The autocorrelation function of a binary relaxed Poisson process is derived. The process is defined as the following series of transformations of a nonhomogeneous Poisson process: 1) the process of energy bursts (a nonhomogeneous Poisson process), 2) relaxation process of the point process, and 3) its binary transformation. For a stationary BRP process, the autocorrelation function is reduced to a doubly exponential function. For a periodic BRP process with a dominant primal periodic component, it is also reduced to a simple expression in terms of the first kind modified Bessel's function of the 0-th order. The present theory is applicable to describe and analyze intermittent time series such as precipitation series, intermittent turbulence in flows, etc.
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