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Consistency of global LSE for MA(1) models

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  • Yang, Yaxing
  • Ling, Shiqing
  • Wang, Qiying

Abstract

It is well known that the first-order moving-average [MA(1)] process, yt=ɛt−θ0ɛt−1, is invertible when θ0∈(−1,1). However, we need to assume the unknown parameter θ∈[−c,c] for the large sample theory of LSE, LAD or other estimates of the true parameter θ0, where c∈(0,1). The challenging issue is that the asymptotic behavior of the objective function is not clear when θ is approaching to 1 and the sample size n→∞. On the parametric space Θn=(−an,an) with an→1 and n/logn(1−an)→∞ as n→∞, this paper shows that the global LSE of MA(1) models is strongly consistent. Some simulation results are reported. A limiting theorem of linear process is included in this paper, which is of independent interest.

Suggested Citation

  • Yang, Yaxing & Ling, Shiqing & Wang, Qiying, 2022. "Consistency of global LSE for MA(1) models," Statistics & Probability Letters, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:stapro:v:182:y:2022:i:c:s0167715221002546
    DOI: 10.1016/j.spl.2021.109292
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    References listed on IDEAS

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    Keywords

    Consistency; MA model; LSE;
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