Long strange intervals in a linear stationary stochastic process with regularly varying tails are studied. Let , where is a sequence of zero mean iid random variables and is a constant. It is assumed that the tails of the distribution of satisfy the regular variation condition , as , for some , and be a slowly varying function at infinity, and balance conditions
. The behavior of the statistic
is studied. can be considered as the greatest length of time interval when the system runs under the nominal value. The main result of the paper is the limit theorem for the distribution of the vector , where . It is assumed that the sum of the modules of the coefficients is finite.