Investigating Structural Change in Predictive Regressions with Applications to Forecasting Stock Returns

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

Abstract

A vast body of empirical research involving econometric methods has been undertaken investigating stock return predictability. These methods have largely been based on predictive regression models and have investigated a wide array of financial and macroeconomic variables as putative predictors for returns. Popular variables investigated for their predictive ability for returns have included valuation ratios such as the dividend-price ratio, earnings-price ratio, book-to-market ratio and various interest rate spreads. Overall, these empirical studies have tended to find either no or only relatively weak statistical evidence of in-sample predictability in stock returns. Yet for many variables there are good theoretical reasons to expect them to provide some form of predictive power for returns. For example, a finding that the price-dividend ratio has some predictive power for returns is consistent with orthodox financial theory, because if the dividend-price ratio is time-varying then according to the present value model it must forecast either the dividend growth rate or returns to some extent. A more general explanation for predictability is that expected returns vary with expected business conditions for which those variables found to have some predictive ability are good proxies.

The overwhelming majority of empirical studies of stock return predictability have assumed that the coefficients in the prediction regression models do not change over the available sample data. However, market efficiency arguments suggest that if stock returns are predictable then it is likely to be a temporary rather than a permanent phenomenon. More specifically, if exploiting the predictive power of a regression model can be used to generate abnormal trading profits, then in an efficient market the model will be exploited by large numbers of investors thereby causing the predictive power of the relevant predictor to be eliminated. If a variable begins to have predictive power for stock returns, then a short window of predictability might exist before investors learn about the new relationship between that variable and returns, but market efficiency implies that it will eventually disappear. In such cases, standard predictive regression models based on the full sample of available data will have almost no power to detect these short predictive regimes.

It therefore seems reasonable to consider the possibility that the predictive relationship might change over time, so that over a long span of data one may observe windows of time during which predictability occurs and others where it does not. This project will develop the rigorous econometric methods that are needed to: (i) be capable of effectively detecting the presence of structural change in the coefficients of predictive regression models when applied to the full sample of data, and (ii) use methods of sub-sample data analysis designed to be effective in uncovering such windows of predictability and to enable real-time monitoring for early detection of these windows of predictability as they occur. The project will additionally investigate the role and impact of the forecasting horizon (either short, eg quarterly or monthly, or longer) being considered when using these methods.

The theoretical developments will be conducted using large sample econometric theory and will involve state-of-the-art bootstrap methods. The practical relevance of the theoretical results will be explored using simulation experiments. Clear guidance will also be given to empirical researchers through worked examples and applications of the techniques to key international equity data sets. The empirical aspects of the project will investigate both traditional predictors (such as those discussed above) as well as more recently considered so-called technical analysis indicators (where only price or volume data is used to predict returns).

Planned Impact

Practitioners from a range of sectors will benefit: those in research divisions of central banks, government treasuries and US federal reserve banks. Researchers in private sector economic and financial consultancy firms, particularly those providing investment portfolio advice to investors and groups of investors, will also benefit from being able to apply the new techniques developed in the project to the prediction of stock returns and other equity data.

The expected impact to these researchers will take the form of the provision of new theoretically rigorous econometric techniques designed to allow for predictability testing in unstable environments. Specifically, the project will deliver two main features that will substantially increase the scope and reliability of the regression-based methods for detecting predictability in practice:

(i) Tests will be developed to detect, for a given set of sample data and putative predictors, the presence of structural instability in the coefficients of estimated predictive regression models;

(ii) Sub-sample modelling and testing procedures will be developed, for a given set of data and putative predictors, designed to uncover any windows of predictability that may exist in the data and to also enable real-time monitoring for early detection of such windows of predictability as they occur. The latter will provide the practitioner with an early indication of the presence of a valid prediction window.

Principally, the proposed methods are aimed at enabling practitioners to investigate whether and from what predictor variables any episodes of predictability are present in data such as stock returns. Scenarios where predictability is episodic within the available sample could explain both the lack of strong empirical evidence for predictability and the documented weak out-of-sample predictive power of the typical predictor candidates, and allowing for this richer class of time-varying models will provide practitioners with the necessary techniques to uncover such relationships.

To ensure longer-term impact of the research, the PI will discuss with established econometric software manufacturers the inclusion of the procedures developed in the project in their software programs. Producing better econometric software will not only benefit manufacturers but also practitioners that use this software.
 
Title Software - Software to implement the methods developed in the paper "Testing for Episodic Predictability in Stock Returns" 
Description A Matlab program to implement the methods developed in the paper "Testing for Episodic Predictability in Stock Returns", by Matei Demetrescu, Iliyan Georgiev, Paulo Rodrigues and Robert Taylor, forthcoming in the Journal of Econometrics (2020). The data sets analysed in the paper are also available from http://rtaylor-essex.droppages.com/esrc2/default.htm and can be run with this software 
Type Of Technology Software 
Year Produced 2020 
Impact not known 
URL http://rtaylor-essex.droppages.com/esrc2/default.htm
 
Title Software to implement the methods developed in the paper "A Bootstrap Stationarity Test for Predictive Regression Invalidity" 
Description A Gauss program to implement the methods developed in the paper "A Bootstrap Stationarity Test for Predictive Regression Invalidity", by Iliyan Georgiev, David Harvey, Stephen Leybourne and Robert Taylor, Essex Finance Centre Working Paper number 28, 2018, University of Essex (also published in the RePEc working paper series and available from https://econpapers.repec.org/paper/esyuefcwp/21006.htm )". 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 . The data sets analysed in the paper are available from http://rtaylor-essex.droppages.com/esrc2/default.htm and can be run with this software 
Type Of Technology Software 
Year Produced 2018 
Impact Not known 
URL http://rtaylor-essex.droppages.com/esrc2/default.htm
 
Title Software to implement the methods developed in the paper "Testing for Parameter Instability in Predictive Regression Models" 
Description A Gauss program to implement the methods developed in the paper "Testing for Parameter Instability in Predictive Regression Models", by Iliyan Georgiev, David Harvey, Stephen Leybourne and Robert Taylor, published in the Journal of Econometrics (2018), volume 204, pages 101-118 https://doi.org/10.1016/j.jeconom.2018.01.005 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 . The data sets analysed in the paper are available from http://rtaylor-essex.droppages.com/esrc2/default.htm and can be run with this software 
Type Of Technology Software 
Year Produced 2018 
Impact Not known 
URL http://rtaylor-essex.droppages.com/esrc2/default.htm
 
Description Keynote address given by Robert Taylor of the paper "Detecting Regimes of Predictability in the U.S. Equity Premium" at the 2019 Nordic Econometric Meeting 
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 titled "Detecting Regimes of Predictability in the U.S. Equity Premium" at the 2019 Nordic Econometric Meeting Conference at the Stockholm School of Economics, May 23-26, 2019.

The talk attracted an audience of academic colleagues, PhD students and some academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with these colleagues and students after the talk.
Year(s) Of Engagement Activity 2019
URL https://www.hhs.se/en/research/centers/center-for-data-analytics/nem-2019/
 
Description Nuffield Econometrics Seminar 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact Robert Taylor presented the paper "Testing for Episodic Predictability in Stock Returns" at the Nuffield Econometrics Seminar, Oxford University Department of Economics on Friday 31 January 2020. The talk was attended by academics and postgraduate students from both the Economics Department and Said Business School at Oxford. Many useful discussions around the content of the presentation were raised by the audience during and immediately after the talk and I had many useful discussions with audience members later in the afternoon and over dinner.
Year(s) Of Engagement Activity 2020
URL https://talks.ox.ac.uk/talks/id/fc4c8765-c779-4bbe-9ab8-e044be4c9201/
 
Description One day workshop on the theme "Predictive Regression Models: Theory and Applications to Returns" held on September 9th 2019 
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 "" was held at the University of Essex on Monday September 9th 2019. Attendees and presenters at the event came from both the university sector (both UK and international universities) and from central banks (Bank of England, Bank of Portugal) and the NIESR. Papers were presented by Amit Goyal, Paulo Rodrigues Matei Demetrescu, Tassos Magdalinos, Ekaterini Panopoulou, Peter Boswijk, Jean-Yves Pitarakis and Robert Taylor. 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 and other third sector researchers) attendees.
Year(s) Of Engagement Activity 2019
URL http://rtaylor-essex.droppages.com/esrc2/ESRC%20draft%20prgramme.pdf
 
Description Presentation given of the paper "Detecting Regimes of Predictability in the U.S. Equity Premium" at the 2019 Royal Economic Society Conference 
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 Professor Robert Sollis (Newcastle University) presented the paper "Detecting Regimes of Predictability in the U.S. Equity Premium" at the 2019 Royal Economic Society Conference.

The talk attracted an audience of academic and some 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 2019
URL https://www.res.org.uk/resources-page/2019-annual-conference.html
 
Description Presentation given of the paper "Testing for Episodic Predictability in Stock Returns" at the 2019 CFE Conference, London 
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 Episodic Predictability in Stock Returns" at the 2019 CFE Conference, London.

The talk attracted an audience of academic and some 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 2019
URL http://www.cfenetwork.org/CFE2019/
 
Description Research Seminar given by Robert Taylor to the weekly Banking and Finance Research Group Seminar Series, Kings College London on March 8th 2018 
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 delivered a research seminar in the Banking & Finance Research Weekly Seminar Series at Kings College London on March 8th 2018 entitled "Testing for Parameter Instability in Predictive Regression Models" The talk stimulated a lively discussion with excellent feedback.
Year(s) Of Engagement Activity 2018
URL https://www.kcl.ac.uk/events/event-series.aspx?id=dc0c4274-9d0d-4344-a61b-5a9636572bcf
 
Description Robert Taylor delivered a keynote presentation at the 2019 Econometric Society Australasian Meeting in Perth, Australia July 1-3 2019 
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 titled "Detecting Regimes of Predictability in the U.S. Equity Premium" at the 2019 Econometric Society Australasian Meeting held in Perth, Australia, July 1-3, 2019.

The talk attracted an audience of academic colleagues, PhD students and some academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with these colleagues and students after the talk.
Year(s) Of Engagement Activity 2019
URL https://esam2019.org/
 
Description Robert Taylor delivered a presentation at the "Fifty Years of Econometrics at Keynes College" conference at the University of Kent, 7-8th September 2018 
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 "Detecting Regimes of Predictability in the US Equity Premium" at the "Fifty Years of Econometrics at Keynes College" conference held at the University of Kent, September 7-8th 2018.

The talk attracted a great deal of interest from the audience inclduding a number of questions and a general discussion. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2018
URL https://kenthospitality.kent.ac.uk/Register/Registration/Welcome.aspx?e=C77A46F57F289944CBC3078FB0C5...
 
Description Robert Taylor delivered a presentation at the 2018 International Association of Applied Econometrics Annual Conference, MontrĂ©al, Canada, on June 28th 2018 
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 talk "Testing for Parameter Instability in Predictive Regression Models" at the 2018 International Association of Applied Econometrics Annual Conference, Montréal, Canada, on June 28th 2018.

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 2018
URL http://iaae2018.org/
 
Description Robert Taylor delivered a presentation to the time-series seminar series run by the Mathematics Department at the University of Lancaster, 5th March 2019 
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 delivered a research seminar in the time-series seminar series run by the Mathematics Department at Lancaster University on March 5th 2019 entitled "Detecting Regimes of Predictability in the U.S. Equity Premium" The talk was very well attended and stimulated a great deal of discussion both during and after the seminar. This discussion has also led to Taylor planning some follow-up research work with Rebecca Killick from Lancaster University, directly following up on the research presented at the seminar.
Year(s) Of Engagement Activity 2019
URL https://www.lancaster.ac.uk/events/time-series-seminar-robert-taylor
 
Description Robert Taylor delivered a research presentation at the Brunel Conference on Financial and Macro Economics and Econometrics, May 25th 2018 
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 a research presentation titled "Testing for Parameter Instability in Predictive Regression Models" at the Brunel Conference on Financial and Macro Economics and Econometrics, May 25th 2018

The talk attracted a large audience of both academic and academic-related colleagues and postgraduate students. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2018
 
Description Robert Taylor gave an invited lecture, titled "Detecting Regimes of Predictability in the U.S. Equity Premium", at the 2019 DAGStat (German Statistical Association) conference hosted by the Statistics Institute, Ludwig-Maximilians University, Munich on 18-22 March 2019. 
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 an invited lecture, titled "Detecting Regimes of Predictability in the U.S. Equity Premium", at the 2019 DAGStat (German Statistical Association) conference hosted by the Statistics Institute, Ludwig-Maximilians University, Munich on 18-22 March 2019.

The talk attracted an audience of academic and some 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 2019
URL https://www.dagstat2019.statistik.uni-muenchen.de/scientific-programs/plenary-and-invited-speakers/i...
 
Description Robert Taylor organised session CO576 titled "Theory and application of predictive regressions" held on Saturday 14th December at the 2019 CFE conference, London 
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 organised and ran an invited session titled "Theory and application of predictive regressions" [session code CO576] on Saturday 14th December at the 2019 CFE conference in London. Four papers were presented in the session. Attendees and presenters at the event came from both the university sector and from central banks. . The session was highly productive with very useful interactions and discussions held between the academic and academic-related attendees.
Year(s) Of Engagement Activity 2019
URL http://www.cfenetwork.org/CFE2019/schedule_slot.php?slot=D
 
Description Robert Taylor presented a paper at the 29th (EC)^2 Conference organised by the Bank of Italy and Italy and the Italian Econometric Association and hosted by the Bank of Italy on December 13-14, 2018 
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 "Detecting Regimes of Predictability in the U.S. Equity Premium" at the 29th (EC)^2 Conference themed "Big Data Econometrics with Applications" organised by the Bank of Italy and Italy and the Italian Econometric Association (SIdE-IEA) and hosted by the Bank of Italy on December 13-14, 2018.

The talk attracted a large audience of both academic and academic-related colleagues, the latter including many researchers and staff from the Bank of Italy. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2018
URL https://www.side-iea.it/sites/side-iea.it/files/program_ec2_december_2018_v14_web.pdf
 
Description Robert Taylor presented a paper at the Cambridge-INET institute "Big Data Methods in Econometrics and Finance" Conference (Trinity College Cambridge 20-21 May 2019) 
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 a presentation titled "Testing for EpisodicPredictability in Stock Returns" at the Cambridge-INET institute "Big Data Methods in Econometrics and Finance" Conference held at Trinity College Cambridge, 20-21 May 2019.
Year(s) Of Engagement Activity 2019
URL https://www.inet.econ.cam.ac.uk/our-events/big-data-conf-may-2019
 
Description Robert Taylor presented a paper at the one day workshop on the theme "Predictive Regression Models: Theory and Applications to Returns" held at the University of Essex on 9th September 2019 
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 titled "Simple Tests for Stock Return Predictability with Improved Size and Power Properties" at a one day workshop held on the theme "Predictive Regression Models: Theory and Applications to Returns" at the University of Essex on 9th September 2019.

The talk attracted an audience of academic colleagues, PhD students and academic-related colleagues. The talk sparked interest and a number of questions. Many useful discussions with these colleagues and students after the talk.
Year(s) Of Engagement Activity 2019
URL http://rtaylor-essex.droppages.com/esrc2/ESRC%20draft%20prgramme.pdf
 
Description Robert Taylor presented the paper "Detecting Regimes of Predictability in the U.S. Equity Premium" at the pi-day conference in honour of Pierre Perron organised and hosted by the Department of Economics, Boston University, on 14th and 15th March 2019. 
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 "Detecting Regimes of Predictability in the U.S. Equity Premium" at the pi-day conference in honour of Pierre Perron organised and hosted by the Department of Economics, Boston University, on 14th and 15th March 2019.

The talk attracted a large and distinguished audience of academic colleagues as well as a number of academic-related colleagues and graduate students from universities in the greater Boston area. The talk sparked interest and a number of questions. Many useful discussions with colleagues after the talk.
Year(s) Of Engagement Activity 2019