A random walk model with no memory (i.e. change from previous value to next is independent of all other movements).
St=St-1+Normal(m,s)
The simplest random walk model. The variable is a random displacement from its previous value irrespective of the size of that previous value. Other distributions can, of course, be used in place of the Normal.
m in this case, but in general the mean of the distribution used, is the linear trend of the model.
At any time t:
St=S0+Normal(mt,s√t)
from Central Limit Theorem. Thus, St expands with increasing t, and easily go negative.
The links to the Random Walk 1 software specific models are provided here:
