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

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.

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.