2015/05/11 by Jakub Ślęzak, Aleksander Weron · 10 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Computer science #Geology #Mathematics #Series (stratigraphy) #Statistics #Time Series Analysis and Forecasting #Time series #physics.data-an
paper · pdf · doi:10.1103/physreve.91.053302
published in Physical Review E 91(5), 053302 (American Physical Society) · 7 pages, 4 figures
openalex publication_date 2015/05/11 · arxiv created 2017/03/17 · arxiv updated 2017/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Modeling physical data with linear discrete-time series, namely, the autoregressive fractionally integrated moving average (ARFIMA) model, is a technique that has attracted attention in recent years. However, this model is used mainly as a statistical tool only, with weak emphasis on the physical background of the model. The main reason for this lack of attention is that the ARFIMA model describes discrete-time measurements, whereas physical models are formulated using continuous-time parameters. In order to eliminate this discrepancy, we show that time series of this type can be regarded as sampled trajectories of the coordinates governed by a system of linear stochastic differential equations with constant coefficients. The observed correspondence provides formulas linking ARFIMA parameters and the coefficients of the underlying physical stochastic system, thus providing a bridge between continuous-time linear dynamical systems and ARFIMA models.