Time series from complex systems with interacting nonlinear
and stochastic sub-systems and hierarchical regulations are
often multiscaled. With the rapid accumulation of complex
data in many disciplines of science and engineering, it has
become increasingly important to simultaneously characterize
the behaviors of the complex data on a wide range of scales.
We describe a new multiscale complexity measure, the scale
dependent Lyapunov exponent, and discuss how it can classify
various types of motions, distinguish chaos from noise, cope
with nonstationarity, and characterize irregular behaviors of
complex data on small scales, and orderly behaviors, such as
oscillatory motions, on large scales. We shall also report some
interesting results on the analysis of real world data, including
economic time series, electroencephalogram (EEG) signals, heart
rate variability data, and sea clutter radar return data.