A strong convergence rate of estimator of variance change in linear processes and its applications

Abstract

Let {Yn,n≥1} be a linear process such that Yi=μ+σ1ei,i≤k0 and Yi=μ+σ2ei,i≥k0+1, where k0 is a change point, μ, σ1 and σ2 are unknown parameters and {ei,i≥1} is an infinite-order moving average process which satisfies some assumptions. In this paper we investigate the strong convergence rate of the estimator of the variance change and derive a strong convergence rate o(M(n)/n), where M(n) is a natural number sequence and increase to infinity as the sample size n increase to infinity. On the basis of the results, we apply an iterative algorithm to search for the variance change more effectively. A simple simulation study demonstrates that the algorithm is efficient. Additionally, an empirical application is given for illustration.

Cite this work

No public copy is stored for this record, so only the metadata is cited.

Stored only when both papers are in the corpus — 6 citations exist upstream.

Papers that cite the same references — the relational fallback while embeddings are still backfilling.