Abstract: Suppose that an order restriction is imposed among several means in time series. We are interested in testing the homogeneity of these unknown means under this restriction. In the present paper, a test based on the isotonic regression is done for monotonic ordered means in time series with stationary process and short range dependent sequences errors. A test statistic is proposed using the penalized likelihood ratio (PLR) approach. Since the asymptotic null distribution of test statistic is complicated, its critical values are computed by using Monte Carlo simulation method for some values of sample sizes at different significance levels. The power study of our test statistic is provided which is more powerful than that of the test proposed by Brillinger (1989). Finally, to show the application of the proposed test, it is applied to real dataset contains monthly Iran rainfall records.