| EPSRC Reference: |
EP/N024435/1 |
| Title: |
Change-point detection for high-dimensional time series with nonstationarities |
| Principal Investigator: |
Cho, Dr HH |
| Other Investigators: |
|
| Researcher Co-Investigators: |
|
| Project Partners: |
|
| Department: |
Mathematics |
| Organisation: |
University of Bristol |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
25 June 2016 |
Ends: |
24 December 2017 |
Value (£): |
98,470
|
| EPSRC Research Topic Classifications: |
| Non-linear Systems Mathematics |
Statistics & Appl. Probability |
|
| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
|
|
| Related Grants: |
|
| Panel History: |
|
|
Summary on Grant Application Form |
Time series data are encountered in many areas such as finance, economics, medicine, engineering, natural and social sciences. The fundamental objectives of time series analysis are (i) to describe stochastic structure of the observed time series by identifying and fitting an appropriate model, and (ii) to predict the future behaviour by using the information extracted from current and past observations. In practical applications, the assumption of stationarity is commonly made: that the stochastic properties of time series data are invariant over time. However, real-life time series often exhibit nonstationarities and this poses as a growing problem, since the use of standard modelling and estimation techniques for stationary processes is inappropriate and may even result in misleading models and forecasts for such data.
Piecewise stationarity is one of the simplest forms of departure from stationarity, where some stochastic properties are modelled as varying over time in a piecewise constant manner. That is, the process is regarded to be stationary between any two adjacent structural change-points. Under the assumption of piecewise stationarity, multiple change-point detection provides useful insights with regards to the estimated change-points, as well as enabling prediction of future values. However, a challenge which many areas in modern statistics commonly face is that, due to technological advances, observed datasets are increasingly being recorded in higher dimensions as well as larger volumes.
The abundance of high-dimensional observations over time in many fields calls for new tools in time series analysis. Motivated by routinely observed nonstationarities in large time series data, change-point detection in high-dimensional time series has received steadily growing attention in recent years. Still, there are several challenging research questions which need to be addressed for both theoretical and methodological advances in this area, and the main goal of this proposal is to provide solutions to such open problems.
More specifically, one key objective is to develop a change-point detection methodology which not only detects and locates change-points over time, but also identifies those components of high-dimensional data that undergo the changes. It is readily envisaged that such information will play an important role in interpreting the detected change-points. Also, classical change-point analysis chiefly concerns with the detection of abrupt, jump-like changes in time-varying stochastic properties. In contrast, the proposed methodology aims at reflecting real-life applications more efficiently by allowing for changes that are smooth and gradual. Finally, the methodology will be equipped with a bootstrap technique that is applicable to re-sample high-dimensional time series data and permits rigorous inference on the detected change-points, and thus enables users to draw meaningful conclusions on the structure of the observed time series.
|
|
Key Findings |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Potential use in non-academic contexts |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
|
Impacts |
|
| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
|
| Date Materialised |
|
|
|
|
Sectors submitted by the Researcher |
|
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
|
| Project URL: |
|
| Further Information: |
|
| Organisation Website: |
http://www.bris.ac.uk |