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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