# Detection of signals by Monte Carlo singular spectrum analysis: Multiple testing

## TL;DR

This paper investigates the statistical detection of signals in noisy time series using Monte Carlo singular spectrum analysis, focusing on multiple hypothesis testing and error control to improve detection reliability.

## Contribution

It introduces a multiple testing procedure for MC-SSA that controls the family-wise error rate and compares different criteria for error management.

## Key findings

- The multiple MC-SSA test effectively controls family-wise error rate.
- Proposed techniques balance type I and type II errors in signal detection.
- Comparison of different MC-SSA criteria enhances detection accuracy.

## 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.