Comments and Questions

This is an interesting paper that makes two important contributions: 1. it helps to explain why the "average practitioner" who apply ADF-type tests on individual variables (starting from levels and moving to differences successively) may fail to detect a double unit root in a class of time series whose data generating process is near-I(2) with small signal-to-noise ratio; 2. it suggests that deviations from the rational expectations hypothesis, and in particular the Imperfect Knowledge Economics (IKE) paradigm discussed by Frydman and Goldberg (2007, 2011), may potentially be used to explain the long swings we observe in variables like e.g. exchange rates and asset prices. The paper emphasizes the benefits of treating near-I(2) systems as I(2) (to my knowledge, a recent paper which provides a similar idea by exploring a different route is Di Iorio et al. (2013), who devote attention to testing issues). We all know that "the problem" with I(2) processes is that aside from some special cases, many macroeconomists do not easily manage "polynomial cointegration", because the equilibria they have in mind do not generally feature levels and differences of the variables jointly (Katarina has several empirical papers which show how this issue can be takled; Bacchiocchi and Fanelli (2005) show how polynomial cointegrating PPP-like relationships can be justified by appealing to models of deviations from the law-of-one-price). This paper delivers some original insights about the mechanics underlying long swings and suggests an implicit modelling approach based on "our" cornerstore, the cointegrated VAR. I have two considerations. The first concerns the empirical results in Table 8. It would be nice to explore, in future research, whether using suitable designed bootstrap versions of the LR test would change some of the conclusions. For instance, the fact that the real exchange (bond rate differential) rate is perceived as I(2) by the LR test with a p-value of 0.03 (0.02), might reflect the over-rejection phenomenon we observe when testing cointegration restrictions in samples of length typically available to macroeconomists. Secondly, it would be nice to compare/contrast, always in future research, the viewpoint provided by Katarina about near-I(2) time-series with the results stemming from fractionally integrated/cointegrated VARs (Johansen and Nielsen, 2010, 2012). Luca REFERENCES - Bacchiocchi, E., Fanelli, L. (2005), Testing the purchasing power parity through I(2) cointegration techniques, Journal of Applied Econometrics 20, 749-770. - Di Iorio, F., Fachin, S., Lucchetti, R. (2013), Can you do the wrong thing and still be right ? Hypothesis testing in I(2) and near-I(2) cointegrated VARs, Quaderni di Ricerca n. 395, Dipartimento di Scienze Economiche e Sociali, Università Politecnica delle Marche.- Frydman, R. and Goldberg, M. (2007), Imperfect knowledge economics: Exchange rates and risk, Princeton, NJ: Priceton University Press.- Frydman, R. and Goldberg, M. (2011), Beyond mechanical markets: risk and the role of asset price swings, Priceton University Press.- Johansen, S. and Nielsen, M.Ø. (2010), Likelihood inference for a nonstationary fractional autoregressive model, Journal of Econometrics 58, 51-66- Johansen, S. and Nielsen, M.Ø. (2012), Likelihood inference for a fractionally cointegrated vector autoregressive model, Econometrica 80, 2667-2732.