Random Walk Model

There are complicated 10 lines. The values of average and dispersion is different.

But difference data shows that the phenomena of 10 is same.

Difference data is seen as noise . So the model might be
Difference ( =X(t+1) - X(t) ) = Random value(Normal distriburion, Average = 0, Standard deviation = 1)

So the data might be
X(t+1) = X(t) + Random value(Normal distriburion, Average = 0, Standard deviation = 1)
This is right because I used this rule to make the data.

This model is called "random walk".

Random walk model is the simlest model in ghe Dispersion Model for Time Series . And data of random walk model is one of " Made by Normal Distribution But Not Normal Distribution ".

Use of Random Walk Model

If the model is random walk, Single Self Correlation is high.

If self correlation is high, we can use the value of present step as the predicted value of next step.

And if the model might be the random walk we also predict the dispersion of the predicted value. This is useful for Judge of Outlier .