A higher-order moment formula for non-zero-mean AR processes

An autoregressive (AR) model which is excited by a non-zero-mean, independent and identically distributed stationary random process is investigated. As in the zero-mean case, a cumulant-based higher-order Yule-Walker equation is derived. By expanding the cumulants in terms of their moments, a higher-order moment formula is obtained. This formula not only relates the higher-order moment with the lower-order moment, but also makes it possible to estimate the AR parameters and the output mean simultaneously. The formula is computationally more efficient than the cumulant formula.<
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