In the paper the authors assume that observed telecommunication and bank processes may be represented with the aid of time-dependent parameters. Since these parameters sometimes change very rapidly, the wavelet transform was used to identify them.

The paper begins with definitions of the stationary process, the self-similarity stationary process, and the Wang et al. dependence of local power spectra on local self-similarity Hurst parameter.

After making calculations the authors have arrived at the following conclusions:

1⁰ The telecommunication processes such as line occupation time or talking time in the study data have local Hurst parameter values in the range. This implies that these processes are self-similar and stationary. Independently of the above calculations the tails of the wavelet transform coefficients at the highest scale were approximated by a generalized Pareto distribution and indicated a shape parameter . This is in accordance with the previously calculated local Hurst parameter and suggests that the studied telecommunication process should be classified as self-similar stationary increment processes (type H-sssi).

Unlike for the studied telecommunication processes, the Hurst parameters calculated for bank WIBOR data show that these processes are non-stationary. In the next part our paper generalized Pareto distributions are used to check whether the bank rate of WIBOR (Warsaw interbank deposit rates) consists of independent and identical distributed random variables (iid). The results of these calculations did not agree with the above presented hypothesis and showed that:

2⁰ The set of WIBOR processes are dependent on one another.

The authors suggest that this dependence may be due to the monetary authority decisions. In this situation values of shape parameter ? for each WIBOR level may be representative of the strength of the NBP reference rates influence on the money market situation.

Calculations similar to the above were performed for other bank processes. In particular, the commercial bank free reserves over the required reserve level in NBP were investigated. The positive valued shape-parameter ? indicated that this process also does not include independent random variables and it may indicate that:

3⁰ The free reserves level processes in the years 1996-2003 were quite determined, not random.