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Let $X_1,X_2,\ldots$ and $Y_1,Y_2,\ldots$ be two random sequences so thatevery random variable takes values in a finite set $\mathbb{A}$. We consider aglobal similarity score $L_n:=L(X_1,\ldots,X_n;Y_1,\ldots,Y_n)$ that measuresthe homology (relatedness) of words $(X_1,\ldots,X_n)$ and $(Y_1,\ldots,Y_n)$.A typical example of such score is the length of the longest commonsubsequence. We study the order of central absolute moment $E|L_n-EL_n|^r$ inthe case where two-dimensional process $(X_1,Y_1),(X_2,Y_2),\ldots$ is a Markovchain on $\mathbb{A}\times \mathbb{A}$. This is a very general model involvingindependent Markov chains, hidden Markov models, Markov switching models andmany more. Our main result establishes a general condition that guarantees that$E|L_n-EL_n|^r\asymp n^{r\over 2}$. We also perform simulations indicating thevalidity of the condition.

Lower bounds for moments of global scores of pairwise Markov chains