Quaderni di Statistica
Vol. 7, 2005
Common long memory in
the Italian stock market
Maria Simona Andreano
Dipartimento di Teoria Economica, Università degli Studi di Roma
La Sapienza"
E-mail: s.andreano@dte.uniroma1.it
Summary: The mixture of distribution hypothesis originally introduced by Clark (1973)
and Epps and Epps (1976) suggests that returns and trading volume are driven by the
same underlying latent information ßow. According to this Þnding, Bollerslev and Ju-
binski (1999) have recently shown that the latent aggregate information-arrival process
hitting the stock market should be fractionally integrated. This long-run dependency
passes to both the trading volume and the volatility series, and their long-run decay rates
are the same. This paper shows the existence of such common memory behaviour in the
Italian stock market. The multivariate spectral method of Bollerslev and Jubinski is ap-
plied on the trading volume and absolute returns series of the individual Þrms composing
the MIB30 index.
Keywords: Fractional integration, Return volatility, Common dependencies.
1. Introduction
Over the past decade, temporal dependencies in Þnancial market volati-
lity have increasingly attracted the attention of empirical literature. Nu-
merous empirical Þndings have demonstrated a positive contemporane-
ous volume-absolute price change correlation (Karpoff, 1987, Stickel and
Verrecchia, 1994). An explanation of this correlation comes from re-
search on the distribution of speculative daily prices sampled from a set
of distributions with different variances. According to this mixture of
distribution hypothesis (MDH), Epps and Epps (1976) derive a MDH
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M.S. Andreano
model in which the variance of the price change on a single transaction
is conditioned by the volume of that transaction. Clark (1973) posits a
joint dependence of returns and volume on an underlying latent event or
information ßow variable. The volume is driven by the identical factors
that generate return volatility.
Early tests of the implications