Semi-parametric real exchange rates dynamics

See Nieh and Wang (2005), Okunade et al. (1996), Mishra (2011), Bayraktar (2009), Yongjian et al. (2009), Karemera and Cole (2010), Chiu (2008), and Hung and Jan (2002) among others.

Taylor et al. (2001), using ADF-ESTAR, found nonlinear mean-reversion. Sollis et al. (2002) and Kapetanios et al. (2003), using a STAR and an ESTAR approach reached an opposite conclusion.

Sercu et al. (1995) and Ohanian and Stockman (1997) suggest that transaction costs in goods arbitrage give rise to nonlinear real exchange rate adjustment paths, without specifying the form of nonlinearity and thus highlighting the need of a non-parametric approach.

Non-parametric estimation has also been used in Tanggaard (1997), Lipe and Kormendi (1994), and Chu (2016).

According to Keele (2008), these two approaches yield similar results in practice.

Thanks are due to Claude Lopez for kindly providing the data.

Running these models did not require extra computing resources, did not consume significant computational time, and thus did not entail computational costs. All estimations were conducted on an ordinary PC with Intel Pentium (i5) with 1.86 GHz processor and 4.0 GB RAM, with estimations taking a few seconds to converge, in line with the computing time required in Wang and Yang (2007). Indeed, Wang and Yang (2007), using Monte Carlo simulations, concluded that splines-based estimators of additive models are computationally expedient. This is due to the fact that in the present study, we follow Engle et al. (1986) and employ penalized regression splines instead of other competing nonlinear smoothers to estimate the semi-parametric ADF regression. Penalised regression splines use fewer parameters than other smoothers and are computationally efficient (Keele 2008).

Japan is added to these countries as the confidence interval encompasses 0. For Norway, there is a very small range of values for which the relation becomes marginally negative.

The inclusion of a deterministic trend yields qualitatively similar results (as in Lopez et al. 2005).

The dimension-reduction principle refers to the properties of the convergence rate of statistical models, and is analytically discussed in Stone (1985).