  We investigate statistical properties of daily international market indices
of seven countries, and high-frequency $S&P500$ and KOSDAQ data, by using the
detrended fluctuation method and the surrogate test. We have found that the
returns of international stock market indices of seven countries follow a
universal power-law distribution with an exponent of $\zeta \approx 3$, while
the Korean stock market follows an exponential distribution with an exponent of
$\beta \approx 0.7$. The Hurst exponent analysis of the original return, and
its magnitude and sign series, reveal that the long-term-memory property, which
is absent in the returns and sign series, exists in the magnitude time series
with $0.7 \leq H \leq 0.8$. The surrogate test shows that the magnitude time
series reflects the non-linearity of the return series, which helps to reveal
that the KOSDAQ index, one of the emerging markets, shows higher volatility
than a mature market such as the {S&P} 500 index.
