Arima model foreign language literature

We show that a stationary ARMA(p, q) process {Xn, n = 0, 1, 2, •••} whose moving-average polynomial has a root on the unit circle cannot be embedded in any continuous-time autoregressive moving-average (ARMA) process {7(t), t ^ 0}, i.e. we show that it is impossible to find a continuous-time ARMA process {7(t)} whose autocovariance function at integer lags coincides with that of {Xn}. This provides an answer to the previously unresolved question raised in the papers of Chan and Tong (J Time Ser. Anal. 8 (1987), 277-81), He and Wang (J Time Ser. Anal. 10 (1989), 315-23) and Brockwell (J. Time Ser. Anal. 16 (1995), 451—60).