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Table 1 MSE performance of the proposed SMC methods for ARMA models (known 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 \(\sigma _{u}^{2}\)

Unknown \(\sigma _{u}^{2}\)

AR(1), H=0.5

1.1081

1.1945

AR(1), H=0.7

1.3946

1.4397

AR(1), H=0.9

1.1195

1.1970

MA(1), H=0.5

1.0223

1.0686

MA(1), H=0.7

1.0585

1.1136

MA(1), H=0.9

0.87374

0.94053

ARMA(1,1), H=0.5

1.5947

1.6197

ARMA(1,1), H=0.7

1.7852

1.8516

ARMA(1,1), H=0.9

1.7214

1.7362