This paper deals with the speaker verification system similar to a fingerprint or an eye scanner. For these purpose a long-term words' model and its spectral characteristics were used. The speaker verification method uses the word's sound parametric spectrum factorization in composite vector stochastic process representation based on the multiplicative autoregressive model. The developed method enables to receive the words' features with stable characteristics for the same speaker and differ for different speakers. During the training phase speaker's etalon frequencies has to be estimated for a pronounced word repeated several times. In the verification phase a speaker pronouncing the same word, word's frequencies are estimated and compared with the etalon frequencies database to find the best match or his deny. The results presented in the paper showed the high correct identification probability.