The Analysis of Non-stationary Time Series in Economics and Finance: Co-integration, Trend Breaks, and Mixed Frequency Data

Lead Research Organisation: University of Essex
Department Name: Essex Business School

Abstract

Macroeconomic and financial time series are typically non-stationary (or unstable), in that their means, variances and autocovariances evolve over time, such that standard multivariate time series models can only be validly applied to the changes in these variables. Such models, however, contain no information about any long run relationships between the series, as are often predicted by economic or finance theory. A solution is provided by co-integration analysis which recognises that certain combinations of the variables are stationary (stable). A key example is term structure data, where it is often found that while individual interest rates appear to be unstable, the spreads between the rates appear stable.

Practical co-integration analysis is complicated by the fact that economies periodically undergo episodes of structural change, such as stock market crashes or changes in government regime/policy. Empirical evidence suggests that these episodes often manifest themselves in the form of multiple changes in the underlying deterministic trend component of the variables and/or changes in the volatility of the unanticipated random shocks. Extant co-integration tests can result in misleading inference regarding the presence or otherwise of long run relationships between the variables when these forms of structural change are present. This will typically result in misspecified econometric models with poor forecasting ability. It is therefore important to develop new co-integration tests which can deliver reliable inference in such environments. Doing so constitutes the first part of this project and will involve the development of a new simulation-based (bootstrap) procedure.

In light of the recent financial crisis, attention has increasingly focused on understanding the interactions between the macroeconomy and the financial sector. To do so effectively, econometric methods are needed that are capable of handling the mismatch between the frequencies at which data on the financial sector (eg exchange rates, stock prices) and the macroeconomy (eg GDP) become available, and this constitutes the second part of the project. While financial data can be observed at very high frequencies, macroeconomic data are typically available only monthly at best. The vast majority of methods for modelling multivariate time series assume a common sampling frequency; this typically entails discarding information in the high frequency data by converting it to the lowest frequency. However, high frequency financial data contains information that can affect the future time path of the low frequency data, and its utilisation can enable policymakers to act promptly prior to the macroeconomic data becoming available. For example, a financial crisis can be observed long before its effects on GDP are observed, but the ability to predict what those effects might be, using an econometric model capable of dealing with mixed frequency data, can be an important aid to policy making. Methods to allow for structural changes when dealing with mixed frequency data will also be considered.

The theoretical development, to be conducted using large sample econometric theory, will exploit the expertise and experience of the applicants. Taylor has already examined the behaviour of non-constant volatility on co-integration tests which do not allow for structural change in the trend. Chambers has recently developed methods of combining mixed frequency data that preserve the underlying relationships between the series and has also analysed co-integrated systems under temporal aggregation. This project will build on these foundations.

The practical relevance of the theoretical results will be explored using simulation experiments. We will also provide clear guidance to empirical researchers, through worked examples on key international datasets, and make freely available computer programs, to facilitate the implementation of the new techniques.

Planned Impact

Beyond traditional university-based researchers, beneficiaries will include those in research divisions of central banks, government treasuries and federal reserve banks of the US, as well as macroeconomic modellers, forecasters and policy makers at institutions such as the World Bank, International Monetary Fund and the Organisation for Economic Co-operation and Development.

As discussed in the Objectives and Academic Beneficiaries sections, the expected impact to these researchers will take the form of the provision of new techniques for multivariate time series modelling. Principally, the proposed methods are aimed at enabling practitioners to better determine the properties of key macroeconomic and financial variables, and to provide more reliable and more widely applicable foundations for modelling and forecasting with such data. Since the effectiveness of models, their associated forecasts and policy predictions are directly contingent on the quality of the inference provided by these phases of the analysis, it is vital that robust and reliable multivariate procedures, such as the ones we plan to develop in this project, are made available to practitioners.

The PI is Director of the Essex Centre for Financial Econometrics and the Co-I is the Deputy Director. This provides additional opportunities for disseminating the results from this project to the anticipated beneficiaries. These will include an on-line open-access discussion paper series, an on-going occasional seminar series, and an annual conference. Research papers from the project will be made available through the discussion paper series while the associated computer routines will also be made available (in both Gauss and Ox format, the latter being open-source) through the Centre's website in order that others can apply the methods to their own data.

The Centre also has good links with research divisions of central banks: external fellows include researchers at the Bank of England (Professors Simon Price and Martin Weale), the Bank of Italy (Dr Fabio Busetti) and the Bank of Portugal (Dr Paulo Rodrigues). Dissemination will build on these links, with papers from the project also sent to individual central bank researchers and offered to workshops they organise.

A number of the PI's earlier contributions on co-integration methods (see publications 7, 8 and 9 on Taylor's CV) have been integrated into the latest release of the popular econometric software package, Microfit. We will explore the possibility of incorporating the procedures developed in this project into widely-used econometrics software packages in order to increase impact among practitioners.

We will run two one-day workshops at Essex based around the themes of the research project. Each will consist of papers given by four invited speakers, at least two of whom will be international, and one of the Investigators. Researchers from outside the academic community will be invited to attend and, where they have relevant research, to present at the workshop. In addition, project papers will be submitted to two regional meetings (Europe and either the U.S. or Australasia) of the Econometric Society (the leading international econometric conferences) and two other national or international conferences including the 2015 and/or 2016 International Conference on Computational and Financial Econometrics (the largest in its field).

The project will also provide a platform for mentoring existing and new PhD and MSc students at Essex.
 
Description 1. Development of a rigorous econometric methodology for modelling the long and short run relationships between macroeconomic and/or financial variables allowing for episodes of structural change in the economy.

This first achievement has developed new techniques, based either on the industry-standard co-integrated vector autoregressive [CVAR] model or fractionally integrated models, to enable practitioners to perform reliable empirical econometric analysis and forecasting of series which undergo structural breaks at unknown points in time in their trend component. New estimators of the number and timing of such breaks are developed and incorporated into the modelling procedure.
We have also developed the statistical theory for consistent estimation of the timing and number of trend breaks in data which also display within-sample variation in the level of volatility. This new statistical theory has been employed to extend the reach of the aforementioned new techniques to allow for both trend and volatility regime changes in the CVAR framework, using novel bootstrap methods.
The research from this first achievement has been widely presented at national and international meetings held by universities and central banks and at a workshop at Essex. The research will result in four publications in leading journals. Computer code to implement the methodology, together with data examples, and working paper versions are available at http://privatewww.essex.ac.uk/~rtaylor/esrc/default.htm

2. Development of methods for incorporating mixed frequency and mixed sample data in dynamic models of long run equilibrium subject to temporal aggregation

The second achievement has developed methods to enable practitioners to use mixed frequency and mixed sample data in the estimation and analysis of dynamic models that are subject to temporal aggregation. Exact discrete time representations corresponding to continuous time models are derived for a wide range of stationary and nonstationary (including cointegrated) systems that contain stock or flow variables (or mixtures of both) observed at different frequencies. Statistical procedures for estimating and testing long run equilibrium relationships with mixed frequency and mixed sample data have also been developed and have the advantage that only weak assumptions are required for the dynamic interactions within the system. In addition the new techniques have been applied to areas of interest empirically in economics and finance.

The research from this second achievement has been disseminated at national and international seminars and conferences and a workshop on this topic was hosted at the University of Essex. The research will result in three publications in leading journals and a survey chapter in an international interdisciplinary book on continuous time methods in the behavioural and social sciences. Computer code and working papers are available at http://privatewww.essex.ac.uk/~mchamb/research.html
Exploitation Route The research produced in this project is of benefit to theoretical researchers and researchers in applied econometrics, empirical macroeconomics and empirical finance in academia and also academic-related researchers in government institutions such as central banks and practitioners and researchers in private sector economic and financial consultancy firms. For theoretical researchers, we have provided significant advances in the corpus of large sample theory available for analysing multivariate time series methods measured at different data frequencies and subject to environmental structural change. Moreover, the methodology we have established lays important foundations needed for further methodological developments in this area. For the other beneficiaries, our research has delivered significant and novel advancements in directions that are important for empirical practice previously lacking in the literature. In particular, we have developed a rigorous toolbox of statistical methods which can be used by academics and practitioners to analyse the properties and inter-relationships between economic and financial data which are subject to structural change in both their underlying trend and volatility and where the data series under investigation may be observed at different frequencies. We are also in discussion with leading software providers to include statistical procedures from the project in established econometric software packages.
Sectors Education,Financial Services, and Management Consultancy

URL http://privatewww.essex.ac.uk/~rtaylor/esrc/default.htm
 
Description As noted in the Pathways to Impact section of our application, the impact from research in this project was primarily oriented towards beneficiaries in the academic research community. Notwithstanding this, we did outline mechanisms in our Pathways to Impact by which we hoped to potentially gain impact beyond the purely academic sphere, including the presentation of our work at two workshops we organised at Essex around the themes of the research which involved participants from central banks and other non-academic institutions. The first of these workshops was held in July 2016 on the theme `Co-integration, Multivariate Time Series Modelling and Structural Change' with contributions from a number of researchers from non-academic institutions including Martin Weale and Ivan Petrella from the Bank of England and Andreas Beyer from the European Central Bank. The second workshop was held in July 2017 under the title `Econometric Modelling with Mixed Frequency and Aggregated Data' and invited speakers included Peter Zadrozny of the U.S. Government Bureau of Labor Statistics and Claudia Foroni of the Deutsche Bundesbank. Taylor also presented research from the project at a conference organised and run by the Bank of England titled `Time Variation and NonLinear Models in Econometrics and Macroeconomics' in June 2016. All three events provided excellent opportunities for further discussion with non-academic attendees and a number of informal conversations were had where interest in using or at least knowing more about the work from the project was indicated. As a result of interactions following on from the second Essex workshop, Chambers and Zadrozny are currently co-guest editing a special issue of the Journal of Time Series Analysis around the theme of the workshop with papers from both the academic and non-academic attendees being peer-reviewed for inclusion. Taylor also gave a keynote invited lecture to the `Conference on New Trends and Developments in Econometrics' organised and run by the Bank of Portugal on June 3-4 2016. Taylor's keynote presentation was titled `Testing for Cointegration Rank in Heteroskedastic VAR Models in the presence of possible Trend Breaks', which included material from the paper, `Tests of the Co-integration Rank in VAR Models in the Presence of a Possible Break in Trend at an Unknown Point' (published as an output from this award under gold open access in the Journal of Econometrics DOI https://doi.org/10.1016/j.jeconom.2016.02.010 ). During the conference discussions took place between Taylor and staff working in the Structural Studies Group of the Bank of Portugal regarding how the methodology discussed in Taylor's keynote presentation and the aforementioned journal publication could be used in their work. Subsequently, the econometric methodology developed in the paper has been implemented into the toolkit of econometric and statistical methods used by the Structural Studies Group and has been used in connection with its work on the monitoring and forecasting of house price determinants.
First Year Of Impact 2017
Sector Financial Services, and Management Consultancy
Impact Types Economic,Policy & public services

 
Description Chambers included material from the research developed on the grant in a two-hour lecture entitled "Continuous Time Models" for an MSc/MRes module, EC965 Time Series Econometrics, at Essex in 2016/2017.
Geographic Reach Local/Municipal/Regional 
Policy Influence Type Influenced training of practitioners or researchers
 
Description Taylor incluced material from the research developed on the grant in lectures under the module title "Identifying and Dealing with Structural Breaks in Economic Time Series" he delivered as part of the PhD training course, EC958 - Research Topics in Applied Economics , run by the Economics Department at Essex to PhD students.
Geographic Reach Local/Municipal/Regional 
Policy Influence Type Influenced training of practitioners or researchers
 
Title A Gauss program to implement the methods developed in the paper "Tests of the Co-integration Rank in VAR Models in the Presence of a Possible Break in Trend at an Unknown Point", by David Harris, Stephen Leybourne and Robert Taylor 
Description A Gauss program to implement the methods developed in the paper "Tests of the Co-integration Rank in VAR Models in the Presence of a Possible Break in Trend at an Unknown Point", by David Harris, Stephen Leybourne and Robert Taylor, published as: Harris D, Leybourne S, Taylor A. (2016). Tests of the co-integration rank in VAR models in the presence of a possible break in trend at an unknown point. Journal of Econometrics, 192 (2), pp. 451-467. DOI: 10.1016/j.jeconom.2016.02.010. PubMed: This program can be run as freeware by using the OxGauss facility in the freeware version of the Ox package available from http://www.doornik.com/products.html . 
Type Of Technology Software 
Year Produced 2016 
Impact Not known 
URL http://rtaylor-essex.droppages.com/esrc/VECMBreaks.g
 
Description Amsterdam Bootstrap Workshop (2015) paper presentation by Robert Taylor 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor presented his work on `Tests of the Co-integration Rank in VAR Models in the Presence of a Possible Break in Trend at an Unknown Point' at the Bootstrap Workshop, held at the Amsterdam School of Economics, Universty of Amsterdam, 18-19 November 2015.

The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2015
 
Description Bank of England Workshop on `Time Variation and NonLinear Models in Econometrics and Macroeconomics' paper presentation by Robert Taylor 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor gave a presentation of his work under the title `Tests of the Cointegration Rank in VAR Models in the Presence of a Possible Break in Trend at an Unknown Point' at a two-day workshop on `Time Variation and NonLinear Models in Econometrics and Macroeconomics' run by and held at the Bank of England, London, June 9-10, 2016.

The talk attracted an audience of both academic and academic-related colleagues, the latter from central bank positions. The talk sparked interest and a nu
Year(s) Of Engagement Activity 2016
URL https://www.essex.ac.uk/ebs/documents/ECFE-workshop-2016.pdf
 
Description CFE 2017 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I gave a talk entitled "Frequency Domain Estimation of Cointegrating Vectors with Mixed Frequency and Mixed Sample Data" in the session on "Co-integration, trend breaks, and mixed frequency data" at the 11th International Conference on Computational and Financial Econometrics, Senate House, University of London, 17 December, 2017.
Year(s) Of Engagement Activity 2017
URL http://cfenetwork.org/CFE2017/index.php
 
Description Conference Presentation (CFE 2015) by Robert Taylor 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Type Of Presentation paper presentation
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor presented his work on `Tests of the Co-integration Rank in VAR Models in the Presence of a Possible Break in Trend at an Unknown Point' at the 9th International Conference on Computational and Financial Econometrics, Senate House, University of London, UK, 12-14 December 2015.

The talk attracted a large audience of both academic and academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.

Many researchers asked Robert Taylor for his paper after the talk and expressed considerable interest in using the new methodological tools for testing for co-integration in the presence of trend breaks that he outlined.
Year(s) Of Engagement Activity 2015
URL http://cfenetwork.org/CFE2015/fullprogramme.php
 
Description Conference on `New Trends and Developments in Econometrics', Bank of Portugal, Keynote Presentation by Robert Taylor 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor gave a keynote presentation under the title `Testing for Cointegration Rank in Heteroskedsastic VAR Models in the presence of possible Trend Breaks' at the Conference on New Trends and Developments in Econometrics, held by the Bank of Portugal in Lisbon, June 3-4 2016.

The talk attracted a large audience of both academic and academic-related colleagues, the latter from central bank positions. The talk sparked interest and a number of questions. Many useful discussions took
Year(s) Of Engagement Activity 2016
URL http://www.bportugal.pt/en-US/EstudosEconomicos/Conferencias/Pages/2016Econometrics.aspx
 
Description Conference presentation (CFE 2015) by Marcus Chambers 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I presented my work on "The Estimation of Continuous Time Models with Mixed Frequency Data" at the 9th International Conference on Computational and Financial Econometrics, Senate House, University of London, UK, 12-14 December 2015
Year(s) Of Engagement Activity 2015
 
Description Conference presentation by Robert Taylor at an international conference in honour of Professor Maxwell King held at Monash University, Australia, December 8-9th 2016. 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor presented the paper "Testing for Co-integration Rank in VAR Models allowing for Multiple Breaks in Trend and Variance with an Application to cay" at an international conference in honour of Professor Maxwell King held at Monash University, Australia, December 8-9th 2016. The talk attracted a large audience of both academic and academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2016
URL https://business.monash.edu/events/max-king-conference
 
Description Conference presentation by Robert Taylor at the joint meeting of the European Economic Association and the Econometric Society European Meeting 2016 in Geneva 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor presented his work on `Breakpoint Estimation, Heteroskedasticity and Unit Root Tests' at the joint 31st Annual Congress of the European Economic Association and 69th European Meeting of the Econometric Society held in Geneva 22-26 August 2016.

The talk attracted a large audience of both academic and academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2016
URL http://www.eea-esem-congresses.org/
 
Description Department seminar (Southampton) by Marcus Chambers 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact The seminar took place on 1 June 2016 and the title was "Econometrics with Mixed Frequency Data". The seminar was attended by approximately 15 academics and postgraduate students and helpful feedback was received.
Year(s) Of Engagement Activity 2016
 
Description Department seminar (UEA) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact This was a presentation in UEA's weekly Economics seminar series on 17 November 2016. My talk was entitled "Econometrics with Mixed Frequency Data".
Year(s) Of Engagement Activity 2016
 
Description Departmental Seminar (Economics and Finance Seminar Series, University of Tasmania) given by Robert Taylor 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Robert Taylor presented the paper `Tests of the Co-integration Rank in VAR Models in the Presence of a Possible Break in Trend at an Unknown Point' in the Economics and Finance Seminar Series at the University of Tasmania (Tasmanian School of Business and Economics) on Monday 1st February 2016. The talk was attended by academic staff and PhD students in the Department. Useful feedback was received from the audience and it sparked some interesting conversation with both staff and some of the PhD students.
Year(s) Of Engagement Activity 2016
URL http://www.utas.edu.au/business-and-economics/research/research-seminars/seminar-series
 
Description Departmental Seminar (Economics, Manchester) given by Robert Taylor 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact Robert Taylor presented the paper `Tests of the Co-integration Rank in VAR Models in the Presence of a Possible Break in Trend at an Unknown Point' at the Manchester Economics Department Seminar on Thursday 26th November 2015. The talk was attended by academic staff and PhD students in the Department. Useful feedback was received from the audience and it sparked some interesting conversation with both staff and some of the PhD students.

Discussions with PhD students very productive.
Year(s) Of Engagement Activity 2015
URL http://www.socialsciences.manchester.ac.uk/subjects/economics/our-research/workshop-and-seminars/eco...
 
Description Departmental seminar (Reading) by Marcus Chambers 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact I presented my work on "The Estimation of Continuous Time Models with Mixed Frequency Data" to an academic audience in the Department of Economics at the University of Reading.
Year(s) Of Engagement Activity 2015
 
Description ESRC Workshop 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I organised a workshop, entitled "Econometric Modelling with Mixed Frequency and Aggregated Data", held at Wivenhoe House Hotel, University of Essex, 5 July 2017. The purpose was to bring together an international group of experts in this field to present their work to an audience of academics and postgraduate students. As a result of the workshop a special issue of the Journal of Time Series Analysis is being prepared on this topic.
Year(s) Of Engagement Activity 2017
URL http://marcuschambers.droppages.com/files/Workshop_programme.pdf
 
Description One-day workshop on the theme "Co-integration, Multivariate Time Series Modelling and Structural Change" on Monday July 11th 2016. 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact A one-day workshop on the theme "Co-integration, Multivariate Time Series Modelling and Structural Change" was held at Essex Business School on Monday July 11th 2016. Attendees at the event came from both the university sector (both UK and international universities) and from the Bank of England and the European Central Bank. Presenters at the workshop included Martin Weale (Bank of England), Ivan Petralla (Bank of England) and Andreas Beyer (European Central Bank). A link to the programme of the event is given in the URL box below. The workshop was intensive and highly productive. In particular, very useful interactions and discussions were held between the academic and academic-related (central bank researchers) attendees.
Year(s) Of Engagement Activity 2016
URL http://rtaylor-essex.droppages.com/PDFs/ESRC%20draft%20prgramme.pdf
 
Description Robert Taylor delivered the paper "Testing for Cointegration Rank in VAR Models allowing for Multiple Breaks in Trend and Variance" at an international symposium entitled "Advances in Time Series and Macroeconometrics" held at the Department of Economics, University of York, 15-16 June 2017. 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor delivered the paper "Testing for Cointegration Rank in VAR Models allowing for Multiple Breaks in Trend and Variance" at an international symposium entitled "Advances in Time Series and Macroeconometrics" held at the Department of Economics, University of York, 15-16 June 2017. The talk attracted a large audience of both academic and academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2017
URL https://www.york.ac.uk/media/economics/YES10.pdf
 
Description Robert Taylor delivered the paper "Testing for Cointegration Rank in VAR Models allowing for Multiple Breaks in Trend and Variance" at an international workshop entitled "W orkshop on Time-Varying Uncertainty in Macro" held at the Centre for Dynamic Macroeconomic Analysis, School of Economics and Finance, University of St Andrews, 2-3 September 2017. 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor delivered the paper "Testing for Cointegration Rank in VAR Models allowing for Multiple Breaks in Trend and Variance" at an international workshop entitled "Workshop on Time-Varying Uncertainty in Macro" held at the Centre for Dynamic Macroeconomic Analysis, School of Economics and Finance, University of St Andrews, 2-3 September 2017. The talk attracted a large audience of both academic and academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2017
URL https://www.st-andrews.ac.uk/cdma/files/workshop-uncertainty-programme.pdf
 
Description Robert Taylor gave a keynote address delivering the paper "Testing for Cointegration Rank in VAR Models allowing for Multiple Breaks in Trend and Variance" at an international workshop entitled "Macroeconomic and Financial Time Series Analysis" held at Lancaster University Management School on June 1-2nd 2017. 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor gave a keynote address delivering the paper "Testing for Cointegration Rank in VAR Models allowing for Multiple Breaks in Trend and Variance" at an international workshop entitled "Macroeconomic and Financial Time Series Analysis" held at Lancaster University Management School on June 1-2nd 2017. The talk attracted a large audience of both academic and academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2017
URL http://www.lancaster.ac.uk/media/lancaster-university/content-assets/documents/lums/economics/Final_...
 
Description Robert Taylor gives research seminar to the Statistics Department, Bristol University 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Professional Practitioners
Results and Impact Robert Taylor presented the paper "Testing for co-integration rank in VAR models allowing for multiple breaks in trend and variance" to the weekly departmental seminar series of the Statistics Department, University of Bristol on 12th May 2017.
Year(s) Of Engagement Activity 2017
URL http://www.bristol.ac.uk/maths/events/2017/robert-taylor.html
 
Description Robert Taylor presented paper at conference to celebrate the retirement of Professor Jayasri Dutta, University of Birmingham, June 9th 2017. 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Robert Taylor presented the paper "Testing for Co-integration Rank in VAR Models allowing for Multiple Breaks in Trend and Variance with an Application to cay" at a conference in honour of Professor Jayasri Dutta held at the University of Birmingham on June 9th 2017. The talk attracted a large audience of both academic and academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2017
 
Description Talk at 10th York Econometrics Symposium, 15 June 2017 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact I gave a talk entitled "Frequency Domain Estimation of Cointegration Vectors with Mixed Frequency and Mixed Sample Data" at the 10th York Econometrics Symposium at the University of York on 15 June 2017.
Year(s) Of Engagement Activity 2017
URL https://www.york.ac.uk/media/economics/YES10.pdf