  Discrete-time fractional-order dynamical systems (DT-FODS) have found
innumerable applications in the context of modeling spatiotemporal behaviors
associated with long-term memory. Applications include neurophysiological
signals such as electroencephalogram (EEG) and electrocorticogram (ECoG).
Although estimating the spatiotemporal parameters of DT-FODS is not a new
problem, when dealing with neurophysiological signals we need to guarantee
performance standards. Therefore, we need to understand the trade-offs between
sample complexity and estimation accuracy of the system parameters. Simply
speaking, we need to address the question of how many measurements we need to
collect to identify the system parameters up to an uncertainty level. In this
paper, we address this problem under the assumption that long-term memory
dependencies at the state variables level do not change over time. The main
result is the first result on non-asymptotic sample complexity guarantees of
identifying DT-FODS. Finally, we provide evidence of the efficacy of our method
in the context of forecasting real-life EEG time series.
