On buffered moving average models

Yipeng Zhuang, Dong Li, Philip L. H. Yu and Wai Keung Li

Journal of Time Series Analysis, 2025, vol. 46, issue 4, 599-622

Abstract: There has been growing interest in extending the popular threshold time series models to include a buffer zone for regime transition. However, almost all attention has been on buffered autoregressive models. Note that the classical moving average (MA) model plays an equally important role as the autoregressive model in classical time series analysis. It is therefore natural to extend our investigation to the buffered MA (BMA) model. We focus on the first‐order BMA model while extending to more general MA model should be direct in principle. The proposed model shares the piecewise linear structure of the threshold model, but has a more flexible regime switching mechanism. Its probabilistic structure is studied to some extent. A nonlinear least squares estimation procedure is proposed. Under some standard regularity conditions, the estimator is strongly consistent and the estimator of the coefficients is asymptotically normal when the parameter of the boundary of the buffer zone is known. A portmanteau goodness‐of‐fit test is derived. Simulation results and empirical examples are carried out and lend further support to the usefulness of the BMA model and the asymptotic results.

Date: 2025
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