This study investigates the stationarity of fish telemetry data, specifically the root mean square (RMS) acceleration measurements of Atlantic salmon in sea cages. The dataset, spanning 148 days, was analyzed using advanced statistical and signal processing techniques to understand the temporal behavior of the fish. The analysis applied the Augmented Dickey-Fuller (ADF) test to confirm stationarity and the Chapman -Kolmogorov equation (CKE) test to evaluate the Markovian property. The stationarity implies the application of the Wiener–Khinchin theorem. Iterative filtration using Hamming windows, guided by dominant periods from power spectral density (PSD) analysis, decomposed the time series into distinct periodic components. These included baseline trends, circadian rhythm, and shorter periodic patterns, with the final residuals representing system noise. The study identified significant periodicities, such as circadian cycle and semi-diurnal tidal influences. Each filtration step preserved the stationarity and Markovian properties, ensuring robust data interpretation. The methodology highlights the importance of recognizing stationary characteristics in telemetry data to enhance the accuracy of behavior modeling and welfare monitoring in aquaculture systems.