Robust econometric inference in cointegrated systems and systems of predictive regressions
Lead Research Organisation:
University of Southampton
Department Name: School of Social Sciences
Abstract
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Organisations
People |
ORCID iD |
| Anastasios Magdalinos (Principal Investigator) |
Publications
Arvanitis S
(2018)
Mildly Explosive Autoregression Under Stationary Conditional Heteroskedasticity
in Journal of Time Series Analysis
Kasparis I
(2012)
Non-Linearity Induced Weak Instrumentation
in SSRN Electronic Journal
Kostakis A.
(2015)
Robust econometric inference for stock return predictability
in Review of Financial Studies
Phillips P
(2013)
INCONSISTENT VAR REGRESSION WITH COMMON EXPLOSIVE ROOTS
in Econometric Theory
| Description | The project proposes a new econometric estimation and inference procedure that resolves a longstanding problem in the predictive regression and co-integrating regression literature, namely the lack of robustness of existing methods to the (unobserved) stochastic properties of the economic and financial variables that are used as predictors. The proposed "IVX" methodology provides a unifying framework of inference in multivariate systems of predictive regressions that encompasses the whole range of empirically relevant generating mechanisms for the explanatory variables, from stationary processes to purely non-stationary random walks. The key findings of the project that justify the above assertions are summarised below: 1) A new econometric estimator, termed "IVX" estimator is introduced. Unlike standard instrumental variable procedures, the new estimator is constructed from the data without assuming additional information (e.g. orthogonality and relevance conditions) by means of a data-filtering method that controls the persistence degree of the instruments in the region of near stationary processes. 2) The asymptotic statistical properties of the IVX estimator are analysed. In particular, asymptotic mixed normality of the normalised and centred IVX estimator is established under all empirically relevant data generating mechanisms, a statistical property that is crucially important for the robustness of IVX-based hypothesis tests. Asymptotic mixed normality of the IVX estimator implies that self-normalised test statistics will have a standard chi-squared limit distribution. In particular, under all empirically relevant data generating mechanisms, a newly constructed IVX-Wald test statistic for testing general linear restrictions on the coefficient matrix of the predictive regression system will have a chi-squared limit distribution with degrees of freedom equal to the number of restrictions imposed by the null hypothesis. 3) The mixed normality property of the IVX estimator is extended to accommodate predictive regression systems with unknown and possibly different persistence degree along each equation of the system. This extension presents significant theoretical complications as sample moment matrices require matrix normalisation. 4) A general limit distribution theory for Wald statistics in regression models that require matrix normalisation is established. Simple sufficient conditions for preservation of asymptotic rank (and subsequent standard limit distribution theory) are established. In particular the IVX-Wald test is shown to have a standard chi-squared limit distribution under the general situation of systems with multiple persistence degrees of point 3) above. Testing general hypothesis in multivariate systems of predictive variables is an issue of fundamental empirical importance as it allows to assess the joint predictive power of economic and financial variables. 5) The finite sample performance of IVX-based tests was assessed and compared with existing (less general) methods. A size-stabilising finite sample correction was introduced. A comprehensive simulation study was conducted which shows very strong evidence of the superiority of IVX based hypothesis tests over existing methods. 6) Financial application: IVX methodology is applied to empirically assess stock return predictability via lagged financial variables. An empirical analysis based on the IVX procedure is conducted for US stock returns during the period 1927-2012. Some evidence of short-horizon predictability are present over the full sample period, but this evidence almost entirely disappears in the post 1952 period. 7) The construction of the IVX estimator and the IVX-Wald test is extended to accommodate long-horizon predictability tests. Asymptotic analysis and simulation experiments confirm the robustness of the procedure in the long horizon case. 8) IVX limit distribution theory is extended to accommodate conditionally heteroskedastic innovation errors (multivariate GARCH processes). |
| Exploitation Route | The conventional medium to maximise the academic impact of the key findings of the project is to publish the project's results in top international academic journals. The project's results have been collected and their presentation is organised into scientific papers that are in different stages of the submission/publication process. The completed papers that contain the results of the research carried out under the project are listed below. The numbering of findings refers to the Summary of Project Findings section. 1) Econometric inference in the vicinity of unity (contains findings 1, 2, 3, 5). 2) Wald tests under matrix normalisation (contains finding 4). 3) Robust econometric inference for stock return predictability (contains findings 5, 6, 8). 4) IVX limit theory for long-horizon predictive regressions (contains finding 7). 5) Conditional heteroskedasticity in stochastic regression (generalises finding 8). From the above papers, paper 3) was published by the Review of Financial Studies (RFS). RFS is considered to be among the top three scientific journals in Finance internationally with very high impact factor. Consequently, the results of paper 3) are likely to reach a very wide academic audience in Finance, increasing the paper's academic impact and citations. Papers 1) and 2) are in the final stage before submission and will be submitted to a top journal in Economics (Econometrica). Papers 4) and 5) will be submitted to top field journals in Econometrics. The results of the project were presented in leading international conferences and research seminars in leading academic institutions. These presentations, as well as the working papers presenting the results of the project have already had considerable impact in the academic community, a fact that manifests itself by the considerable number of papers (authored by academics without involvement to the project) that have applied the proposed IVX methodology. To ensure maximum impact and facilitate the implementation of the proposed IVX methodology, MATLAB and GAUSS computer programmes have been developed that automatically implement the procedure for a given data set. These programmes will shortly be made available on the web. In summary, the project's findings can be used by: (i) Academics in the field of Econometrics and Statistics, who will employ the methodological econometrics-theoretic contributions of the project. (ii) Academic researchers in the fields of Macroeconomics and Finance which constitute the main fields of application of the IVX methodology developed in the project. (iii) Non-academic users in the financial industry or applied economists in central banks and economic institutions who will apply the IVX based hypothesis tests to real financial and economic data. |
| Sectors | Financial Services and Management Consultancy Other |
| Description | The main corps of the IVX methodology developed in the project is econometric-theoretical and concerns inference in systems of economic and financial variables that is robust to misspecification of the stochastic properties of the variables in the system. This robustness yields an important empirical application of the IVX methodology: predictability tests were hitherto able to assess the predictability of stock returns using one financial variable as predictor, provided that the stochastic properties of the predictor variable were known to the empirical researcher. This modelling restriction resulted to conflicting empirical evidence for the stock return predictability issue, as different modelling assumptions are consistent with different estimation and testing procedures, which generally yield different empirical conclusions. The IVX inference established in the project is an econometric procedure that encompasses all empirically relevant models employed by financial analysts and is able to accommodate hypotheses concerning the predictive power of various combinations of persistent explanatory variables, providing reliable empirical evidence on a very large class of models. As explicitly stated in the project's proposal, this aspect of the IVX methodology's application is of sufficient importance to empirical researchers in the financial industry, as well as empirical researchers in central banks, government institutions and international economic organisations, to merit publication by a leading journal in Finance, whose readership includes non-academic users. This aim was achieved by the publication of the article "Robust econometric inference for stock return predictability", written under the auspice of the ESRC project, to the Review of Financial Studies in May 2015. While the publication of the article is recent, it has attracted significant attention by industry-based users in Finance in view of the robustness of its empirical conclusions as well as the simplicity of its implementation (the latter being an important factor for non-academic users). To provide some examples of the empirical conclusions in the paper: (i) individual predictability (i.e. predictability of the stock return variable by a single financial predictor) is not present in modern market conditions (it almost entirely disappears in the post 1952 era); (ii) there are examples of combinations of financial predictors, such as earnings-price ratio and T-bill rate that exhibit significant joint predictive power despite being insignificant individually. The ability to conduct joint predictability tests is a major breakthrough in the literature with applications that are readily employable by non-academic users. In summary, the publication of part of the project's outputs in a top-3 journal in Finance that receives attention from academia, the financial industry as well as economic institutions constitutes, in my opinion, a very strong signal for the importance of these outputs to non-academic empirical applications. Since the publication is recent (May 2015), some time should be allowed for the dissemination of the methodology to reach industry-related applications. To this end, we provide open access computer programmes to facilitate the implementation of the method by non-academic practitioners. |
| First Year Of Impact | 2015 |
| Sector | Financial Services, and Management Consultancy,Other |
| Impact Types | Economic |
| Description | BA/Leverhulme small research grant |
| Amount | £9,945 (GBP) |
| Organisation | The British Academy |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 08/2015 |
| End | 08/2016 |
| Title | IVX implementation software |
| Description | The programme provides the GAUSS code for the implementation of the IVX-Wald test of the paper: Kostakis, Alexandros, Tassos Magdalinos, and Michalis P. Stamatogiannis. "Robust econometric inference for stock return predictability." Review of Financial Studies 28, no. 5 (2015): 1506-1553. Both the above paper and the associated computer programmes have been written with support from the ESRC grant. |
| Type Of Technology | Webtool/Application |
| Year Produced | 2014 |
| Impact | The programmes provide an easy way of automated implementation of IVX methodology. This expected to facilitate the implementation of the method by non-academic users in the industry and financial institutions. |
| URL | https://sites.google.com/site/mpstamatogiannis/research/code |
| Description | 64th European Econometric Society Meeting, Barcelona |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Schools |
| Results and Impact | Conference presentation |
| Year(s) Of Engagement Activity | 2009 |
| Description | 65th European Econometric Society Meeting, Oslo |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Schools |
| Results and Impact | Conference presentation |
| Year(s) Of Engagement Activity | 2011 |
| Description | Academic Visit, Cowles Foundation, Yale University |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Schools |
| Results and Impact | 2-3 months spent (during each visit) at the Cowles Foundation (Yale University). Cowles is an internationally leading academic department and research centre; arguably the most prestigious academic institution for econometrics worldwide. During each visit, I delivered 2 seminar presentations and engaged in collaborative research with members of the Foundation. |
| Year(s) Of Engagement Activity | 2009,2011,2015 |
| Description | Academic visit, Singapore Management University (SMU) |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Schools |
| Results and Impact | The Sim Kee Boon Institute (SKBI) for Financial Economics is based at Singapore Management University (SMU) and acts as a think-tank that encompasses research in Finance, training and consultancy, executive education and research dissemination through organising courses, seminars and conferences. Positioned in a world-leading financial centre, it maintains strong links with the banking and financial industry, as well as government and international financial institutions. My academic visits to SKBI are aimed to disseminate the outputs of the research project to a mixed audience of academics and non-academic practitioners in empirical finance and macroeconomics. |
| Year(s) Of Engagement Activity | 2009,2010,2012,2014 |
| Description | Conference presentation at the Bank of Portugal |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Conference presentation at the Bank of Portugal in a mixed audience involving both academics and central bank policy makers. |
| Year(s) Of Engagement Activity | 2016 |
| URL | https://www.bportugal.pt/en/evento/june-3-4-conference-new-trends-and-developments-econometrics |
| Description | Econometrics workshop; Bar-Ilan university |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Study participants or study members |
| Results and Impact | Presentation of the project's research outcomes to an academic workshop. |
| Year(s) Of Engagement Activity | 2016 |
| Description | Invited speaker: Recent developments in financial econometrics (University of Essex) |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Schools |
| Results and Impact | Conference presentation; invited speaker |
| Year(s) Of Engagement Activity | 2014 |
| Description | Keynote Lecture at the Sim Kee Boon Institute (SKBI) for Financial Economics |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Schools |
| Results and Impact | I delivered a Keynote Lecture at the Institute for Financial markets at the Singapore Management University. |
| Year(s) Of Engagement Activity | 2012 |
| Description | RCEA Time Series Econometrics Workshop |
| Form Of Engagement Activity | A formal working group, expert panel or dialogue |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | Presentation of the project's research outcomes to the RCEA Time Series Econometrics Workshop |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://www.rcea.org/images/RCEA_4th_Time_Series_Econometrics_Workshop_2016 |
| Description | Royal Economic Society Conference, Cambridge |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Schools |
| Results and Impact | Conference presentation |
| Year(s) Of Engagement Activity | 2012 |
| Description | Seminar presentation in the Computational Finance and Econometrics conference |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Study participants or study members |
| Results and Impact | Seminar presentation in the Computational Finance and Econometrics conference |
| Year(s) Of Engagement Activity | 2016 |
| URL | http://cfenetwork.org/CFE2016/ |
| Description | Session organiser for the International Society of Non-Parametric Statistics conference |
| Form Of Engagement Activity | A formal working group, expert panel or dialogue |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Study participants or study members |
| Results and Impact | Session organiser for the International Society of Non-Parametric Statistics conference |
| Year(s) Of Engagement Activity | 2016 |
| Description | Session organiser: International Society for Non-parametric Statistics |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Schools |
| Results and Impact | Session organiser and seminar presenter |
| Year(s) Of Engagement Activity | 2014 |