### Abstract:

This paper extends the classical Samuelson multiplier–accelerator model
for national economy. Actually, this new modeling structure removes the basic shortcoming of the original model producing stable business cycles when realistic values
of the parameters (multiplier, accelerator) are entered into the system of equations.
Under this new approach, we introduce some kind of randomness and memory into
the system. We assume that consumption, private investment and governmental expenditure depend upon the national income values of the last n (n > 1) years and
further assume that multiplier and accelerator factors are stochastic variables. Then
stochastic delayed difference equations of higher order are employed to describe the
model, while the respective solutions of higher order polynomials for the expectation
of national income variables correspond to the typical observed business cycles of
real economy. Stability and controllability conditions are investigated while numerical
examples provide further insight and better understanding as regards the control
actions, system design, and produced business cycles.