论文标题
通过自适应过度差异来推断可能非平稳过程
Likelihood Inference for Possibly Non-Stationary Processes via Adaptive Overdifferencing
论文作者
论文摘要
我们进行了一个观察，该观察促进了流行Arfima模型参数的基于精确的可能性推断，而无需平稳性，通过允许内存的上限$ \ bar {d} $用于内存参数$ d $超过$ 0.5 $：估算单个非稳定的Arfima模型的参数，即估计一个模型的单个模型，以估算该序列的序列。这允许使用现有方法来评估可逆和固定的Arfima模型的可能性。这可以改善推理，因为当估计接近参数空间的边界时，许多标准方法的性能较差。它还使我们能够利用为估计固定过程参数而引入的可能性近似值的财富。我们探讨了内存参数$ d $的估计如何取决于上限$ \ bar {d} $，并引入自适应过程以选择$ \ bar {d} $。我们通过仿真显示，当真实值大至2.5时，我们的自适应过程如何相对于现有替代方案很好地估计内存参数。
We make an observation that facilitates exact likelihood-based inference for the parameters of the popular ARFIMA model without requiring stationarity by allowing the upper bound $\bar{d}$ for the memory parameter $d$ to exceed $0.5$: estimating the parameters of a single non-stationary ARFIMA model is equivalent to estimating the parameters of a sequence of stationary ARFIMA models. This allows for the use of existing methods for evaluating the likelihood for an invertible and stationary ARFIMA model. This enables improved inference because many standard methods perform poorly when estimates are close to the boundary of the parameter space. It also allows us to leverage the wealth of likelihood approximations that have been introduced for estimating the parameters of a stationary process. We explore how estimation of the memory parameter $d$ depends on the upper bound $\bar{d}$ and introduce adaptive procedures for choosing $\bar{d}$. We show via simulation how our adaptive procedures estimate the memory parameter well, relative to existing alternatives, when the true value is as large as 2.5.
