Last year I published the results of Rescaled
Range analysis of returns of Bulgarian stock market index SOFIX and Romanian
BET on this blog. Now I changed the methodology a bit and implementation is now
based on a Matlab function. However, the results for Romanian stock market
index BET and Bulgarian SOFIX do not differ much. The analyzed period this time is Jan 3,
2011-Oct 3, 2014.
Briefly, the underlying idea of this analysis
is find patterns that may repeat in the future changes. As the name (Rescaled range) may hint it is
about the range that has been rescaled (by the standard deviation), hence the
abbreviation R/S. Fitting logarithm of
the R/S to the logarithm of the size of the data, we can derive the slope of
the curve and it is the slope that is named Hurst-exponent (H). Data with Hurst
–exponent between 0.0 and 0.49 exhibits mean-reverting behavior, H=0.5 is
random, while H-exponent between 0.51 and 1.0 reveals long-memory pattern of
the data. Again, I prefer to use ranges as follows: 0.0-0.33 for mean-reverting
behavior, 0.34-0.67 for random behavior and 0.68-1 for persistent behavior.
The return series of the 4 stock indices show that: (1) Romanian stock
market index BET exhibits the strongest random behavior with H value of 0.5585;
(2) Bulgarian stock market index SOFIX is on the opposite side – with H value
of 0.7255 it exhibits the strongest persistence among the 4 markets. (3)
Slovenian SBITOP exhibits randomness with strong bias towards persistence as H
value of 0.6602 is very close to the threshold; (4) CROBEX index (Croatia) behavior
seems similar to BET as the H value of 0.568 reveals a random behavior.
The mathematics behind Rescaled range in a
nutshell could be outlined in the following steps:
(1)
Calculate
the mean return (return is logarithmic change);
(2)
Adjusting
the mean series via subtracting the calculated mean from each single daily
return;
(3)
Sum
all adjusted mean series;
(4)
Compute
the range that is the difference between the highest and lowest value as well
as the standard deviation.
(5)
Compute
the Rescaled range that is the ratio between the range and the standard
deviation;
(6)
The
H-exponent is the ratio between the logarithm of the Rescaled range and logarithm
of the size (number of the returns).
The results for the four markets are presented
as follows (p-values are not reported but both slope and intercept are statistically significant at the level of 0.05 for all indices):
BET index (Romania)
SOFIX index (Bulgaria)
SBITOP index (Slovenia)
CROBEX index (Croatia)
This publication is for information purposes
only and should not be construed as a solicitation or an offer to buy or sell
any securities.
