The properties of nearly unstable ARp models - Kligienė, Nerutė; Kligys, Vytautas (Lietuvos matematikos rinkinys, 1997)
Second order properties of nearly nonstacionary autoregressive (AR) processes are investigated in the cases when an autoregressive polynomial equation has: (i) a real root close to 1; (ii) a real mot close to —1; (iii) a pair of complex roots close to the unit circle.The effect of the closeness to the unit circle of AR poles on its covariance and spectral density functions is considered. The obtained results demonstrate three specific ways of degeneracy of these functions, as the roots tend to 1 in modulus. The case of complex roots is investigated in details.