One interpretation of the statistical complexity is that it is the minimum amount of historical information required to make optimal forecasts of bits in \(x\) at the error rate \(h_\mu\).
For periodic sequences, \(C_\mu(x) = 0\) and for ideal random sequences \(C_\mu(x) = 0\) too.
Several researchers have tried to capture the properties of statistical complexity with practical alternatives. The resulting complexity metrics include:
- Crutchfield, James P., and Karl Young. July 10, 1989. "Inferring Statistical Complexity". Physical Review Letters 63 (2):105–8. DOI.