Published on February 18, 2022 Updated on March 7, 2022

Heino Bohn NIELSEN

Heino Bohn Nielsen
Heino Bohn Nielsen
University of Copenhagen - Denmark
Visiting Scholar invited by research center THEMA
Curriculum Vitae


Research project

Unit root tests and non causal autoregressive models : non parametric versus parametric tests

This project is in line with the one we have conducted last year during Heino’s visit at the IEA, now released as THEMA working paper #2019-07 («Mixed Causal-Noncausal Auto-regressions : Bimodality Issues in Estimation and Unit Root Testing»), and which has been submitted for publication to Oxford Bulletin of Economics and Statistics and presented in Québec (Annual congress of the Economics Canadian Society), Marseille (Quantitative Finance and Financial Econometrics annual conference) and London (13th International Conference on Computational and Financial Econometrics). Introduced decades ago in statistics theory, noncausal autoregressions (NCAR hereafter) have recently known a revival of interest amongst researchers in economics, finance and econometrics. NCAR models have the particularity that they allow for dependence on both past and future times, by contrast with the well-known backward-looking, causal autoregression --- namely the AR model --- which rules out dependence on future observations.
The recent popularity of noncausal autoregressions is due mainly to three reasons. Firstly, NCAR models have been found to provide a better fit and/or forecast performance than the causal ARMA framework for various economics and financial series. Secondly, NCAR models can accommodate omitted variables and various nonlinearities without explicit specification. Thirdly, NCAR models are very parsimonious compared to e.g. nonlinear models. Indeed, they contain the same number of parameters as the simple causal autoregression. For that reason, they could be considered as a parsimonious way to approximate nonlinear and/or multivariate processes.
Importantly, all the aforementioned research assumes stationarity of the NCAR process. In particular, the asymptotic distribution theory for parameters maximum likelihood estimator has been developed under the stationarity assumption. The same stationarity assumption is required for the econometric theory of the nonlinear models often used to fit macroeconomic and financial time series. Yet, as stressed by Gouriéroux et Zakoian (2017, J. R. Statist. Soc.B), when written in reverted time, noncausal processes turn out to look like nonlinear causal processes of Double AutoRegression (DAR) type with dependant residuals (see Ling and Li (2008), Biometrika, or Bohn Nielsen and Rahbek (2014), Journal of Empirical Finance).
Consequently, noncausal processes can easily be mistaken for nonlinear ones and vice versa. It is also worth remarking that the series typically used in recent NCAR applications have, so far, been typically modeled with nonlinear models, such as (S)TAR, DAR, Markow-Switching and/or (G)ARCH models. This raises the issue of unit root testing when the specification under the alternative is unknown (noncausal or nonlinear).
To circumvent this issue, it seems natural to have recourse to non-parametric unit root tests since they do not require the specification of the stationary alternative. The goal of this project is twofold. First, we aim to evaluate the performance of non-parametric unit root tests against stationary alternatives of various kinds (causal, noncausal or nonlinear). Then, the power of these non-parametric tests will be compared to the ones of the main existing unit root tests against linear, nonlinear and noncausal alternatives. To sum up, we seek to provide some grounded guidance to practitioners for their choice of a unit root test when noncausality is suspected or turns out to be a relevant parsimonious representation of more complex dynamics.