**4. Discussion**

The results obtained from the Tables 1–4 sugges<sup>t</sup> that segmen<sup>t</sup> size may not always be hard-coded in the DFA algorithm based on the length of the time series in question. Especially for time series with odd lengths, the process can be automated using the fractal phenomena of the Cantor set to obtain equal segmen<sup>t</sup> sizes and satisfactory Hurst exponents.

Furthermore, multiplying Hurst exponents of the DFA and CDFA with the scaling exponents (*α*) of the Truncated Lévy flight (TLF) suggests that *Hc* is a better estimate. For the monofractal and multifractal noise-like time series, we observe that *Hcα* is approximately

equal to 1 while *Hα* exceeds 1. This deviates from the inverse relationship between the Hurst exponents and the scaling exponents of the TLF for Gaussian noise as discussed in the paper [4]. This highlights the overestimation of the Hurst exponent of the DFA approach that happens in practice.
