Locally Stationary Time Series and Multiscale Methods for Statistics (LuSTruM)

Lead Research Organisation: University of Bristol
Department Name: Mathematics

Abstract

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.)

Planned Impact

The beneficiaries of the proposed research fall into two groups: direct and indirect.

The direct beneficiaries consist of Shell Research, the Bank of England and Prof. Ina Hoeschele and the wider medical team at the Virginia Bioinformatics Institute (VBI) and the Wake Forest School of Medicine: these groups are named and their interests are explained in the proposal and pathways to impact document. I intend to work closely with these beneficiaries and provide added value as described in the proposal in each case. For example, the VBI would value being able to use the "best-in-class" signal extraction benefits of wavelets (which they already use) but directly on irregularly spaced data via lifting (which we will work on); the Bank of England is interested in new approaches to financial stability and, in particular, the benefits of local stationarity for economic modelling in terms of more accurate forecasts or attempting to understand the sampling scheme that gives maximum information to such public bodies with least cost; Shell, like many other energy companies, are interested in many aspects of nonstationarity particularly the multivariate situation in a world where massively high-dimensional data collection is a reality. Specific aspects of the project, of interest to particular partners, is described in the Case for Support.

Another important group of indirect beneficiaries are the energy companies that I am already working with on a separate EPSRC grant (LETS) funded by the Mathematics and Energy programme. These energy companies are EDF (Paris), Vattenfall and GL Garrad Hassan. The current proposal and the Maths/Energy proposal are supportive and complementary in the sense that the latter has a narrower focus on energy-related issues, and also a small amount of my time. However, it is likely that new developments in the current proposal will also be of interest to these energy partners (for example, continuous time nonstationary processes, new regression methods) and we would seek to continue any productive LETS interactions as part of this proposal after LETS finishes in March 2015. On the (statistical) economics side we are building relationships with Antonis Michis at the Central Bank of Cyprus who has already worked on applications of multiscale methods to economics.

Another key group of beneficiaries will be the RAs themselves and, in particular, those organisations that later employ them or work with them. I have a strong record of developing excellent people and helping them start productive academic and non-academic careers. Many of these people are themselves further creating and innovating in cognate statistical areas and this is a powerful way of initiating impact.

Another constituency are those that will take ideas and, particularly, software developed by the proposed research. Much of what we develop is generic and can be used in many application areas where time series or regression problems occur. It is difficult to quantify precisely the number and identity of such groups who might use our work. However, from our experience with earlier software, such as WaveThresh, it is clear that the distribution and use of such free software is very wide, both in terms of research publications that use such software and in direct communication with users in banking (Bank of America, Reserve Bank of New Zealand), government (Centers for Disease Control, NIMR-MRC, NIST, Los Alamos National Lab) and industry (Detica, Merck, AC Nielsen, Plant Automation Services, Siemens, Unilever) and a large number in academic institutions.

Overall, we intend our impact to be specific (with the partners mentioned) and generic/widespread as a result of our publications and software. Through these routes we intend to have a positive impact on national/global economic competitiveness, increasing the efficiency of analysis, forecasting and hence policy and enhancing health through our bioinformatics work.

Publications

10 25 50
 
Description New methods for the analysis of locally stationary time series. This includes new methods for tests of stationarity, new methods for forecasting, new methods for assessing sampling rate, checking aliasing, analysis of network time series. Various software packages produced and uploaded.
Exploitation Route Most of our methods are statistical methodologies which can be used by a wide variety of users of time series.
Sectors Aerospace, Defence and Marine,Agriculture, Food and Drink,Chemicals,Communities and Social Services/Policy,Construction,Creative Economy,Digital/Communication/Information Technologies (including Software),Education,Electronics,Energy,Environment,Financial Services, and Management Consultancy,Healthcare,Leisure Activities, including Sports, Recreation and Tourism,Government, Democracy and Justice,Manufacturing, including Industrial Biotechology,Culture, Heritage, Museums and Collections,Pharmace

URL http://www.maths.bris.ac.uk/~guy/
 
Description Office for National Statistics 
Organisation Office for National Statistics
Country United Kingdom 
Sector Public 
PI Contribution Developed/developing new methods for finding optimal sampling rate for official statistics and also methods for analysing web-scraped price data.
Collaborator Contribution Helped with the research, provided data/examples
Impact GPN, Powell, B., Elliott, D. and Smith, P. (2017) Should We Sample a Time Series More Frequently? Decision Support via Multirate Spectrum Estimation (With Discussion). J. Roy. Statist. Soc. A, 180, 353--407. Powell, B., Nason, G.P., Elliott, D. Mayhew, M., Davies, J. and Winton, J. (2018) Tracking and modelling prices using web-scraped price microdata: toward automated daily CPI forecasting. J. Roy. Statist. Soc., A. 181, 737--756.
Start Year 2013
 
Title BootWPTOS 
Description Test Stationarity using Bootstrap Wavelet Packet Tests 
Type Of Technology Software 
Year Produced 2016 
Open Source License? Yes  
Impact N/A 
URL https://cran.r-project.org/web/packages/BootWPTOS/index.html
 
Title Software - GNAR 
Description Software to model and fit generalized network autoregressive processes. Joint with Kathryn Leeming, Matt Nunes and Marina Knight 
Type Of Technology Software 
Year Produced 2018 
Open Source License? Yes  
Impact None yet. 
URL https://cran.r-project.org/web/packages/GNAR/index.html
 
Title Software - PP3 
Description Software to compute three-dimensional projection pursuit solutions of a multivariate data set. This was joint work with Robin Sibson. 
Type Of Technology Software 
Year Produced 2018 
Open Source License? Yes  
Impact None known at this point 
URL https://cran.r-project.org/web/packages/PP3/index.html
 
Title hwwntest 
Description Freeware R software to carry out tests of global white noise 
Type Of Technology Software 
Year Produced 2015 
Open Source License? Yes  
Impact Software 
URL https://cran.r-project.org/web/packages/hwwntest/index.html
 
Title liftLRD 
Description Wavelet Lifting Estimators of the Hurst Exponent for Regularly and Irregularly Sampled Time Series 
Type Of Technology Software 
Year Produced 2016 
Open Source License? Yes  
Impact N/A 
URL https://cran.r-project.org/web/packages/liftLRD/index.html
 
Title locits 
Description New test of second-order stationarity and confidence intervals for localized autocovariance 
Type Of Technology Software 
Year Produced 2013 
Open Source License? Yes  
Impact Several users in economics and other areas 
URL http://cran.r-project.org/web/packages/locits/index.html
 
Title regspec 
Description Non-Parametric Bayesian Spectrum Estimation for Multirate Data 
Type Of Technology Software 
Year Produced 2016 
Open Source License? Yes  
Impact Freeware package uploaded to CRAN 
URL https://cran.r-project.org/web/packages/regspec/index.html
 
Description Birkbeck Seminar 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact An overview of non-stationary spatio-temporal modelling of natural events. Department of Economics, Mathematics and Statistics, Birkbeck given by SD
Year(s) Of Engagement Activity 2016
 
Description CMStatistics Conference: Non-stationary and high-dimensionality in time series analysis 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact International research conference
Year(s) Of Engagement Activity 2017
 
Description Invited Talk Royal Statistical Society International Conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Policymakers/politicians
Results and Impact Invited Talk, Royal Statistical Society International Conference, Newcastle.
Year(s) Of Engagement Activity 2013
 
Description Invited Talk at COMPSTAT International Conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Bayesian nonparametric spectral density estimation: with application to under-sampled time series, Invited Talk at COMPSTAT 2014 conference, Geneva, Switzerland
Year(s) Of Engagement Activity 2014
 
Description Invited Talk at Joint Statistical Meetings 2017 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Optimising Inflation Forecasts based on Web-Scraped price data, Topic Contributed Talk, JSM, Baltimore, 2017
Year(s) Of Engagement Activity 2017
 
Description Invited Talk, CMStatistics 2015 International Conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact CMStatistics 2015, 8th International Conference of the ERCIM Working Group on Computational and Methodological Statistics on 'Robust and Efficient Regression', Senate House, University of London, by GPN
Year(s) Of Engagement Activity 2015
 
Description Invited Talk, Howell Tong 70th Birthday celebration 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Analysis and forecasting of locally stationary time series, Invited Talk, London School of Economics
Year(s) Of Engagement Activity 2014
URL http://www.lse.ac.uk/statistics/events/SpecialEventsandConferences/Nonlinear-time-series-analysis/Ho...
 
Description Invited Talk, Office for National Statistics, Time Series Workshop, RSS HQ, London 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Time Series Workshop, talks + interaction activities
Year(s) Of Engagement Activity 2015
 
Description Invited Talk, STOR-i workshop, Lancaster 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Workshop on Analysis of nonstationary multivariate time series, STOR-i Workshop, Lancaster University, UK.
Year(s) Of Engagement Activity 2016
 
Description Invited Talk, Shanghai Centre for Mathematical Sciences 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact 'Some Experiments in Network Time Series', Workshop on Statistical Network and High-Dimensional Data Analysis: Theory and Application, Shanghai Centre for Mathematical Sciences, Shanghai, China.
Year(s) Of Engagement Activity 2016
 
Description Invited Talk: Centre International de Recontres Mathematiques, Luminy, France 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Policymakers/politicians
Results and Impact Invited Talk by GPN
Year(s) Of Engagement Activity 2016
URL http://library.cirm-math.fr/ListRecord.htm?list=request&table=3&idinlist=0&NumReq=112&cluster_1=naso...
 
Description Invited Talk: Maurice Priestley Commemoration Day 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Policymakers/politicians
Results and Impact Talk on wavelet packet processes, Maurice Priestley Commemoration Event, Manchester University
Year(s) Of Engagement Activity 2013
URL http://www.maths.manchester.ac.uk/~gb/events/Priestley/MauricePriestley.html
 
Description Invited talk at Royal Statistical Society International Conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Should we sample more frequently? Quantifying the cost of under- or over-sampling via a stationary process's spectral density: Invited talk at Royal Statistical Society International Conference 2015, Exeter by BP
Year(s) Of Engagement Activity 2015
 
Description Invited talk at Time Series in official Statistics workshop, London 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Policymakers/politicians
Results and Impact Time Series in Official Statistics Workshop, London, organised by the ONS.
Year(s) Of Engagement Activity 2017
 
Description Keynote Talk, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Keynote Talk
Year(s) Of Engagement Activity 2014
URL http://newton.cam.ac.uk/seminar/20140113153016301
 
Description Network Time Series, Alan Turing Institute Scoping Workshop 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Scoping Workshop
Year(s) Of Engagement Activity 2015
 
Description Plenary Lecture, Royal Statistical Society Conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Plenary Lecture at Royal Statistical Society Conference, 2016 on "Should we sample a time series more frequently?, by GPN and BP
Year(s) Of Engagement Activity 2016
 
Description Presentation, Joint Statistical Meetings, Chicago, 2016. 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Contributed presentation JSM 2016 on "Can we rank a time series for non-stationarity? " by SD
Year(s) Of Engagement Activity 2016
 
Description Research Presentation at European Meeting of Statisticians, Helsinki 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact European Meeting of Statisticians Invited Talk, many interesting discussions + future work discussed
Year(s) Of Engagement Activity 2017
 
Description Research Presentation given to US Census Bureau by BP 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Improving Inflation Forecasts Based on Web-Scraped Price Data to the Center for Statistical Research and Methodology Seminar, US Census Bureau, Washington
Year(s) Of Engagement Activity 2017
 
Description Research Seminar Talk at Southampton University 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Policymakers/politicians
Results and Impact Research seminar on `A test for aliasing'
Year(s) Of Engagement Activity 2018
 
Description Research Talk at the Alan Turing Institute 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Research talk at the Alan Turing Institute on Network Time Series
Year(s) Of Engagement Activity 2018
 
Description Research presentation at MRC Biostatistics Unit, Cambridge 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Talk to MRC Biostatistics unit, a mixed audience of statisticians and medical associates.
Year(s) Of Engagement Activity 2017
 
Description Seminar Glasgow 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Estimation of spatio-temporal parameters in spectral Domain. School of Mathematics and Statistics, University of Glasgow by SD
Year(s) Of Engagement Activity 2016
 
Description Seminar Lancaster Uni 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Estimation of spatio-temporal parameters in spectral Domain. School of Mathematics, Lancaster University by SD
Year(s) Of Engagement Activity 2015
 
Description Seminar talk, Edinburgh 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Model-based inflation estimation with application to web-scraped data, seminar talk at University of Edinburgh by BP
Year(s) Of Engagement Activity 2016
 
Description Seminar, School of Mathematics and Statistics, University of Melbourne 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Seminar delivered by Sourav Das on Modelling Spatio-Temporal Data
Year(s) Of Engagement Activity 2017
 
Description Talk at TSIMF Workshop on "Complex Time Series Modelling and Forecasting", Sanya China 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact International Research Workshop
Year(s) Of Engagement Activity 2018
 
Description Talk, Royal Statistical Society International Conference, Manchester, 2016 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Policymakers/politicians
Results and Impact Talk "Can we rank a time series for non-stationarity? " by SD
Year(s) Of Engagement Activity 2016
 
Description Talk, University of Southampton 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Model-based inflation estimation with application to web-scraped data, seminar talk at Uni. Southampton
Year(s) Of Engagement Activity 2016
 
Description Time Series in Official Statistics Workshop, Presentation 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Modelling high-frequency on-line price data, presentation by BP and workshop meetings/discussions
Year(s) Of Engagement Activity 2017
 
Description UCL Big Data Conference 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Research presentation on network time series to UCL Big Data Conference
Year(s) Of Engagement Activity 2017
URL http://www.ucl.ac.uk/bigdata-theory/
 
Description University of Lancaster Seminar Series 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Have I been sampling this time series frequently enough?, University of Lancaster, Statistics: Nonstationary Time Series and Changepoint Seminar Series by BP
Year(s) Of Engagement Activity 2015
 
Description `Calculating the CPI from web-scraped data', Talk, University of York 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Policymakers/politicians
Results and Impact `Calculating the CPI from web-scraped data' by BP
Year(s) Of Engagement Activity 2017