Covariance and Stationary process

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Difference between Covariance and Stationary process

Covariance vs. Stationary process

Covariance in probability theory and statistics is a measure of the joint variability of two random variables. In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.

Autocovariance

In probability theory and statistics, given a stochastic process, the autocovariance is a function that gives the covariance of the process with itself at pairs of time points.

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Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.

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Hilbert space

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional.

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Joint probability distribution

Given two random variables that are defined on the same probability space, the joint probability distribution is the corresponding probability distribution on all possible pairs of outputs.

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Linear map

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication.

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Marginal distribution

In probability theory and statistics, the marginal distribution of a subset of a collection of random variables is the probability distribution of the variables contained in the subset.

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Mean

A mean is a numeric quantity representing the center of a collection of numbers and is intermediate to the extreme values of a set of numbers.

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Moment (mathematics)

In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.

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Random variable

A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events.

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Statistics

Statistics (from German: Statistik, "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

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Variance

In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.

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