Oracally efficient estimation and testing for an ARCH model with trend

Huan Gong

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 14, 3384-3402

Abstract: This article investigates an ARCH model with trend and proposes a two-step estimation method and develops an ARCH effect test. The trend is estimated by the linear B-spline method, and then the least squares estimation (LSE) and a Lagrange multiplier (LM) test based on the residuals are presented. Under mild conditions, it is shown that the proposed LSE and the test statistic enjoy the oracle properties; namely, they perform as well as if the true trend function were known and then removed to obtain the ARCH errors. Simulation studies assess the finite-sample performance of the LSE and the test statistic. An empirical example on the US gross private saving series is analyzed to illustrate the usefulness of our procedure.

Date: 2021
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DOI: 10.1080/03610926.2019.1702696

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