## 3 Results  
### Demonstration of the Efficiency of the Algorithms  
Figure 2(a) shows the Fourier and Lomb periodograms for the time series in Figure 1, which was previously normalized and centered. The Fourier periodogram is shown in blue, the Lomb periodogram is shown in red [20], and the spectrum obtained by the REDFIT method is shown in green in Figure 2(b). Let us consider the observed Milankovitch cycles. Figure 2(a) shows that all six main peaks in the Fourier and Lomb periodograms are located at the frequencies (in decreasing order of spectral power): 0.0094, 0.0250, 0.0153, 0.0432, 0.0184, and 0.0339. This corresponds to the periods: 106,380 (eccentricity), 40,000 (tilt cycle), 65,360, 23,150 (precession), 54,350 and 29,500 years.  
The coincidence of the frequency maxima of the Fourier and Lomb periodograms (Figure 2(a)) can be explained by several factors. Firstly, the initial data have a uniform temporal distribution of observations. For data such as these, in the absence of white noise, there is an identical coincidence of the Fourier and Lomb periodograms [21]. Secondly, the differences in periodograms are caused by the presence of minor noise in the original data. The Lomb method [15] better distinguishes periods of 106,380 and 65,360 years from this noise.  
The REDFIT spectrum (Figure 2(b)) shows five peaks at the frequencies (in descending order of spectral power): 0.0094, 0.0250, 0.0163, 0.0425, and 0.0325. Note that the two main peaks in the REDFIT spectrum are located at the same frequencies as the main peaks in the Fourier and Lomb periodograms. In this case, two REDFIT peaks are shifted in the frequency domain, and one peak combines two Fourier and Lomb peaks. The discrepancies may be because REDFIT considers the spectrum of red noise in the time series, which is not accounted for in the Fourier and Lomb transforms.  
Figure 3: (a) Fourier and Lomb periodograms; (b) REDFIT spectrum. Constructed for the time series in Figure 1.  
Figure 2: Magnetic susceptibility of deposits of the Zhelezny Rog Cape section: (a) Lower-Upper Pontian; (b) Lower Maeotian.  
The results shown in Figure 3 demonstrate that spectral methods for studying time series are valuable tools in mathematical geology, particularly in cyclostrattigraphy for detecting orbital periodicities.  
On the example of time series presented in Figure 1, the efficiency of the developed DMA-algorithm is also demonstrated. Figure 4 shows the calculated constancy exponent of the series in blue and its smoothed version in red. As mentioned previously, the required periods of the time series are the points of the minimum of the constancy exponent _C(f, T)_. Figure 4 shows that the strong periods are 115,000, 44,000 and 85,800 years. Weakly expressed periods are 58,600 and 67,600 years. Note that the identified periods are relatively close to the periods defined by spectral methods. Four out of five periods in Figure 4 closely match the periods in Figure 3. A possible explanation for the appearance of the 85,800 years period may be that it is a multiple of the 44,000 years period.  
The results shown in Figure 4 and their comparison with results obtained in Figure 3 indicate that the proposed DMA-algorithm for determining the periods of time series can be applied in cyclostrattigraphy tasks.