How to detect changing variance in a random variable? Say I have a random variable, and its mean or variance is changing over time, how do I detect this, given back-data? One idea is just to look at the recent values vs the less recent values and detect changes that way? Is there a standardized way to do this? A name for the method?

You could consider the dglm package from CRAN, which will do log-linear modelling for the variance at the same time as linear model modelling of the mean.
Here are some references:
References
Aitkin, M. (1987). Modelling variance heterogeneity in normal regression using GLIM. Journal of the Royal Statistical Society: Series C (Applied Statistics), 36(3), 332-339.
Smyth, G. K. (1989). Generalized linear models with varying dispersion. Journal of the Royal Statistical Society B 51(1), 47-60.
Rigby, R. A., & Stasinopoulos, M. D. (1995). Mean and dispersion additive models: applications and diagnostics. In Statistical Modelling (pp. 249-256). Springer, New York, NY.
