Calculation of the moments of sums for the autoregression process with signum by management

An autoregression sequence with simple management is considered. There is a sign of the previous term used in the recurrent equation determining this sequence. Multiplying this sign transforms this equation to a nonlinear one and essentially complicates the process. Such a signature management seems to be expedient, when an increment of the initial process is adjusted.
The distributions and the moments of some random variables concerned with this process are investigated. The autoregression processes and examples of their application are described in detail in the literature [1–4].