When Long Memory Meets the Kalman Filter: A Comparative Study

State space modeling of Gegenbauer processes with long memory

“…As an alternative, the corresponding AR(m) approximation could be derived by truncating the AR(∞) representation π (B)X t = ϵ t , π (B) = (1 − 2uB + B 2 ) d . See Chan and Palma (1998) and Grassi and Santucci de Magistris (2014) for a comparison of the two approximations in the fractionally integrated case. The general GARMA (p, q) case can be treated similarly: a finite order (m) autoregressive/moving average of the polynomial is computed and cast in a suitable form state space.…”

Are Central Bankers Inflation Nutters? A Bayesian MCMC Estimator of the Long Memory Parameter in a State Space Model

“…Several estimators of the fractional integration order have been proposed in the literature. Grassi and Magistris (2011) show that a state-based maximum likelihood estimator is superior to other estimators, but our simulations show that their finding is over-biased for a nearly non-stationary time series. We resolve this issue by using a Bayesian Monte Carlo Markov Chain (MCMC) estimator.…”

“…The most current study on the state space model long memory estimation is the one conducted by Grassi andMagistris in 2011. However, Chan andPalma (1998) and Grassi and Magistris (2011) only consider stationary series with 0 0.4 d  where 2   =1 and is assumed to be known.…”

“…Chan and Palma (1998) show that the approximate MLE-based state space model has desirable asymptotic properties and a rapid converging rate. Recently, Grassi and Magistris (2011) conducted a simulation study to compare the state space model-based long memory estimation with several widely applied parametric and semi-parametric methods. Grassi and Magistris (2011) show that compared with the other estimations, the state space model method is robust to the t distribution and is missing value, measurement error and level shift.…”

Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks

“…is the integer differencing parameter, i d is the fractional differencing parameter [31]. Extensions of the Markov switching [7], logistic [11] and random level shift [15]- [18] models to the long memory case have also been contributed by [32] [33] and [34], respectively.…”