Parameter estimation in Manneville–Pomeau processes

In this paper, we study a class of stochastic processes $ \{X_t\}_{t\in \mathbb {N}} $, where X_t = (\varphi \circ T_s^t)(X_0) is obtained from the iterations transformation T_s invariant for an ergodic probability \mu_s on [0,1] and certain constant by partial function \varphi:[0,1] \to {R} $. We consider here family transformations T_s:[0,1]\to indexed parameter s>0 known as Manneville–Pomeau transformations. The autocorrelation resulting process decays hyperbolically (or polynomially) obtain efficient methods to estimate s finite time series. As consequence, also rate convergence decay these processes. compare different estimation based periodogram function, smoothed variance sum, wavelet theory. To our results analyzed properties spectral density associated Fourier