Distance of a time series from the white noise

Question

Are there any ways to assign a metric to time series that measures its distance from the white noise? By white noise I mean a time series sampled from $N(0,\sigma^2)$ for some $ \sigma$. This metric should assign non-negative numbers to the times series with a given confidence interval, that somehow measures the similarity between this times series and one sampled from a white noise. When this metric is zero it should imply that the time series is sampled from the white noise with that given confidence interval.