The article clearly states that the test extends to many forms of randomness beyond Gaussian:<p>&quot;Nevertheless, the desired effect of stochastic volatility namely, fatter tailed distributions ...&quot;<p>&quot;... we want a test for the random walk hypothesis which passes (it concludes the market is random) even if the returns demonstrate heteroskedastic increments and large drifts. Why? Because both of these properties are widely observed in most historical asset price data (just ask Nassim Taleb) and neither invalidate the fundamental principle underpinning the random walk hypothesis, namely the Markov property (unforecastibility of future asset prices given past asset prices)&quot;