Question

RANDOM VALUES

1) What is the difference and similarities (if any) between Variance Vs. Covariance Vs. Cross covariance?

2) What is the difference and similarities (if any) between Autocorrelation and cross correlation?

3) What is the difference between covariance and correlation?

Answer 1

1) Variance Vs. Covariance Vs. Cross

Variance is the expectation of the squared deviation of a random variable from its mean. It measures how far a set of numbers are spread out from their average value.

Covariance, as we can guess from its name, indicates the tendency of two variables to co-vary or "move" together. If cov(X, Y) is positive, then larger values of X are associated with larger values of Y and smaller values of X are associated with smaller values of Y.

Cross-covariance is a function that gives the covariance of one process with the other at pairs of time points.It is often called cross-correlation and is a measure of similarity of two signals, commonly used to find features in an unknown signal by comparing it to a known one. It is a function of the relative time between the signals.

2) Autocorrelation and cross correlation

The auto-correlation function is the correlation between the value at position/time t is with values at other positions (t?1), (t?2), etc. High autocorrelations may indicate that the series changes slowly, or, equivalently, that the present value is predictable from previous values.

Cross-correlation compares two series by shifting one of them relative to the other. Like auto-correlation, it produces a vector. The middle of the vector is just the correlation between X and Y.

3) Covariance and Correlation

Covariance is defined as a systematic relationship between a pair of random variables where a change in one variable reciprocated by an equivalent change in another variable.

Covariance can take any value between -? to +?, wherein the negative value is an indicator of negative relationship whereas a positive value represents the positive relationship. Further, it ascertains the linear relationship between variables. Therefore, when the value is zero, it indicates no relationship.

Correlation is described as a measure in statistics, which determines the degree to which two or more random variables move in tandem. During the study of two variables, if it has been observed that the movement in one variable, is reciprocated by an equivalent movement another variable, in some way or the other, then the variables are said to be correlated.

Correlation is of two types, i.e. positive correlation or negative correlation.The value of correlation lies between -1 to +1, wherein values close to +1 represents strong positive correlation and values close to -1 is an indicator of strong negative correlation.