seasonalizing, de-trending and extracting business cycles, among others.