Review of Quantitative Finance and Accounting, 24: 93–107, 2005
2005 Springer Science + Business Media, Inc. Manufactured in The Netherlands.
AVariance Ratio Test of the Behaviour of Some FTSE
Equity Indices Using Ranks and Signs
Department of Economic Analysis, University of Valencia, Campus dels Tarongers, Avgda. dels Tarongers s/n.
46022 Valencia, Spain, Tel: 34-96-3828246, Fax: 34-96-3828249
KWAKU K OPONG
Department of Accounting and Finance, University of Glasgow, 65-71 Southpark Avenue,
Glasgow G12 8LE, Scotland
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.
Keywords: variance ratio, heteroskedasticity, ranks, signs, random walk, martingale difference
JEL Classiﬁcation: G12, G14, G15
The past three decades has witnessed a large volume of research into the behaviour of
asset prices. Weak form market efﬁciency suggests that prices traded in a securities market
that is weak form efﬁcient cannot be predicted by using historical price information. This
implies, therefore, that prices traded in such a market are serially uncorrelated. One method
that has been adopted in the extant literature for testing weak form market efﬁciency has
been an examination of asset prices for evidence of non-random behaviour. Random walk
hypothesis (RWH) posits that successive price changes in an efﬁcient market are random.
However, in practice the RWH is rather restrictive, since it implies that in the process:
= φ X
We are grateful to Jonathan Wright for programming help. We also thank the editor and an anonymous referee
for their constructive comments. All errors and omissions remain ours.