Consistency of global LSE for MA(1) models

Yaxing Yang, Shiqing Ling and Qiying Wang

Statistics & Probability Letters, 2022, vol. 182, issue C

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.

Keywords: Consistency; MA model; LSE (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109292

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