Statistics and Its Interface

Volume 16 (2023)

Number 1

Detection of signals by Monte Carlo singular spectrum analysis: multiple testing

Pages: 147 – 157

DOI: https://dx.doi.org/10.4310/21-SII715

Author

Nina Golyandina (Department of Statistical Modeling, St. Petersburg State University, St. Petersburg, Russia)

Abstract

Detection of a signal in a noisy time series using Monte Carlo singular spectrum analysis (MC‑SSA) is studied from the statistical viewpoint. The MC‑SSA test consists of simultaneous testing of several hypotheses related to the presence of different frequencies. The multiple MC‑SSA test procedure is constructed to control the family-wise error rate. The technique to control both the type I and the type II errors and also to compare criteria is proposed to study several versions of MC‑SSA.

Keywords

singular spectrum analysis, time series, signal detection, multiple testing, family-wise error rate

2010 Mathematics Subject Classification

Primary 62G10, 94A12. Secondary 37M10, 60G35.

The reported study was funded by RFBR, project number 20-01-00067.

Received 1 March 2021

Accepted 30 November 2021

Published 27 July 2022