Density forecasting of the Dow Jones share index

The distribution of differences in logarithms of the Dow Jones share index is compared to the normal (N), normal mixture (NM) and a weighted sum of a normal and an Assymetric Laplace distribution (NAL). It is found that the NAL fits best. We came to this result by studying samples with high, medium and low volatility, thus circumventing strong heteroscedasticity in the entire series. The NAL distribution also fitted economic growth, thus revealing a new analogy between financial data and real growth.