Given a fractional integrated, autoregressive, moving average, ARFIMA(p, d, q) process, the simultaneous estimation of the short and long memory parameters can be achieved by maximum likelihood estimators. In this paper, following a two-step algorithm, the coefficients are estimated combining the maximum likelihood estimators with the general orthogonal decomposition of stochastic processes. In particular, the principal component analysis of stochastic processes is exploited to estimate the short memory parameters, which are plugged into the maximum likelihood function to obtain the fractional differencing d. Key words: ARFIMA processes, Karhunen Lo~ve decomposition, Whittle MLE
Parametric Estimation for ARFIMA Models via Spectral Methods
COLI, Mauro;FONTANELLA, Lara;GRANTURCO, Mariagrazia
2005-01-01
Abstract
Given a fractional integrated, autoregressive, moving average, ARFIMA(p, d, q) process, the simultaneous estimation of the short and long memory parameters can be achieved by maximum likelihood estimators. In this paper, following a two-step algorithm, the coefficients are estimated combining the maximum likelihood estimators with the general orthogonal decomposition of stochastic processes. In particular, the principal component analysis of stochastic processes is exploited to estimate the short memory parameters, which are plugged into the maximum likelihood function to obtain the fractional differencing d. Key words: ARFIMA processes, Karhunen Lo~ve decomposition, Whittle MLEI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
