Fig. 2

Empirical Lomb-Scargle periodogram (LSP) of four standard, aperiodic continuous-time stochastic movement models, showing the expected increase with period, and the rough aspect due to the stochastic nature of the process. “BM” is Brownian motion, “OU-p” is Ornstein-Uhlenbeck position process, “OU-v” is Ornstein-Uhlenbeck velocity process (a.k.a. Integrated Ornstein-Uhlenbeck process), “OUF” is Ornstein-Uhlenbeck position process with foraging, i.e., a combination of autocorrelation in both the velocity and the position of the animal. These four models are described in full detail in [26]. Theoretical periodogram values are plotted with solid lines. Green indicates a slope of 2, blue a slope of 4, and red a slope of 0. The vertical lines represent expected characteristic time scales separating two regimes of the periodogram. These time scales are equal to 2πτ where τ is the characteristic autocorrelation time of the underlying models used to generate the data. The flattening of the curves near the Nyquist frequency (small period values) is an unwanted characteristic of all periodograms, that makes periodicity inference unreliable near the Nyquist frequency