Inference for heavy-tailed and multiple-threshold double autoregressive models supplementary: proofs of theorem 4.1 and lemma 5.1 proofs of theorem 4.1. by the n -consistency of ˆ r , it can be proved that w ( x, ˆ λ , ˆ ) − w r ) = o (1) . hence,

HIGHLIGHTS

• who: from the (UNIVERSITY) have published the article: INFERENCE FOR HEAVY-TAILED AND MULTIPLE-THRESHOLD DOUBLE AUTOREGRESSIVE MODELS SUPPLEMENTARY: PROOFS OF THEOREM 4.1 AND LEMMA 5.1 Proofs of Theorem 4.1. By the n -consistency of u02c6 r , it can be proved that W ( x, u02c6 u03bb , u02c6 ) u2212 W r ) = o (1) . Hence,, in the Journal: (JOURNAL)

SUMMARY

INFERENCE FOR HEAVY-TAILED AND MULTIPLE-THRESHOLD DOUBLE AUTOREGRESSIVE MODELS SUPPLEMENTARY: PROOFS OF THEOREM 4.1 AND LEMMA 5.1 Proofs of Theorem 4.1. By the n-consistency of r̂n . . .

 



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