  Much of the on-going statistical analysis of DNA sequences is focused on the
estimation of characteristics of coding and non-coding regions that would
possibly allow discrimination of these regions. In the current approach, we
concentrate specifically on genes and intergenic regions. To estimate the level
and type of correlation in these regions we apply various statistical methods
inspired from nonlinear time series analysis, namely the probability
distribution of tuplets, the Mutual Information and the Identical Neighbour
Fit. The methods are suitably modified to work on symbolic sequences and they
are first tested for validity on sequences obtained from well--known simple
deterministic and stochastic models. Then they are applied to the DNA sequence
of chromosome 1 of {\em arabidopsis thaliana}. The results suggest that
correlations do exist in the DNA sequence but they are weak and that intergenic
sequences tend to be more correlated than gene sequences. The use of
statistical tests with surrogate data establish these findings in a rigorous
statistical manner.
