  Several studies have investigated the scaling behavior in naturally occurring
biological and physical processes using techniques such as detrended
fluctuation analysis (DFA). Data acquisition is an inherent part of these
studies and maps the continuous process into digital data. The resulting
digital data is discretized in amplitude and time, and shall be referred to as
coarse-grained realization in the present study. Since coarse-graining precedes
scaling exponent analysis, it is important to understand its effects on scaling
exponent estimators such as DFA. In this brief communication, k-means
clustering is used to generate coarse-grained realizations of data sets with
different correlation properties, namely: anti-correlated noise, long-range
correlated noise and uncorrelated noise. It is shown that the coarse-graining
can significantly affect the scaling exponent estimates. It is also shown that
scaling exponent can be reliably estimated even at low levels of
coarse-graining and the number of the clusters required varies across the data
sets with different correlation properties.
