# How can these residuals have homogeneity of variances?

I'm testing the Homogeneity of Variances with Fligner-Killeen test using the function fligner.test in stats

On the chart below I have plotted the residuals that pass this test (p-value > 0.1)

Someone could tell how is it possible that these residuals pass FK test while having a significant movement around the center of the plot?

EDIT:

I'm testing two groups:

A -> res[1:375]

B -> res[376:750]

The residuals are 750, so I'm comparing the two halves.

Thank you

• Are you sure it is applicable for the time series data? And which parts of the plot constituted separate samples that you were comparing? – Alex Sep 5 '11 at 12:19
• @Alex I'm comparing res[1:375] to res[376:750] where res variable has the residuals you see in the image. Total residuals are 750 indeed. Do you think is not applicable to time series? what method should I use? – Dail Sep 5 '11 at 12:25

In my opinion, @Alex's questions are right (+1), the FK test originated for the cross-sectional data, not time series objects. Even in subsamples the data points will be dependent, thus the tests are probably not applicable.

Since heteroscedasticity is a part of some model (you noted these are the residuals, probably from some linear model) you may consider many different alternatives from the lmtest package.

1. One of the most common options is the Goldfeld-Quandt test gqtest(), however its ad hoc nature (how you choose to split the samples) makes it less attractive than
2. Breusch-Pagan test bptest() the test performs additional regression of squared residuals on the explanatory variables, and in the presence of significant dependence rejects the homoscedastic null
3. Another common alternative to the first two tests is a family of White test that are in general presented as LM type of tests comparing original and auxiliary regression models
4. If some more complicated structures for the variance of residuals is considered, you may also look for very rich family of conditionally heteroscedastic models.
• P.S. in my macroeconometric research I usually consider 3.(2.) and 4. both testing for unconditional and conditional heteroscedasticities. – Dmitrij Celov Sep 5 '11 at 13:14
• @Dmitrj do you mean that i have to choose a test to check heteroscedastic instead of a method to check if the variances are homogeneous? I used BpTest but it fails many time using residuals like those in the plot above. It says "homoscedastic" but the residuals have peaks of variance. – Dail Sep 5 '11 at 13:16
• two things: (1) instead of lm residuals do I have to pass the residuals of stat.ucl.ac.be/ISdidactique/Rhelp/library/tseries/html/… to Breusch-Pagan test? right? (2) White test seems not to be covered in lmtest package, what package do i have to use? – Dail Sep 5 '11 at 13:27
• .... last thing, what you wrote ARCH-LM were you referring to rss.acs.unt.edu/Rdoc/library/vars/html/arch.html? – Dail Sep 5 '11 at 13:30
• – Dmitrij Celov Sep 5 '11 at 13:33