# Self Correlation Analysis

We can study the phenomena that the value of the step is lead from previous steps by self correlation analysis.

##
Self Correlation

Usually,
Correlation
is an approach to study the relationship between different variables (X and Y).
But self correlation is an approach to study single variable.

In self correlation, X is a previous value.
So same value could be both X and Y.

###
As the Method of Prediction

Generally, we use various information to predict something.

But if self correlation is strong, we can predict using only single variable.

This approach seems to be something special method.
We use this method for daily use.
For example, it is that "Today's afternoon will be sunny because the sunny days are kept 3 days recently."

##
Use X(n) not X(t)

I use "X(**n**)", not "X(**t**)."

It is a **t**ime series analysis, but I use "**n**."

"**n**" means "the number is n" or "n th."

If the value is measured by 1 hour,

"Number n = n hours"

.
But it is a special case.

In time series analysis,
Meta knowledge
of
sampling
is important.
There are two cases.
One of them is that the sampling is done by same intervals, "every 1 second", "every 1 hour."
The other is that intervals are different, "every lot", "every accident."

For both case, software deals with in a same way.
But we need to take care of the sampling when we understand the output.

###
Discrete Data

In self correlation analysis, the phenomena between samplings are ignored.
In other words, self correlation analysis does not study continuous phenomena.

This is not so important if the change between samplings is not important.
But we need to take care to understand the output when we do not know the information of sampling.

###
Use Mapping Theory

The change between steps could be studied as "mapping" of the logic of mathematics because discrete data is used.

This approach is often used to study
chaos.

##
Variation of Self Correlation Analysis

The relationship between
Single Regression Analysis
and
Multi-Regression Analysis
is similar to that of
Single Self Correlation Analysis
and
AR Model.

Single Regression Analysis
is used in many stages of analysis because it is a simple tool.
In a similar way, the use of
Single Self Correlation Analysis
has variation.

NEXT Single Self Correlation Analysis