# AR Model and Others

Single Self Correlation Analysis
studies the relationship between the value and the value of previous 1 step.
This is the first step of
Self Correlation Analysis.

AR Model is more general formulation of self correlation.

##
AR Model

AR stands for "Auto Regressive."

If each step is affected from some former steps, AR model is useful.
AR model is one of the
Multi Regression Analysis
.

##
Application of AR Model

If we consider the variation of AR model, there are many patterns.
Examples are below.
By the change and fusion of ideas of formulation, there are various patterns.

###
(1) x(n) = f[x(n-1)]

This is the more general formulation of SCA.

If single correlation between x(n) and x(n-1) is strong, the formulation could be

**x(n) = A * (x-1)**.

If single correlation between x(n) and x(n-1) is **not** strong,
we may find suitable formulation between x(n) and x(n-1) by the scatter plot of x(n) and x(n-1).

**x(n) = x(n-1)**

means that the value does not change.

###
(2) x(n) = f[x(n-1),x(n-2)]

This is the application of (1).
It is a general formulation of AR model using former 2 steps.

For example,

**x(n) = x(n-1) + 0.01 x(n-2)**

means that the former 2 step effects by 1%.

###
(3) x(n) = f[u(n),v(n)]

The time of both sides of the formulation is the same.

So it seems that this formulation is not for the time series analysis.
But it is used in
Condition Analysis.
And this formulation is used if the measurement of x(n) needs much time to get.

(3) is needed to understand (4) and (5) more easily.

###
(4) x(n) = f[u(n-1),v(n-1)]

u and v means causes.
And x means an effect.

###
(5) x(n) = x(n-1) + f[y(n-1),z(n-1)]

This is same to

**x(n) - x(n-1) = f[y(n-1),z(n-1)]**.

.
It means that "**difference of x is caused by other variables**."

###
(6) x(n) = x(n - t)

This formulation means that**
"The value of former t hours repeats**."
It means periodicity.

We can use (6) for
Spectrum Analysis.

##
Non-linear Analysis

Analysis for non-linear data is studied in
chaos
field.

NEXT Moving Analysis