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Supplementary Material to Efficient Estimation of the Parameter Path in Unstable Time Series Models

By Ulrich K. Müller

Abstract

Consider the model of Section 2.3 with a linear trend specification for the parameter path θt = θ0 + β t T Condition 2 allows for the special case where G(s) = Zs, Z ∼ N (0,c2/H), so that by Theorem 1, large sample weighted average risk minimizing decisions relative to the weighting function β ∼ N (0,c2/HT) are obtained by replacing the original likelihood by the approximations (7) and (8), or (23). We compare the following modes of inference: (i) MLE estimation of θ0 and β from the log-likelihood P lt(θ0 + βt/T) with sandwich covariance matrix (trend MLE); (ii) Linear trend model estimated using approximation (7) and (8) with c known (kn c, trnd.LL) (that is, inference from the posterior N ( ˆθe + Σˆs, Σ), whereΣδin Σ is generated by G(s) =Zs, Z ∼ N (0,c2/H)); (iii) Linear trend model estimated using approximation (23) as in Table 1withc known (kn c, trnd.Kal); (iv) Equal probability mixture of linear trend model estimated using approximation (7) and (8) with c ∈ C = {0, 5,...,50} (un c, trnd.LL); (v) Equal probability mixture of linear trend model estimated using approximation (23

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.188.7885
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