Change-point detection for high-dimensional time series with nonstationarities

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.

Firstly, academics working in change-point analysis for high-dimensional time series will benefit from the novel theoretical and methodological development furnished by this proposal. Also, outside this immediate circle of beneficiaries, there are academics working on a wide range of inference and estimation problems concerning high-dimensional time series for whom, the successful delivery of Work Package (C) will provide a new re-sampling method that enables rigorous statistical inference and efficient estimation of fundamental quantities involved in modelling such data.

In addition, the proposed research has the potential for generating societal and economic impacts, by facilitating progress across a wide range of disciplines where high-dimensional time series data is collected and analysed. For example, in energy companies, a small improvement in load forecasting can bring in substantial benefits in reducing production costs and increasing trading advantages. Therefore it is strategically important to identify any structural changes in the multi-channel, high-dimensional time series data collected from their customers, prior to employing forecasting models based on the stationarity assumption. Dr. Yannig Goude (an expert researcher-project manager at EDF R&D in Paris) has expressed interest in this proposal, and we intend to instigate a collaborative project where the newly developed methodologies from this proposal will be applied to address the needs in electricity load modelling.

Healthcare is another sector where health, medical and social data of high complexity is increasingly being generated. The proposed methodologies will be applicable to detect clinically important features as change-points in patient records, thus impacting the researchers in the Healthcare Technologies theme via sub-themes "Optimising Treatment" and "Transforming Community Health and Care". Also, the influence of detecting shifts in monetary regimes on improving the quality of inflation forecasts, and thus on macroeconomic policy-making, has been noted by the researchers and the advisers at the Bank of England (Groen et al., 2008). Hence, these methods have close bearing on the grand challenge areas in the Digital Economy theme ("New Economic Models"). We will distribute software implementations of our methodologies, in order to enhance their accessibility and widen the group of potential beneficiaries.

References
Groen, J., Kapetanios, G., and Price, S. (2008), "Real time evaluation of Inflation Report and Greenbook forecasts for inflation and growth," Bank of England Working Paper No. 354.