  Analogs are nearest neighbors of the state of a system. By using analogs and
their successors in time, one is able to produce empirical forecasts. Several
analog forecasting methods have been used in atmospheric applications and
tested on well-known dynamical systems. Although efficient in practice,
theoretical connections between analog methods and dynamical systems have been
overlooked. Analog forecasting can be related to the real dynamical equations
of the system of interest. This study investigates the properties of different
analog forecasting strategies by taking local approximations of the system's
dynamics. We find that analog forecasting performances are highly linked to the
local Jacobian matrix of the flow map, and that analog forecasting combined
with linear regression allows to capture projections of this Jacobian matrix.
The proposed methodology allows to estimate analog forecasting errors, and to
compare different analog methods. These results are derived analytically and
tested numerically on two simple chaotic dynamical systems.
