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Table 2 MSE performance of the proposed SMC methods for ARMA models (unknown a and b) with fGn, known and unknown \(\sigma _{u}^{2}\)

From: Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

PF type State estimation error (MSE)
  Known a,b Known a,b Unknown a,b, DA Unknown a,b,, IS Unknown a,b, DA Unknown a,b IS
  Known \(\sigma _{u}^{2}\) Unknown \(\sigma _{u}^{2}\) Known \(\sigma _{u}^{2}\) Known \(\sigma _{u}^{2}\) Unknown \(\sigma _{u}^{2}\) Unknown \(\sigma _{u}^{2}\)
AR(1), H=0.5 1.0991 1.127 1.6689 1.7337 1.4549 1.5903
AR(1), H=0.7 1.4077 1.4375 2.5759 5.9889 1.9272 3.191
AR(1), H=0.9 1.1336 1.1774 2.4334 6.5974 1.7795 6.4853
MA(1), H=0.5 1.0348 1.0758 1.1033 1.185 1.1384 1.3831
MA(1), H=0.7 1.0878 1.1138 1.1857 1.2688 1.1884 1.3748
MA(1), H=0.9 0.88045 0.90841 0.96348 1.1124 0.97747 1.2517
ARMA(1,1), H=0.5 1.638 1.6512 2.8563 3.6266 2.3157 2.3619
ARMA(1,1), H=0.7 1.7452 1.7926 3.0939 4.1174 2.7807 2.4627
ARMA(1,1), H=0.9 1.7374 1.7533 4.3466 20.617 2.5818 2.569