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A Bayesian method of distinguishing unit root from stationary processes based on panel data models with cross-sectional dependence

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Abstract

In this paper we develop a Bayesian approach to detecting unit roots in autoregressive panel data models. Our method is based on the comparison of stationary autoregressive models with and without individual deterministic trends, to their counterpart models with a unit autoregressive root. This is done under cross-sectional dependence among the error terms of the panel units. Simulation experiments are conducted with the aim to assess the performance of the suggested inferential procedure, as well as to investigate if the Bayesian model comparison approach can distinguish unit root models from stationary autoregressive models under cross-sectional dependence. The approach is applied to real exchange rate series for a panel of the G7 countries and to a panel of US nominal interest rates data.

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Notes

  1. See, e.g., Harris and Tzavalis (1999), Phillips and Moon (1999), Hadri (2000), Levin et al. (2002), Breitung (2002), Im et al. (2003) and, for a recent survey, Hlouskova and Wagner (2006).

  2. See, e.g., Sims (1988), Schotman and van Dijk (1991a, 1991b), Dejong and Whiteman (1991), Lubrano (1995), Marriot and Newbold (2000), inter alia.

  3. See, e.g. Kang and Ferreira (2010). However, these Bayesian methods are not focused on drawing inferences about the presence of unit roots, which is the main focus of our paper. They are mainly interested in extracting common stochastic trends and cyclical components from nonstationary (with a unit root) autoregressive panel data models.

  4. See Elliot and Muller (2003), for a study of the effects of the initial observations on inference about unit roots. In the panel data literature, the analysis is focused on the effects of the initial conditions on the bias of the autoregressive coefficient of dynamic panel data models (see, e.g., Arellano 2003, for a survey, and Jarocinski and Marcet 2008).

  5. See, e.g., O’Connell (1998), Phillips and Sul (2003), Chang (2004), Moon and Perron (2004), Pesaran (2007), Kapetanios (2007) and the survey of Breitung and Pesaran (2008) inter alia.

  6. Note that random walk models are frequently used both in single time series and panel data literature to describe the dynamics of many asset prices (see, e.g., Campbell et al. 1997, for a survey).

  7. The assumption of a common autoregressive coefficient under stationarity corresponds to a classical unit root test that assumes a homogeneous autoregressive coefficient under the alternative hypothesis. This is a convenient assumption which enables us to compute analytically the marginal likelihoods of several competing models and develop a Bayesian approach to distinguishing unit root from stationary processes based on model comparison. Relaxing this assumption may increase the posterior probability of stationarity if a considerable amount of individual units of the panel are stationary series. If interest lies in distinguishing stationary from unit root series within the panel, a completely different approach should be developed within the Bayesian framework.

  8. This data has been obtained from the Penn World table of Alan Heston, Robert Summers and Bettina Aten, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania.

  9. The interest rates data were obtained from the archive of J. Huston McCulloch of Ohio State University of USA (http://www.econ.ohio-state.edu/jhm/ts/ts.html).

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Authors and Affiliations

  1. Department of Mathematics, University of Athens, Panepistemiopolis, Athens, 157 84, Greece

    Loukia Meligkotsidou

  2. Department of Economics, Athens University of Economics and Business, Pattision 76, Athens, 134 76, Greece

    Elias Tzavalis

  3. Department of Statistics, Athens University of Economics and Business, Pattision 76, Athens, 134 76, Greece

    Ioannis D. Vrontos

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  1. Loukia Meligkotsidou
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  2. Elias Tzavalis
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  3. Ioannis D. Vrontos
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Correspondence to Loukia Meligkotsidou.

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Meligkotsidou, L., Tzavalis, E. & Vrontos, I.D. A Bayesian method of distinguishing unit root from stationary processes based on panel data models with cross-sectional dependence. Stat Comput 24, 297–315 (2014). https://doi.org/10.1007/s11222-012-9371-3

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