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Table 1 Results of numerical simulations

From: Constrained expectation maximisation algorithm for estimating ARMA models in state space representation

pNcdim (𝜗)iter.MTLL (EM)F.N. (EM)MTLL (EM+BFGS)AIC (EM+BFGS)F.N. (EM+BFGS)
1282031345.440.577419068.0219084.020.4600
22143327917.360.033113663.7613691.760.0967
32225125368.710.210213343.4113387.410.0110
42327425245.960.300013104.0113168.010.0353
52449826517.650.306413215.4713303.470.0123
625811928181.530.304513208.4313324.430.0170
727414229638.160.311013262.6813410.680.0440
829218731086.830.271616750.9716934.970.4028
9211247430385.520.375828282.5728506.570.0977
10213451330383.590.425929566.9529834.950.2320
2182544391.86-37955.7137971.71-
23203528052.80-13529.0313569.03-
  1. Columns (from left to right) show model order (p), number of ARMA components (Nc), number of model parameters (dim (𝜗)), number of iterations until EM algorithm reaches a minimum (iter.), (−2)log(likelihood) at that minimum (MTLL), Frobenius norm (F.N.), (−2)log(likelihood) after additional optimisation by BFGS, corresponding value of the Akaike Information Criterion (AIC) and corresponding Frobenius norm. Likelihood values were computed omitting a transient of 20 initial samples. Note that Frobenius norm can only be computed for Nc=2