The independence assumption

Investigating the validity of the independence assumption has focused on testing for
serial correlation in changes in price. The general conclusion reached by past
investigations is that successive price changes are autocorrelated, but are too weak
to be of economic importance. This observation has led most investigations to
accept the random walk hypothesis. However, evidence has shown that a lack of
autocorrelation does not imply the acceptance of the independence assumption.
Some investigations has found that security returns are governed by non-linear
processes that allow successive price changes to be linked through the variance.
This phenomenon was observed in the pioneering investigations of the 1960s, where
large price movements were followed by large price movements and vice versa.
More convincing evidence is provided in later investigations in their more rigorous
challenge to the identical and independence assumptions. In the late 1980s much
attention was focused on using different time series data ranging from foreign
exchange currencies to commodity prices to test the validity of the i.i.d. assumptions.
Another development in those investigations is the employment of more sophisticated
models such as the conditional heteroskedastic models (i.e. ARCH/GARCH) used to
establish the extent to which the i.i.d. assumption is violated. These type of models
will be examined below.