Efficient detection of random coefficients in autoregressive models
自回归模型随机系数的有效检测AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究 AR 与随机系数 AR 模型之间的时间序列检验。
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自回归模型随机系数的有效检测
- 研究问题
- 如何检验普通 AR 模型的系数是否存在随机性，同时处理未知创新密度这一干扰参数及多参数单侧备择的推断困难？
- 方法与思路
- 作者建立随机系数模型邻近普通 AR 模型时的非标准局部渐近正态性质，构造有效中心序列并提出单侧检验概念。
- 材料陈述的贡献
- 摘要称揭示该半参数模型的非适应性及非高斯下伪高斯方法的无效性，并提出处理有效推断与单侧备择的方法。
- 阅读关注点
- 应核对随机系数的参数化、边界附近的局部缩放、创新密度条件，以及所提检验效率和严格性的准确比较范围。
- 阅读边界
- OpenAlex 索引摘要未注明版本及检验实现细节；伪高斯方法无效的陈述应限定在文中模型与条件，不能推广到所有 AR 模型。
原文摘要
The problem of detecting randomness in the coefficients of an AR(p) model, that is, the problem of testing ordinary AR(p) dependence against the alternative of a random coefficient autoregressive [RCAR(p)] model is considered. A nonstandard LAN property is established for RCAR(p) models in the vicinity of AR(p) ones. Two main problems arise in this context. The first problem is related to the statistical model itself: Gaussian assumptions are highly unrealistic in a nonlinear context, and innovation densities should be treated as nuisance parameters. The resulting semiparametric model however appears to be severely nonadaptive. In contrast with the linear ARMA case, pseudo-Gaussian likelihood methods here are invalid under non-Gaussian densities; even the innovation variance cannot be estimated without a strict loss of efficiency. This problem is solved using a general result by Hallin and Werker, which provides semiparametrically efficient central sequences without going through explicit tangent space calculations. The second problem is related to the fact that the testing problem under study is intrinsically one-sided, while the case of multiparameter one-sided alternatives is not covered by classical asymptotic theory under LAN. A concept of locally asymptotically most stringent somewhere efficient test is proposed in order to cope with this one-sided nature of the problem.