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Plot with random data showing heteroscedasticity: The variance of the y-values of the dots increases with increasing values of x. In statistics , a sequence of random variables is homoscedastic ( / ˌ h oʊ m oʊ s k ə ˈ d æ s t ɪ k / ) if all its random variables have the same finite variance ; this is also known as homogeneity of variance.
[14] [15] Yet, in the context of binary choice models (Logit or Probit), heteroscedasticity will only result in a positive scaling effect on the asymptotic mean of the misspecified MLE (i.e. the model that ignores heteroscedasticity). [16] As a result, the predictions which are based on the misspecified MLE will remain correct.
How to solve a heterogeneous agent model depends on the assumptions that are made about the expectations of the agents in the model. Broadly speaking, models with heterogeneous agents fall into the category of agent-based computational economics (ACE) if the agents have adaptive expectations (see artificial financial market), or into the ...
Statistical testing for a non-zero heterogeneity variance is often done based on Cochran's Q [13] or related test procedures. This common procedure however is questionable for several reasons, namely, the low power of such tests [14] especially in the very common case of only few estimates being combined in the analysis, [15] [7] as well as the specification of homogeneity as the null ...
Such models assist in controlling for omitted variable bias due to unobserved heterogeneity when this heterogeneity is constant over time. This heterogeneity can be removed from the data through differencing, for example by subtracting the group-level average over time, or by taking a first difference which will remove any time invariant components of the model.
The simplest methods of estimating parameters in a regression model that are less sensitive to outliers than the least squares estimates, is to use least absolute deviations. Even then, gross outliers can still have a considerable impact on the model, motivating research into even more robust approaches.
Integrated Generalized Autoregressive Conditional heteroskedasticity (IGARCH) is a restricted version of the GARCH model, where the persistent parameters sum up to one, and imports a unit root in the GARCH process. [9]
An alternative to explicitly modelling the heteroskedasticity is using a resampling method such as the wild bootstrap. Given that the studentized bootstrap, which standardizes the resampled statistic by its standard error, yields an asymptotic refinement, [13] heteroskedasticity-robust standard errors remain nevertheless useful.