Re: [Swarm-Modelling] [Fwd: Re: [ABMs in finance]

[glen e. p. ropella]

address@hidden wrote:
> Could you elaborate on what you mean by the " "inertial" aspect" of this
> concept?

Pietro was talking specifically about the build up of historical dependence over
time.  For example, a system might be such that the state at time t_i is solely
dependent on the system state at time t_(i-1).  Or, the state at time t_i might
be a function of its previous states over some window:

    S(0) = F(X), where "X" is some set of factors that govern the system, and
    S(t_i) = F(X, S(t_(i-1)), S(t_(i-2)), ..., S(t_(i-n))).

(Sorry for the notation.)  What I referred to as this "inertial" aspect is
basically a result of the size of that window, n.  If n is large, then it takes
a longer time for the system to change trajectories via changes in X than it
would if n were small.

I know there are appropriate terms for this concept... I just keep drawing a
blank.  "Hysteresis" is the closest I can come.  But it's not really adequate
because it could refer to a lagged, but impulsive effect.  Where the effect I
want to name has to do with this cumulative build up.

Ultimately, it results in a kind of "continuity" or differentiability for the
trajectory which specifies "how different" one data point can be from its
neighbors.  In highly nonlinear systems, even if n is big, one might have a
lagged, impulsive change in the trajectory that is ultimately a response to
something that happened a long time ago.  But, in more linear systems, there
would be a kind of smoothing effect so that the bigger the n, the less impulsive
the response of the system.  So, a flat "hysteresis" concept isn't going to cut 
it.

-- 
glen e. p. ropella, 971-219-3846, http://tempusdictum.com
The fear of death follows from the fear of life. A man who lives fully is
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