Non-stationarity in the distribution

The empirical evidence does not support the hypothesis of serial dependence (autocorrelation)
in security returns. This has caused investigators to focus more directly
on non-stationary nature of the two statistical moments, the mean and the variance,
which arises when both moments vary over time. Changes in the means and variance
of security returns is an alternative explanation to the existence of leptokurtosis in
the distribution. Investigations that focus on the non-stationarity in the means have
been found to be inconclusive in their findings. However, more concrete evidence is
provided when focusing on non-stationarity with respect to the variance. It has been
found that it is the conditional dependency in the variance that causes fatter tails in
the unconditional distribution that is greater than that of the conditional one. Fatter
tails and the non-stationarity in the distribution in the second moments are caused
by volatility clustering in the data set. This occurs where rates of return are characterized
by very volatile and tranquil periods. If the variances are not stationary then the
formula DEaR t does not hold.