Coloured stochastic time-series are not normally distributed.

<p>The proportion of coloured stochastic (environmental) time-series that fail a normality test increases as they change colour, even when the same methods produce normally distributed white noise (10,000 step series; 1000 replicates for each parameter value), under both (A) Autoregressive and (B) Spectral synthesis methods (<i>x</i>-axis values reversed for comparison). Inlays illustrate frequency distributions for series of <i>ε_t</i> values from sample blue (A: <i>α</i>≈<b>−</b>0.999, B: <i>β</i>≈1), white (<i>α</i>, <i>β</i>≈0) and red (<i>α</i>≈0.999, <i>β</i>≈<b>−</b>1.86) stochastic series.