Root reflection of an ARMA representation

Reflecting zeros across the unit circle can convert a noncausal or noninvertible ARMA representation to a causal invertible one with the same time-series spectral density. Scale the driving white noise variance according to the modulus factors. Define the new noise as a filter of the actual process; equality of two spectra alone proves equality of second-order structure, not equality of non-Gaussian laws. The resulting noise is weak white noise and need not be independent across time.