A Variance Ratio Test of the Behaviour of Some FTSE Equity Indices Using Ranks and Signs

Abstract

This study utilises tests based on ranks and signs suggested by Wright (2000) in addition to the traditional variance ratio test to examine the behaviour of some UK Financial Times Stock Exchange (FTSE) stock indices. The results suggest that the null hypothesis of martingale difference behaviour of the index returns series examined in the study is rejected. The use of the nonparametric based variance ratio tests provide stronger evidence against the martingale difference behaviour than the conventional variance ratio tests, under conditions of both homoskedasticity and heteroskedasticity for the examined series. Moreover, the application of Wright’s variance ratio tests in a rolling window framework, indicates that the results for the FTSE returns are consistent neither with a linear AR assumption nor with the white noise hypothesis. Copyright Springer Science + Business Media, Inc. 2005variance ratio, heteroskedasticity, ranks, signs, random walk, martingale difference,

On the efficiency of the global gold markets

“…Fourth, the findings show that the RWS hypothesis is rejected more frequently than its MDS alternative, implying that most of the rejections of the weak-form efficiency in the global gold markets are due to heteroscedascity problems instead of simple autocorrelation ones. Finally, consistent with the findings of past studies (Belaire-Franch & Opong, 2005a,b, 2010Ntim, 2012;Ntim et al, 2007, 2011), LM's (1988 variance-ratio tests (M 1 and M 2 ) generally produce mixed results, whereas those of Wright's (2000) ranks (R 1 and R 2 ) and signs (S 1 and S 2 ) based alternatives are fairly consistent.…”

“…Indeed, since Fama's (1965Fama's ( , 1970 simple, but powerful testable specification of relative market efficiencies depending on a taxonomy of information set available to market participants (i.e., weak-form, semi strong-form and strong-form), a large amount of literature has emerged on the weak-form efficiency of financial assets, primarily relating to whether stock prices are randomly generated (Ayadi & Pyun, 1994;Belaire-Franch & Opong, 2005a;Campbell, Lo, & MacKinlay, 1997;Lo & MacKinlay, 1988Ntim, 2012;Ntim, Opong, & Danbolt, 2007;Ntim, Opong, Danbolt, & Dewotor, 2011;Smith, Jefferis, & Ryoo, 2002;Urrutia, 1995), but also other securities, such as exchange rates, bonds and precious metals (Belaire-Franch & Opong, 2005bChuluun, Eun, & Kilic, 2011;Hsieh, 1991;Liu & He, 1991).…”

“…Consequently, and with the availability of more powerful computers coupled with advances in econometric and mathematical modelling (Belaire-Franch & Opong, 2005a,b, 2010, recent studies examining whether gold prices follow random walk behaviour mainly employ powerful and sophisticated statistical techniques (e.g., chaos, fractals, neural networks, variance-ratios, and ARCH-GARCH models) (Parisi et al, 2008;Pierdzioch et al, 2014;Shafiee & Topal, 2010;Wang, Wei, et al, 2011). These advanced mathematical techniques are generally capable of dealing with security return series with non-linear distributions, and thereby providing a more precise test of the RWS hypothesis.…”

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“…1991; Lee and Wirjanto 1998;Tung 1998;Belaire-Franch and Opong 2005). When the errors are heteroskedastic the ordinary least squares estimator (OLS) for the LRM coefficients remains unbiased and consistent but the usual OLS covariance matrix estimator becomes biased and inconsistent, thus leading to invalid t, F and LM tests (Wooldridge 2000).…”

Can Emerging African Stock Markets Improve Their Informational Efficiency by Formally Harmonising and Integrating Their Operations?

“…The potential improvement in efficiency to be gained is much higher in economic sectors indices than in size and regional indices. Finally, consistent with prior evidence, (eg., Wright, 2000;Belaire-Franch and Opong, 2005, Ntim, et al, 2007), the results of the Lo and MacKinlay (1988) parametric variance-ratios test are ambiguous. By contrast, the ranks and signs alternative offer consistent results throughout.…”