# What is the meaning of heteroscedasticity?

## What is the meaning of heteroscedasticity?

As it relates to statistics, heteroskedasticity (also spelled heteroscedasticity) refers to the error variance, or dependence of scattering, within a minimum of one independent variable within a particular sample. This provides guidelines regarding the probability of a random variable differing from the mean.

## What is heteroscedasticity example?

Examples. Heteroscedasticity often occurs when there is a large difference among the sizes of the observations. A classic example of heteroscedasticity is that of income versus expenditure on meals. As one’s income increases, the variability of food consumption will increase.

What is heteroscedasticity PPT?

Heteroscedasticity is a systematic pattern in the errors where the variances of the errors are not constant. Heteroscedasticity occurs when the variance of the error terms differ across observations HETEROSCEDASTICITY. 6.

### Why is heteroskedasticity a problem?

Heteroscedasticity is a problem because ordinary least squares (OLS) regression assumes that all residuals are drawn from a population that has a constant variance (homoscedasticity). To satisfy the regression assumptions and be able to trust the results, the residuals should have a constant variance.

### How is Heteroscedasticity detected?

A formal test called Spearman’s rank correlation test is used by the researcher to detect the presence of heteroscedasticity. The researcher then fits the model to the data by obtaining the absolute value of the residual and then ranking them in ascending or descending manner to detect heteroscedasticity.

What is Homoscedasticity example?

Example of Homoskedastic For example, suppose you wanted to explain student test scores using the amount of time each student spent studying. In this case, the test scores would be the dependent variable and the time spent studying would be the predictor variable.

## What is the difference between Homoscedasticity and Heteroscedasticity?

is that homoscedasticity is (statistics) a property of a set of random variables where each variable has the same finite variance while heteroscedasticity is (statistics) the property of a series of random variables of not every variable having the same finite variance.

## Is heteroscedasticity good or bad?

Heteroskedasticity has serious consequences for the OLS estimator. Although the OLS estimator remains unbiased, the estimated SE is wrong. Because of this, confidence intervals and hypotheses tests cannot be relied on. Heteroskedasticity can best be understood visually.

How do you solve Heteroscedasticity?

The solution. The two most common strategies for dealing with the possibility of heteroskedasticity is heteroskedasticity-consistent standard errors (or robust errors) developed by White and Weighted Least Squares.

### How is Heteroscedasticity calculated?

One informal way of detecting heteroskedasticity is by creating a residual plot where you plot the least squares residuals against the explanatory variable or ˆy if it’s a multiple regression. If there is an evident pattern in the plot, then heteroskedasticity is present.

### Which is the formal test for heteroskedasticity?

Formal test for heteroskedasticity: “Breusch-Pagan” test 1) Regress Y on Xs and generate squared residuals 2) Regress squared residuals on Xs (or a subset of Xs) 3) Calculate , (N*R2) from regression in step 2. 4) LM is distributed chi-square with kdegrees of freedom.

How to estimate the coefficient of heteroscedasticity?

Estimating the coefficient of heteroscedasticity, gamma, from the e_i is an approximation such that they would not be exactly homoscedastic, even if the ε_i were homoscedastic. This is discussed on page 31 in Carroll, R.J., and Ruppert, D. (1988), Transformation and Weighting in Regression, Chapman and Hall.

## How is heteroscedasticity modeled in the GARCH model?

Heteroscedasticity is usually modeled using one the following specifications: H1 : σt2is a function of past εt2and past σt2(GARCH model). H2 : σt2 increases monotonically with one (or several) exogenous variable(s) (x1,,…, xT). H3 : σt2increases monotonically with E(yt).

## When do you use WLS to correct for heteroscedasticity?

When there is heteroscedasticity andΩis unknown, we need to be estimate it fromthe data and useWeighted Least Squares(WLS). The GLS for correcting for het-eroscedasticity is called WLS. The idea is the same as in GLS, we have to weighteach of the observations in such a way that the resulting weighted residuals haveconstant variance.