Covariance Là Gì

[Jacquelyne Betance]

Thesign of the covariance, therefore, shows the tendency in the linear relationship between the variables. If greater values of one variable mainly correspond with greater values of the other variable, and the same holds for lesser values (that is, the variables tend to show similar behavior), the covariance is positive.[2] In the opposite case, when greater values of one variable mainly correspond to lesser values of the other (that is, the variables tend to show opposite behavior), the covariance is negative. The magnitude of the covariance is the geometric mean of the variances that are in common for the two random variables. The correlation coefficient normalizes the covariance by dividing by the geometric mean of the total variances for the two random variables.

A distinction must be made between (1) the covariance of two random variables, which is a population parameter that can be seen as a property of the joint probability distribution, and (2) the sample covariance, which in addition to serving as a descriptor of the sample, also serves as an estimated value of the population parameter.

In this case, the relationship between Y \displaystyle Y and X \displaystyle X is non-linear, while correlation and covariance are measures of linear dependence between two random variables. This example shows that if two random variables are uncorrelated, that does not in general imply that they are independent. However, if two variables are jointly normally distributed (but not if they are merely individually normally distributed), uncorrelatedness does imply independence.[9]

X \displaystyle X and Y \displaystyle Y whose covariance is positive are called positively correlated, which implies if X > E [ X ] \displaystyle X>E[X] then likely Y > E [ Y ] \displaystyle Y>E[Y] . Conversely, X \displaystyle X and Y \displaystyle Y with negative covariance are negatively correlated, and if X > E [ X ] \displaystyle X>E[X] then likely Y

In fact these properties imply that the covariance defines an inner product over the quotient vector space obtained by taking the subspace of random variables with finite second moment and identifying any two that differ by a constant. (This identification turns the positive semi-definiteness above into positive definiteness.) That quotient vector space is isomorphic to the subspace of random variables with finite second moment and mean zero; on that subspace, the covariance is exactly the L2 inner product of real-valued functions on the sample space.

The sample covariances among K \displaystyle K variables based on N \displaystyle N observations of each, drawn from an otherwise unobserved population, are given by the K K \displaystyle K\times K matrix q = [ q j k ] \displaystyle \textstyle \overline \mathbf q =\left[q_jk\right] with the entries

The covariance is sometimes called a measure of "linear dependence" between the two random variables. That does not mean the same thing as in the context of linear algebra (see linear dependence). When the covariance is normalized, one obtains the Pearson correlation coefficient, which gives the goodness of the fit for the best possible linear function describing the relation between the variables. In this sense covariance is a linear gauge of dependence.

Covariance is an important measure in biology. Certain sequences of DNA are conserved more than others among species, and thus to study secondary and tertiary structures of proteins, or of RNA structures, sequences are compared in closely related species. If sequence changes are found or no changes at all are found in noncoding RNA (such as microRNA), sequences are found to be necessary for common structural motifs, such as an RNA loop. In genetics, covariance serves a basis for computation of Genetic Relationship Matrix (GRM) (aka kinship matrix), enabling inference on population structure from sample with no known close relatives as well as inference on estimation of heritability of complex traits.

In the theory of evolution and natural selection, the price equation describes how a genetic trait changes in frequency over time. The equation uses a covariance between a trait and fitness, to give a mathematical description of evolution and natural selection. It provides a way to understand the effects that gene transmission and natural selection have on the proportion of genes within each new generation of a population.[13][14]

Covariances play a key role in financial economics, especially in modern portfolio theory and in the capital asset pricing model. Covariances among various assets' returns are used to determine, under certain assumptions, the relative amounts of different assets that investors should (in a normative analysis) or are predicted to (in a positive analysis) choose to hold in a context of diversification.

The covariance matrix is important in estimating the initial conditions required for running weather forecast models, a procedure known as data assimilation. The 'forecast error covariance matrix' is typically constructed between perturbations around a mean state (either a climatological or ensemble mean). The 'observation error covariance matrix' is constructed to represent the magnitude of combined observational errors (on the diagonal) and the correlated errors between measurements (off the diagonal). This is an example of its widespread application to Kalman filtering and more general state estimation for time-varying systems.

The eddy covariance technique is a key atmospherics measurement technique where the covariance between instantaneous deviation in vertical wind speed from the mean value and instantaneous deviation in gas concentration is the basis for calculating the vertical turbulent fluxes.

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

Ariel Courage is an experienced editor, researcher, and former fact-checker. She has performed editing and fact-checking work for several leading finance publications, including The Motley Fool and Passport to Wall Street.

Possessing financial assets with returns that have similar covariances does not provide very much diversification. Therefore, a diversified portfolio would likely contain a mix of financial assets that have varying covariances.

While the covariance does measure the directional relationship between two assets, it does not show the strength of the relationship between the two assets; the coefficient of correlation is a more appropriate indicator of this strength.

A covariance of zero indicates that there is no clear directional relationship between the variables being measured. In other words, a high value for one stock is equally likely to be paired with a high or low value for the other.

Covariance and variance are used to measure the distribution of points in a data set. However, variance is typically used in data sets with only one variable and indicates how closely those data points are clustered around the average. Covariance measures the direction of the relationship between two variables. A positive covariance means that both variables tend to be high or low at the same time. A negative covariance means that when one variable is high, the other tends to be low.

Covariance measures the direction of a relationship between two variables, while correlation measures the strength of that relationship. Both correlation and covariance are positive when the variables move in the same direction and negative when they move in opposite directions. However, a correlation coefficient must always range from -1 to +1, with extreme values indicating a strong relationship.

For a set of data points with two variables, the covariance is measured by taking the difference between each variable and their respective means. These differences are then multiplied and averaged across all of the data points. In mathematical notation, this is expressed as:

In C#, covariance and contravariance enable implicit reference conversion for array types, delegate types, and generic type arguments. Covariance preserves assignment compatibility and contravariance reverses it.

Covariance and contravariance support for method groups allows for matching method signatures with delegate types. This enables you to assign to delegates not only methods that have matching signatures, but also methods that return more derived types (covariance) or that accept parameters that have less derived types (contravariance) than that specified by the delegate type. For more information, see Variance in Delegates (C#) and Using Variance in Delegates (C#).

In .NET Framework 4 and later versions, C# supports covariance and contravariance in generic interfaces and delegates and allows for implicit conversion of generic type parameters. For more information, see Variance in Generic Interfaces (C#) and Variance in Delegates (C#).

A generic interface or delegate is called variant if its generic parameters are declared covariant or contravariant. C# enables you to create your own variant interfaces and delegates. For more information, see Creating Variant Generic Interfaces (C#) and Variance in Delegates (C#).

I am trying to figure out the exact meaning of the words Covariance and Contravariance from several articles online and questions on StackOverflow, and from what I can understand, it's only another word for polymorphism.

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