A0304
Title: Innovation algorithm of fractionally integrated processes and applications to the estimation of parameters
Authors: Junichi Hirukawa - Niigata University (Japan) [presenting]
Kou Fujimori - Shinshu University (Japan)
Abstract: The long memory phenomena frequently occur in the empirical studies of various fields. The fractionally integrated process is one of the suitable candidates which appropriately represents the long memory property. There are two recursive algorithms for determining the one-step predictors of time series, that is, the Durbin-Levinson algorithm and the innovation algorithm. The Durbin-Levinson algorithm for fractionally integrated processes is well-known and widely used. It naturally derives the Cholesky factorization of the inverse matrix of the covariance matrix of the process. We derive the innovation algorithm for the fractionally integrated process. The result is also applied to the derivation of the Cholesky factorization of the covariance matrix of the process in the explicit form. Moreover, the asymptotic theory of the Gaussian maximum likelihood estimator (GMLE) is derived in terms of the innovation algorithm.
