# Is there a non-parametric test for whether a series' unconditional variance has changed over time?

I'm not sure how this would look. It seems you've have to specify regime breakpoints within the data, right? Or is there some rolling method that could compare window sizes against each other?

Also key, is it possible to do this without specifying a model?

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Along the same lines, you could set up a prior distribution over the value of $\sigma^{2}_{u}$ (in the paper's notation for the random walk variance) and use your regression/ARMA/whatever to obtain a likelihood model for $P(y_{t}|\sigma^{2}_{u})$, and then use simulations to draw lots of samples from $P(\sigma^{2}_{u}|y_{t})$. Then you can use posterior predictive checking and Bayesian p-values to test whether $\sigma^{2}_{u}$ is meaningfully different than 0. If not, you have reason to suspect the variance is not changing.