to give more stable and reliable estimates for the parameters of interest. With this
method we were able to obtain results with a relatively narrow (1,000 observations)
rolling time window of daily returns.
As we are studying 49 different countries, we need to have a robust method (to ensure
comparability) that would be suitable for all fundamentally different countries possible.
Thus we do not impose any parameter restrictions for the model and use a skewed
t-distribution which ensures that the model can be automatically applied to different
countries with slightly different return distributions. Altogether this ensures both
comparable results and that not too general a model is used for every country.
Using GARCH-type models has disadvantages when the timespan is relatively short
(usually fewer than 2,000 observations) and/or return data contain jumps. To cope with
such problems we use outlier detection methods with kernel weighting for model input
returns.^1 Handling jumps is one of the key problems that need to be addressed when
applying more popular GARCH-type models. Eliminating jumps enables us to receive
more stable results with higher reliability and only a small loss of approximately 1%–
2% of data. Eliminating jumps could be a high price to pay when trying to forecast
volatility in turbulent times.
Our robustness checks show that removing outliers from the sample does not
qualitatively change asymmetry estimates but improves the reliability of estimates for
shorter datasets. And using shorter datasets is a prerequisite for us to be able to obtain
a time-series of asymmetry estimates at all. Using a rolling time window with skewed
t-distribution for APARCH model estimation also ensures that such a small number of
eliminated outliers would not start to affect results even if their economic impact on
volatility asymmetry was larger than our robustness checks show. All that enables us to
conclude that the eliminated jumps do not qualitatively affect volatility asymmetry
estimates and thus do not have any significant impact on the results.
11.2.2 Volatility asymmetry comparison
To compare volatility asymmetry in different countries, we use daily stock market
returns from the 49-country Morgan Stanley Capital International (MSCI) index pro-
vided by Thomson’s Datastream. We include all data that are available in our sample.
For a better comparison we use MSCI index returns measured in US dollars. As a proxy
for volatility asymmetry we use gammas obtained by repeatedly estimating equation
(11.1) for each country with a moving time window. Using a moving time window of a
size of 1,000 observations gives us a unique time-series dataset of the volatility asym-
metry for each country. As described in Talpsepp and Rieger (2009) we adjust the
obtained measures for volatility asymmetry to exclude an impact of different return
patterns. The adjustment also allows for better comparison of estimated volatility
asymmetry across countries. We still use both adjusted and unadjusted measures for
volatility asymmetry (both time-series and cross-sectional data) for testing different
factors that can cause the asymmetry. When comparing volatility asymmetry across
countries we can conclude that developed countries tend to have a higher level of
asymmetry. The United States ranks first in all measures. Japan, Germany, and France
Volatility asymmetry, news, and private investors 257(^1) Please see Talpsepp and Rieger (2009) for details of the APARCH model and additional measures taken to ensure better
stability of the estimated parameters to cope with short timespans.