Taken somewhere from Internet.

Variance, covariance and autocovariance:

**Variance** is one of the parameter to describe the distribution. It tells how the distribution extends from the mean value.
**Moments** are always used to describe the distribution due to its computational simplicity (i.e. the power series). 1st moment is mean value, 2nd moment is variance, 3rd moment is skewness.
- Let and denote two random variables.
**Covariance** is a measure of how much and change together.
- In this case, variance is a special case of the covariance when two variables are identical.
- Given a stochastic process , the
**autocovariance** is the covariance of againsts itself in a time-shifting. That is .

Correlation and Autocorrelation:

**Correlation** is the measure of the strength of association between two variables. For example, there is a strong correlation between black eyes and and black hair as you may seem them moving together all the time. But, there is a weak correlation between blue wallpaper and puppies. Bear in mind that correlation is not *causation*. Though the death of babies increase with the cases of vehicle accidents. They have a strong correlation. But we cannot say the death of babies causes the happen of vehicle accidents. It does not make sense. [Taken from Yahoo! Answer]
**Autocorrelation** is the cross-correlation of the variable itself, in which separated by certain amount of time delay.

Random Variable:

- Say we run an experiment in which it gives a finite number of possible outcome, named as
**sample space** .
- For the convenience of mathematical calculation, each outcome (denoted as ) of is translated into a real number (if possible) and that translation process is given by a function where . We name as
**random variable** and most of the time we just denote it as if the context is well understood.

Classification of data.

Stationary Random Process:

- Let denote a random process, in which and denote its mean value and autocorrelation function.
- is
*non-stationary* if and vary as varies.
- Otherwise, is said
*stationary* or weakly stationary in wide-sense.
- For
*weakly* stationary process, and .
- For
*strongly* stationary process, all possible moments and join moments are time-invariant.

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