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Details of Grant 

EPSRC Reference: EP/K020951/1
Title: Locally Stationary Time Series and Multiscale Methods for Statistics (LuSTruM)
Principal Investigator: Nason, Professor G
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Bank of England Shell
Department: Mathematics
Organisation: University of Bristol
Scheme: EPSRC Fellowship
Starts: 01 April 2013 Ends: 31 March 2018 Value (£): 901,902
EPSRC Research Topic Classifications:
Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
30 Jan 2013 EPSRC Mathematics Fellowships Interviews - January 2013 Announced
06 Dec 2012 Mathematics Prioritisation Panel Meeting December 2012 Announced
Summary on Grant Application Form
This fellowship proposes research in time series analysis and regression. Time series

analysis is concerned with data recorded through time. Time series occur in a variety

of areas of great importance to society such as medicine (recording of vital signs),

economics and finance (GDP or share prices), the environment (air pollution),

energy (national electricity demand), and transportation (traffic flow), to name but a few.

A common way of displaying time series, often seen in the media, is via the time plot,

which plots the series' values consecutively through time enabling major features,

such as trend or seasonal effects, to be readily observed. Collectively, society needs

to ensure that series are properly collected and recorded, modelled appropriately,

to gain an understanding of their behaviour, and often predicted to estimate their

future values (forecasting).

Much real world analysis assumes that series arise from stationary models, which

permit the values of the series to change at each time, but the underlying statistics

do not change (for example, a stationary share price changes from hour to hour,

but the overall level, or mean, stays constant). It is becoming increasingly clear that

stationary models are not appropriate for many real series. For example, share price

statistics do change, sometimes exceptionally, due to sudden events such as political

upheaval or natural disasters, and often nonstationary models are appropriate and

useful alternatives.

This project intends to develop nonstationary techniques with a focus on energy and

economics applications. For example, energy companies are interested in nonstationary

models because deregulation and increasingly diverse energy sources have caused

many previously stable data sets to become less stationary and more unpredictable.

This project will create new nonstationary models intended to be more realistic, flexible and

lead to better modelling, forecasting and consequently better decision-making.

Nonstationary models can also shed light on tasks that are infeasible for stationary ones

such as ascertaining whether a series has been sampled frequently enough. We will also

research nonstationary functional models, where each observation is not a single number

but an entire curve, such as national electricity consumption recorded across a day.

Regression is concerned with the modelling of relationships between different variables

and is used extensively in the real world. Many important regression methods assume

that data have constant variance and a `bell-curve' distribution. Much real data are not

like that, but operations, such as taking each observation's square root, can make the

data fulfil those constant variance/`bell curve' assumptions, at least approximately.

Recently, a new, promising, very different, multiscale class, called the Haar-Fisz transform,

was developed. The new class works extremely well for count data and has shown some

fascinating theoretical properties, such as mimicking the well-known logarithm. This project

will investigate the intriguing theoretical underpinnings of this new class as well as develop

further methods for cleaning up noisy signals, for example, removing noise from astronomical

or low-light security images. Additionally, we will investigate regression for irregular data

using techniques that make use of multiple scales simultaneously (multiscale).

First generation multiscale methods, highly valued for purposes such as image compression

in JPEG, are not easily adapted to irregular situations. This project seeks to investigate

second generation multiscale methods, suitable for irregular data. For example, to better

estimate and control information on networks (such as identify and mitigate delays on

transport networks) or irregularly-spaced systems (such as identify regions of the genome

that are implicated in several complex diseases such as cancer.)
Key Findings
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Potential use in non-academic contexts
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Description This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Date Materialised
Sectors submitted by the Researcher
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Project URL:  
Further Information:  
Organisation Website: http://www.bris.ac.uk