Heteroscedesticity in regression problems in astronomy has been discussed with various kind of observations since astronomers are interested in correlations and causality between variables in the data set. Perhaps, the heteroscedasticity in volatilty of finance does not have any commonality with astronomical times series data, which could be the primary reason this celebrated model does not appear in ADS. However, there are various times series models branched from ARCH that consider heteroscedasticity in errors and I hope some can be useful to astronomers for analyzing times series data with inhomogeneous errors.

[Note] All links lead to wikipedia.org

Recently I went to JSM 2007 and tried to attend talks about (bayesian) change point problems, which frequently appears in time series models, often found in economics. With ARCH (autoregressive conditional heteroskedecity) or GARCH (generalized ARCH) and by adding a parameter indicates a change point, I thought bayesian modeling could handle astronomical light curves.

Developing algorithms based on statistical theories, writing algorithms down in a heuristics way, making the code public, and finding/processing proper datum examples from huge astronomical data archives should come simultaneously, and this multiple steps make proposing new statistics to astronomical society difficult. I’m glad to know that there are individuals who are devoting themselves to make these steps happened. Unfortunately, they are loners.