Estimation and inference theory for (co)integrated processes in the state space representation
Final Report Abstract
Unit root and cointegration analysis are major cornerstones of applied econometric work, with ubiquitous applications in fields ranging from macroeconomics to finance to (increasingly) climate economics. The underlying reasons are that (i) many economic and financial time series exhibit stochastically trending behavior, i.e., exhibit unit root type behavior and (ii) many series move together over the long-run, i.e., are cointegrated. The first item is consistent with approximately exponential growth as observed for many series and the second aspect is not only an empirically pervasive phenomenon, but also relates empirical analysis with economic theory fundamentally linking many series to few underlying driving forces, referred to as common trends in the literature. A prominent macroeconomic example is the so-called neoclassical growth model, implying close co-movement of private consumption and output, both driven by technological progress. Cointegration, more precisely refers to the fact that linear combinations, e.g., the difference between log consumption and log output, are stationary, i.e., fluctuate without trend around a constant mean. The dominant approach to cointegration analysis in the literature is based on so-called vector autoregressive (VAR) models, regression models with the explanatory variables being lagged, i.e., earlier, values of the variables under consideration. In the cointegration literature VAR models are typically studied in the error correction model (ECM) setting, that conveniently focuses on the long-run relationships. Whilst this approach has some merits, in particular the relative simplicity of statistical analysis and the easy interpretability of the suite of results obtained from such models, there are some major limitations that render this model class too restrictive – for both statistical as well as economic theory reasons. As an example, even if the (true) economic system is jointly described by a VAR model, when one considers a subset of the variables only, these in general do not follow a VAR model. The limitations can be overcome by using the more flexible vector autoregressive moving average (VARMA) rather than VAR models. This is where EICIP comes in, by developing a comprehensive theory and toolkit for performing cointegration analysis for VARMA models, conveniently cast in the (equivalent) state space format. More specifically, the project has developed estimation and inference tools to perform the cointegration modelling cycle in this more general model class. This includes in particular also tests for the number of cointegrating relationships (with economic theory often providing information) as well as for the specific form of such relationships (in the above example log consumption minus log output). The project has developed tools for the empirically most relevant cases; allowing to handle also seasonally unadjusted series and nominal quantities or the analysis of stocks and flows. Furthermore, the project has translated or extended the ECM approach from the VAR to the state space setting, making the results fundamentally easier to be adopted by the cointegration community – given the “structural similarity” of the extended model class to the well-known setting. Simulation results and first empirical applications highlight that the new methodology is useful, i.e., exhibits performance advantages and leads to interesting results.
Publications
- (2019) Periodic and Seasonal (Co-)Integration in the State Space Framework. Economics Letters 174, 165–168
Bauer, D.
(See online at https://doi.org/10.1016/j.econlet.2018.11.018) - (2020) Modeling I(2) Processes Using Vector Autoregressions Where the Lag Length Increases with the Sample Size. Econometrics 8
Li, Y., Bauer, D.
(See online at https://doi.org/10.3390/econometrics8030038) - (2020). Essays on Cointegrating Analysis in the State Space Framework. Dissertation, TU Dortmund, September 2020
Matuschek, L.
- Pseudo Maximum Likelihood Estimation of Cointegrated Multiple Frequency I(1) VARMA Processes Using the State Space Framework. Dissertation, TU Dortmund, September 2020
de Matos Ribeiro, P.
