The inadequacy of linear autoregressive model for real exchange rates: empirical evidence from Asian economies

Abstract

Utilizing the formal linearity test of Luukkonen, Saikkonen and Tera¨svirta (Biometrika, 75, 491-99, 1998) as diagnostic tool, the empirical finding suggests that the linear autoregressive (AR) model is inadequate in describing the real exchange rates behaviour of 11 Asian economies. It is noted that the conventional battery of diagnostic tests is capable of identifying the inadequacy of the linear model in only three of these series. Moreover, the linearity nature of this behaviour has been formally rejected in favour of the non-linear smooth transition autoregressive (STAR) model. The finding of non-linearity in the data generating process of these real exchange rates warrants that the use of linear framework in empirical modelling and statistical testing procedures in the field of exchange rates may lead to an inappropriate policy conclusions.

Linearity and Stationarity of G7 Government Bond Returns

“…From the p-values of the test statistics, which are all well below 0.05 with one exception, it is obvious that all of the bond returns across various maturity periods and countries exhibit a nonlinear nature, with the exception of the US 7-to 10-year bonds, for which the null hypothesis of linear returns can be rejected marginally at the 10% significance level (the corresponding pvalue is 0.1026). This finding of nonlinear bond returns is in line with other recent studies that have found nonlinearities in financial market variables, such as interest rates (Baharumshah et al, 2008;Shively, 2005;Kapetanios et al, 2003;Bachmeier, 2002), exchange rates (Pérez-Rodríguez et al 2009;Liew 2003;Liew et al, 2003;Liew et al 2004;Taylor et al, 2001 and many others) and stock returns (Lim and Liew, 2007;Narayan, 2006;Shively, 2003). Thus, in determining the mean-reverting behavior of bond returns, one should avoid using the traditional linear stationary tests because these tests disregard the presence of nonlinearity and could yield deceptive conclusions.…”

“…Recently, there has been empirical evidence (for example, van Dijk and Franses (2000), Sarno (2000), Baum et al (2001), Kapetanios et al (2003), Liew et al (2003), Shively (2005), Baharumshah and Liew (2006), and Baillie and Kilic (2006)) that shows that financial time series are mostly nonlinear in nature. To cater for nonlinearity, Kapetanios et al (2003) propose to first estimate the following nonlinear autoregressive process: …”

“…1 In addition, various studies have demonstrated that adopting linear methods will lead to incorrect statistical inference when the data are governed by nonlinearity; see, for example, Liew et al (2003) and Liew et al (2004), Kapetanios et al (2003), and others. In particular, if the linear framework is found to be inadequate, the results of conventional linear unit root tests will then lose their power, and thus, any conclusion based on these tests could be misleading.…”

Stationarity of South Asian Real Exchange Rates Under Exponential Star (ESTAR) Framework

“…ADF or KPSS. Other studies that document evidence of nonlinear exchange rate dynamics in the Asian countries include Liew et al (2003Liew et al ( , 2004, Liew (2004) and Zhou (2008). Using the nonlinear unit root tests, this paper finds that the real exchange rates of India, Pakistan and Sri Lanka seem to be conclusively nonstationary, while tests produce mixed results for Bangladesh.…”

Long-run validity of purchasing power parity and rank tests for cointegration for Central Asian countries

“…4 Recently, it has been argued that these linear testing procedures may be defective should the PPP holds with nonlinear adjustment (see, for instance, Taylor and Peel, 2000). Evidences of nonlinear adjustment of real exchange rates are provided by Taylor and Peel (2000), Taylor et al (2001), Kilian and Taylor (2003), Liew et al (2003Liew et al ( , 2004Liew et al ( , 2008, Anuruo et al (2006), and Lothian and Taylor (2008), to name some.…”