# How do I interpret the results of a Breusch–Pagan test?

In R I can perform a Breusch–Pagan test for heteroscedasticity using the ncvTest function of the car package. A Breusch–Pagan test is a type of chi squared test.

How do I interpret these results:

> require(car)
> set.seed(100)
> x1 = runif(100, -1, 1)
> x2 = runif(100, -1, 1)
> ncvTest(lm(x1 ~ x2))
Non-constant Variance Score Test
Variance formula: ~ fitted.values
Chisquare = 0.2343406    Df = 1     p = 0.6283239
> y1 = cumsum(runif(100, -1, 1))
> y2 = runif(100, -1, 1)
> ncvTest(lm(y1 ~ y2))
Non-constant Variance Score Test
Variance formula: ~ fitted.values
Chisquare = 1.191635    Df = 1     p = 0.2750001


First application of ncvTest reports that there is no heteroscedasticity, as it should. The second is not meaningful, since your dependent random variable is random walk. Breusch-Pagan test is assymptotic, so I suspect that it cannot be readily applied for random walk. I do not think that there are tests for heteroscedasticity for random walks, due to the fact that non-stationarity poses much more problems than the heteroscedasticity, hence testing for the latter in the presence of the former is not practical.