Strictly Stationary Solutions of Arma Equations with Fractional Noise

Abstract:     
We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of ARMA equations with fractional noise. Here, the underlying noise sequence of the fractional noise is assumed to be i.i.d. but no a priori moment assumptions are made. We also characterize for which i.i.d. driving noise sequences the series defining fractional noise converges almost surely. In the proofs, we use growth estimates for the moments of random walks developed by Manstavičius (1982) and techniques related to those of Brockwell and Lindner (2010) for the existence of strictly stationary ARMA processes with i.i.d. noise.

Number of Pages in PDF File: 13

Keywords: ARMA with fractional noise, ARIMA, strict stationarity, infinite variance

Accepted Paper Series