Linear approximation of the Threshold AutoRegressive model: an application to order estimation

Francesco Giordano, Marcella Niglio () and Cosimo Damiano Vitale
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Francesco Giordano: Università degli Studi di Salerno
Marcella Niglio: Università degli Studi di Salerno
Cosimo Damiano Vitale: Università degli Studi di Salerno

Statistical Methods & Applications, 2023, vol. 32, issue 1, No 2, 27-56

Abstract: Abstract This paper proposes a linear approximation of the nonlinear Threshold AutoRegressive model. It is shown that there is a relation between the autoregressive order of the threshold model and the order of its autoregressive moving average approximation. The main advantage of this approximation can be found in the extension of some theoretical results developed in the linear setting to the nonlinear domain. Among them is proposed a new order estimation procedure for threshold models whose performance is compared, through a Monte Carlo study, to other criteria largely employed in the nonlinear threshold context.

Keywords: Linear approximation; Threshold model; $$L^2$$ L 2 norm; AIC; 37M10; 47A58 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10260-022-00638-1

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