A set of four pairs of voting and non-voting German stocks will
be subject to our empirical analysis. More precisely, our data
sample retrieved from the data information service Thompson Financial Datastream, consists of daily closing prices of stocks of
WMF, Dyckerhoff, KSB and RWE from January
,
, to
December
,
.
Figure 14.6 shows the performance of WMF stocks in our
data period. The plot indicates an intimate relationship of both
assets. Since the performance of both kinds of stocks are
influenced by the same economic underlyings, their relative value
should be stable over time. If this holds, the log-difference
of the pairs of voting (
) and non-voting stocks (
),
![]() |
(14.6) |
Table 14.1
gives the R/S statistic of each individual stock and of the
log-difference process of voting and non-voting stocks. While
is close to
for each time series taken separately,
we find for the log differences a Hurst coefficient indicating
negative persistence, i.e.
.
|
To test for the significance of the estimated
Hurst coefficients we need to know the
finite sample distribution of the R/S statistic. Usually, if the
probabilistic behavior of a test statistic is unknown, it is
approximated by its asymptotic distribution when the number of
observations is large. Unfortunately, as, for example,
Lo (1991) shows, such an asymptotic approximation is inaccurate
in the case of the R/S statistic. This problem may be solved by means
of bootstrap and simulation methods. A semiparametric bootstrap approach to
hypothesis testing for the Hurst coefficient has been introduced
by Hall et al. (2000),
In the spirit of this chapter we use Brownian
motion () to simulate
under the null hypothesis. Under the null hypothesis
the log-difference process follows a standard Brownian motion and
by Monte Carlo simulation we compute
%,
% and
% confidence intervals of
the R/S statistic.
The results are given in Table 14.2.
While the
estimated Hurst coefficients for each individual stock are at least contained in the
% confidence interval, we consider the R/S statistic for voting/non-voting
log differences as significant.