Change-point detection for a transient change and high-dimensional covering
Lead Research Organisation:
CARDIFF UNIVERSITY
Department Name: Sch of Mathematics
Abstract
The Singular Spectrum Analysis (SSA) technique is a novel and powerful technique of time series analysis incorporating elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. The main purpose of SSA is to decompose an original series of observations (indexed by time) into a sum of series, so that each component in this sum can be identified as either a trend, periodic or quasi-periodic component (perhaps amplitude-modulated), or noise. This is followed by a reconstruction of the original series using selected components. SSA is a useful tool which can be used for solving the following problems: finding trends of different resolution; smoothing a noisy or complex time series; extracting seasonality components; simultaneously extracting cycles with small and large periods from a time series; extracting periodicities with varying amplitudes; simultaneously extracting complex trends and periodicities; finding structure in short time series; forecasting and detecting change-points in a time series (amongst others).
Organisations
People |
ORCID iD |
Andrey Pepelyshev (Primary Supervisor) | |
Jack Noonan (Student) |
Publications
Noonan J
(2018)
Approximations of the boundary crossing probabilities for the maximum of moving weighted sums
in Statistical Papers
Noonan J
(2019)
Approximating Shepp's constants for the Slepian process
in Statistics & Probability Letters
Noonan J
(2019)
Approximations for the boundary crossing probabilities of moving sums of normal random variables
in Communications in Statistics - Simulation and Computation
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/N509449/1 | 30/09/2016 | 29/09/2021 | |||
1934423 | Studentship | EP/N509449/1 | 30/09/2017 | 30/07/2021 | Jack Noonan |
Description | As a result of this award, several very accurate approximations have been developed for monitoring the structural stability of time series. The on-line surveillance of a time series and detecting when behaviour becomes abnormal (monitoring structural stability) is a very important field in mathematics with obvious and numerous applications in quality control. As a very general example, suppose in an industrial setting we are monitoring a piece of equipment whose proper function is essential for the end product and we are able to observe a time series based on this machinery. As soon as this machine behaves in a strange manner suggesting an issue, the end product could become damaged or faulty and is this is picked up with a change in the time series. It is therefore very important to alert the operators to the issue as soon as possible so the machine could be repaired with minimal impact. The developed approximations also have applications in hypothesis testing and approximating high dimensional integrals. As a result of this award, several probabilistic results of Lawrence Alan Shepp (a prominent American statistician) have been extended and new exact formulae have been produced. |
Exploitation Route | The outcomes of this funding have numerous applications in quality control. Under certain statistical assumptions that shall not be discussed here, the user could apply the explicit formulas developed with this funding to monitor a certain time series for particular abnormal behaviour. |
Sectors | Other |