Dierential Geometry of Autoregressive Fractionally Integrated Moving Average Models

The di erential geometry of autoregressive fractionally integrated moving average processes is developed. Properties of Toeplitz forms associated with the spectral density functions of these long memory processes are used to compute the geometric quantities. The role of these geometric quantities on the asymptotic bias of the maximum likelihood estimates of the model parameters and on the Bartlett corrections to the likelihood ratio test statistics for the fractional di erence parameter is discussed.