According to research results, Wavelet coefficients of Fractal Brownian process upper interval bound demonstrate more stability at longest time horizons for higher H (Hurst exponent) values. In this case, Wavelet coefficients form a pyramidal shape with a high centre at large scales and large time horizons. For lower H (Hurst exponent values) Wavelet coefficients of Fractal Brownian process upper interval bound are quite small. Wavelet coefficients form convex - concave shape with unexpressed peak in the high-scales and mid-time. Wavelet coefficients for greater Hurst exponent are much divergent from average, while the fractional Brownian process with lower Hurst exponent consistently demonstrates a return to average, so the deviation from average is smaller.