Heteroskedasticity

From Free net encyclopedia

In statistics, a sequence or a vector of random variables is heteroskedastic if the random variables in the sequence or vector may have different variances. The complement is called homoskedasticity. (In America, it is usually spelled homoscedastic. It is an exception to the rule that American spellings are usually more faithful to the etymologies than British spellings.)

When using a variety of techniques in statistics, 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 will be true if the observations of the error term are assumed to be drawn from identical distributions. Heteroskedasticity is a violation of this assumption.

For example, the error term could vary or increase with each observation, something that is often the case with cross sectional or time series measurements. Heteroskedasticity is often studied as part of econometrics, which frequently deals with data exhibiting it. It comes in two forms, pure and impure. Because there are so many types of each, most textbooks limit themselves to dealing with heteroskedasticity in general, or one or two examples.

Now, with the advent of robust standard errors allowing us to do inference without specifying the conditional second moment of error term, testing conditional homoskedasticity is not as important as it used to be, in every case the most popular test for conditional homoskedasticity is due to White (1980).

1 Consequences
2 Examples
3 See also
4 References

[edit]

Consequences

The consequences are similar, but not quite the same as for serial correlation.

When OLS is applied to heteroskedastic models the estimated variance is a biased estimator of the true variance. That is, it either overestimates or underestimates the true variance, and, in general it is not possible to determine the nature of the bias. The variances, and so the standard errors may therefore be either understated or overstated.

[edit]

Examples

Heteroskedasticity often occurs when there is a large difference between the size of observations.

The classic example of heteroskedasticity is that of income versus food consumption. As one's income increases, the variability of food consumption will increase. A poorer person will spend a rather constant amount by always eating fast food; a wealthier person may occasionally buy fast food and other times eat an expensive meal. Those with higher incomes display a greater variability of food consumption.
Imagine you are watching a rocket take off nearby and measuring the distance it has travelled once each second. In the first couple of seconds your measurements may be accurate to the nearest centimeter, say. However, 5 minutes later as the rocket recedes into space, the accuracy of your measurements may only be good to 100 m, because of the increased distance, atmospheric distortion and a variety of other factors. The data you collect would exhibit heteroskedasticity.

[edit]