76 research outputs found
Time series aggregation, disaggregation and long memory
We study the aggregation/disaggregation problem of random parameter AR(1)
processes and its relation to the long memory phenomenon. We give a
characterization of a subclass of aggregated processes which can be obtained
from simpler, "elementary", cases. In particular cases of the mixture
densities, the structure (moving average representation) of the aggregated
process is investigated
Langevin diffusions on the torus: estimation and applications
We introduce stochastic models for continuous-time evolution of angles and develop their estimation. We focus on studying Langevin diffusions with stationary distributions equal to well-known distributions from directional statistics, since such diffusions can be regarded as toroidal analogues of the Ornstein–Uhlenbeck process. Their likelihood function is a product of transition densities with no analytical expression, but that can be calculated by solving the Fokker–Planck equation numerically through adequate schemes. We propose three approximate likelihoods that are computationally tractable: (i) a likelihood based on the stationary distribution; (ii) toroidal adaptations of the Euler and Shoji–Ozaki pseudo-likelihoods; (iii) a likelihood based on a specific approximation to the transition density of the wrapped normal process. A simulation study compares, in dimensions one and two, the approximate transition densities to the exact ones, and investigates the empirical performance of the approximate likelihoods. Finally, two diffusions are used to model the evolution of the backbone angles of the protein G (PDB identifier 1GB1) during a molecular dynamics simulation. The software package sdetorus implements the estimation methods and applications presented in the paper
Inversion de la matrice de Toeplitz en d dimensions et développement asymptotique de la trace de l'inverse à l'ordre d
Parameter estimation for a discrete sampling of an intergrated Ornstein-Uhlenbeck process
Parametric Estimation Problem for a Time Periodic Signal in a Periodic Noise
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