◦ *Markov chain with two states of order 2*

For a Markov string of order 2, the state of the variable E(t) at time t depends on its state E(t − 1) at time (t − 1) as well as its state E(t − 2). The probability of having this state can be written:

$$P\_{\rm ijk} = \text{pr (E(t) = k \mid (E(t-1) = j, E(t-2) = i))} \tag{8}$$

Pijk represents the conditional probability of having a state doublet (*j*, *k*) following the state doublet (*i*, *j*) and *i*, *j*, *k* = 0 or 1, calculated using the following relationship [31]:

$$P\_{\rm ijk} = \mathbf{N}\_{\rm ijk} / \mathbf{N}\_{\rm ij} \tag{9}$$

where Nijk is the number of transitions from the state doublet (i, j) to the state doublet (j, k).

The process of transition of conditional probabilities with the Markov 2 chain is as follows (Table 3):


**Table 3.** Markov process of order 2 [35].
