This paper introduces a dual-asymmetry linear double autoregressive (DA‑LDAR) model that can allow for asymmetric effects in both the conditional location and volatility components of time series data. The strict stationarity is discussed for the new model, for which a sufficient condition is established. A self-weighted exponential quasi-maximum likelihood estimator (EQMLE) is proposed for the DA‑LDAR model, and a mixed portmanteau test for goodness-of-fit is constructed based on the self-weighted EQMLE. It is noteworthy that all the asymptotic properties for estimation and testing are established without any moment condition on the data process, which makes the new model and its inference tools applicable for heavy-tailed data. Since all inference tools need to estimate the unknown density function of innovations, we employ a random-weighting bootstrap method to facilitate accurate inference and show its asymptotic validity. Simulation studies provide support for theoretical results, and an empirical application to NASDAQ Composite Index illustrates the usefulness of the new model.

中文翻译：

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关于双不对称线性双 AR 模型

本文介绍了一种双不对称线性双自回归 (DA‑LDAR) 模型，该模型可以在时间序列数据的条件位置和波动性分量中考虑不对称效应。讨论了新模型的严格平稳性，为此建立了充分条件。为DA-LDAR模型提出了一种自加权指数准最大似然估计器（EQMLE），并基于自加权EQMLE构建了拟合优度的混合portmanteau检验。值得注意的是，所有用于估计和测试的渐近性质都是在数据过程中没有任何矩条件的情况下建立的，这使得新模型及其推理工具适用于重尾数据。由于所有推理工具都需要估计创新的未知密度函数，我们采用随机加权自举方法来促进准确推理并显示其渐近有效性。模拟研究为理论结果提供了支持，纳斯达克综合指数的实证应用说明了新模型的有用性。