Sequences of $m$-orthogonal random variables

A sequence of random variables $\{X_n\}$ is called a sequence of $m$-orthogonal random variables if $EX_n^2<\infty$ for any $n$ and $E(X_kX_j)=0$ for $|k-j|>m$. Here $m$ is a nonnegative integer number. A theorem on the law of the iterated logarithm is proved for sequences of $m$-orthogonal random variables.