  The theories of system identification have been highly elaborated so as to
achieve the true system. This paper much discuses regarding the stochastic
processes along with the divergent of whether or not the system has zero-mean
under scenario of either white and coloured noise. The mathematical
foundations, including mean, variance, covariance, optimal parameters, along
with some modified scenarios among them, are presented in detail from various
system along with some basic idea behind them. The families of auto-regressive
(1) and (2) are compared both mathematical and simulation in order to obtain
the best design approaching the true system, Moreover, the least-square
algorithm is used to examine the effectiveness of some number of iteration
along with "batch" theorem
