  This paper provides a framework in order to statistically model sequences
from human genome, which is allowing a formulation to synthesize gene
sequences. We start by converting the alphabetic sequence of genome to decimal
sequence by Huffman coding. Then, this decimal sequence is decomposed by HP
filter into two components, trend and cyclic. Next, a statistical modeling,
ARIMA-GARCH, is implemented on trend component exhibiting heteroskedasticity,
autoregressive integrated moving average (ARIMA) to capture the linear
characteristics of the sequence and later, generalized autoregressive
conditional heteroskedasticity (GARCH) is then appropriated for the statistical
nonlinearity of genome sequence. This modeling approach synthesizes a given
genome sequence regarding to its statistical features. Finally, the PDF of a
given sequence is estimated using Gaussian mixture model and based on estimated
PDF, we determine a new PDF presenting sequences that counteract statistically
the original sequence. Our strategy is performed on several genes as well as
HIV nucleotide sequence and corresponding results is presented.
