Novel wavelet models for nonstationary time series.
Lead Research Organisation:
Lancaster University
Department Name: Mathematics and Statistics
Abstract
In statistics, if a time series is stationary - meaning that its statistical properties, like the mean, do not change over time - there is a huge wealth of methods available to analyse the time series. However, it is normally the case that a time series is nonstationary. For example, a time series might display a trend - slow, long-running behaviour in the data. Nonstationary time series arise in many diverse areas, for example finance and environmental statistics, but these types of time series are less well-studied.
The Numerical Algorithms Group (NAG), the industrial partner of the project, is a numerical software company that provides services to both industry and academia. There is an obvious demand to continually update and improve existing software libraries: statistical software for use with nonstationary time series is no exception.
The main focus of the PhD is to develop new models for nonstationary time series using a mathematical concept known as wavelets. A wavelet is a "little wave" - it oscillates up and down but only for a short time. Wavelets allow us to capture the information in a time series by examining them at different scales or frequencies. The ultimate aim of the PhD is to develop a model for nonstationary time series that can be used to estimate both the mean and variance in a time series. Such a model could then be used, for example, to test for the presence of trend in a time series.
In partnership with Numerical Algorithms Group (NAG).
The Numerical Algorithms Group (NAG), the industrial partner of the project, is a numerical software company that provides services to both industry and academia. There is an obvious demand to continually update and improve existing software libraries: statistical software for use with nonstationary time series is no exception.
The main focus of the PhD is to develop new models for nonstationary time series using a mathematical concept known as wavelets. A wavelet is a "little wave" - it oscillates up and down but only for a short time. Wavelets allow us to capture the information in a time series by examining them at different scales or frequencies. The ultimate aim of the PhD is to develop a model for nonstationary time series that can be used to estimate both the mean and variance in a time series. Such a model could then be used, for example, to test for the presence of trend in a time series.
In partnership with Numerical Algorithms Group (NAG).
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/R511997/1 | 01/10/2017 | 30/09/2022 | |||
| 1803013 | Studentship | EP/R511997/1 | 01/10/2016 | 30/09/2020 | Euan McGonigle |
| Description | The work funded through this award has now led to the completion of a PhD by the award holder. One chapter of the PhD thesis has been accepted for publication in a journal, while the other two chapters are now under review for journal publication. The work of the PhD has led to the development of new techniques for the analysis of time series data - data that is observed sequentially over time. Time series can often display several complex characteristics simultanesouly, including long term trends and short term changes. The results of the work enable the analysis of key properties of time series within a single framework, rather than separately considering these properties. This allows for a more complete analysis of the data, and enables interesting properties of the time series to be more readily discovered. |
| Exploitation Route | Software has been produced that implements the methods that have been developed during this research. This software has been shared with the industrial collaborator of the project, the Numerical Algorithms Group (NAG). At some point in the future the software may be incorporated within the NAG software libraries. |
| Sectors | Digital/Communication/Information Technologies (including Software),Other |
| Description | Numerical Algorithms Group (NAG) |
| Organisation | Numerical Algorithms Group Ltd |
| Country | United Kingdom |
| Sector | Private |
| PI Contribution | Developed new techniques for analysing nonstationary time series, which will be incorporated into the NAG software library. |
| Collaborator Contribution | Gave guidance on developing code. Financial support. |
| Impact | Ongoing. |
| Start Year | 2017 |