thumb|right|plot with random data showing heteroscedasticity. in statistics, a collection of random variables is heteroscedastic if there are sub-populations that have different variabilities from others. here "variability" could be quantified by the variance or any other measure of statistical dispersion. thus heteroscedasticity is the absence of homoscedasticity. the spellings homoskedasticity and heteroskedasticity are also frequently used.j huston mcculluch argued that there should be a k in the middle of the word and not a c. his argument was that the word had been constructed in english directly from greek roots rather than coming into the english language indirectly via the french. the possible existence of heteroscedasticity is a major concern in the application of regression analysis, including the analysis of variance, because the presence of heteroscedasticity can invalidate statistical tests of significance that assume that the modelling errors are uncorrelated and normally distributed and that their variances do not vary with the effects being modelled. similarly, in testing for differences between sub-populations using a location test, some standard tests assume that variances within groups are equal. ==etymology== the term means "differing variance" and comes from the greek "hetero" ('different') and "skedasis" ('dispersion'). ==definition== suppose there is a sequence of random variables {y't}t=1n and a sequence of vectors of random variables, {x't}t=1n. in dealing with conditional expectations of y't given x't, the sequence {y't}t=1n is said to be heteroscedastic if the conditional variance of yt given x't, changes with&nbsp;t. some authors refer to this as conditional heteroscedasticity to emphasize the fact that it is the sequence of conditional variances that changes and not the unconditional variance. in fact, it is possible to observe conditional heteroscedasticity even when dealing with a sequence of unconditional homoscedastic random variables; however, the opposite does not hold. if the variance changes only because of changes in value of x and not because of a dependence on the index t, the changing variance might be described using a scedastic function. when using some statistical techniques, such as ordinary least squares (ols), a number of assumptions are typically made. one of these is that the error term has a constant variance. this might not be true even if the error term is assumed to
Econometrics Statistical_deviation_and_dispersion Time_series_analysis