[R-sig-QA] testing for stationarity of distributions

[Markus Loecher]

Dear fellow R users,
I am struggling with the task of quantifying the "statistical 
significance" of changes in a discrete distribution over time. I am 
not even sure whether this is a well-posed problem to begin with. If 
I was to measure e.g. the age distribution of people entering a 
building on a daily basis, I would naturally observe fluctuations in 
that distribution. Clearly, small variations would be interpreted as 
"sampling noise" whereas major shifts would indicate sth. more 
substantial. How would I quantify this ?
Would a ChiSquare test be an appropriate test for testing overall 
stationarity ? Or a two-way ANOVA decomposition ? Or should I look at 
the variance of a multinomial distribution instead ?
Also, what if wanted to test specific days for significant deviation 
from my Null model instead of overall ?
I am familiar with univariate time series change point detection 
algorithms but am not clear on how to translate these tools to the 
constrained/multivariate distribution setting.

Thanking you!

Markus