Table 3 Efficient particle size M eff of the proposed SMC methods for different ARMA models with fGn
From: Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time
PF type | Effective particle size (M eff ) | |||||
|---|---|---|---|---|---|---|
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 | 737.19 | 710.72 | 753.00 | 210.89 | 619.77 | 173.54 |
AR(1), H=0.7 | 712.37 | 696.36 | 750.13 | 194.98 | 606.86 | 207.05 |
AR(1), H=0.9 | 734.99 | 724.64 | 772.48 | 199.88 | 628.91 | 179.13 |
MA(1), H=0.5 | 766.83 | 745.32 | 784.75 | 219.95 | 711.18 | 193.41 |
MA(1), H=0.7 | 753.40 | 746.07 | 785.24 | 209.51 | 709.84 | 205.89 |
MA(1), H=0.9 | 791.34 | 779.44 | 835.39 | 229.24 | 741.39 | 202.39 |
ARMA(1,1), H=0.5 | 653.89 | 662.80 | 668.61 | 84.061 | 530.88 | 86.080 |
ARMA(1,1), H=0.7 | 610.05 | 605.56 | 626.75 | 78.602 | 466.84 | 83.643 |
ARMA(1,1), H=0.9 | 645.51 | 638.31 | 673.09 | 62.790 | 504.69 | 93.404 |