Two general models that generate long range correlation

Investigating long range correlation in DNA sequences using significance tests of conditional mutual information

“…First we illustrate that when the Markov chain is of low order L, the estimated orderL converges to the true order L with the increase of N. For this, first we use Markov chains of small order (L = 4, 8) and then larger order (L = 12) defined by randomly set transition matrices, as in Kugiumtzis (2013, 2014). Next we use Markov chains of high order (L = 20) as defined in Usatenko et al (2003), and in the last setting the chains have LRC and the symbol sequences are derived from discretization of time series generated by the spectral method (Gan and Han, 2012). In all settings the sequences are binary (K = 2) and for each sequence length N we generate 100 realizations.…”

“…To form LRC processes, we employ the spectral (Fourier) method as follows. For a process possessing a power spectrum of 1/f Á , we apply first Fourier transform on a white noise time series, multiply the spectrum by a power function of the frequency f with a negative spectral exponent Á, and then take the inverse Fourier transform to obtain the time series with LRC of a strength characterized by Á (Prakash et al, 1992;Peng et al, 1994;Makse et al, 1996;Gan and Han, 2012). Then we assign the values of the time series above the sample mean to one and the rest to zero, obtaining in this way the symbol sequence of LRC.…”