局部平稳部分线性面板数据模型的统计推断

部分线性模型是一类非常重要的半参数回归模型,由于它既含有参数部分又含有非参数部分,与常规的线性模型相比具有更强的适应性和解释能力。文章研究带有局部平稳协变量的固定效应部分线性面板数据模型的统计推断。首先提出一个两阶段估计方法得到模型中未知参数和非参数函数的估计,并证明估计量的渐近性质,然后运用不变原理构造出非参数函数的一致置信带,最后通过数值模拟研究和实例分析验证了该方法的有效性。     

Modeling spatial overdispersion via the generalized Waring point process

Modeling spatial overdispersion requires point process models with finite‐dimensional distributions that are overdisperse relative to the Poisson distribution. Fitting such models usually heavily relies on the properties of stationarity, ergodicity, and orderliness. In addition, although processes based on negative binomial finite‐dimensional distributions have been widely considered, they typically fail to simultaneously satisfy the three required properties for fitting. Indeed, it has been conjectured by Diggle and Milne that no negative binomial model can satisfy all three properties. In light of this, we change perspective and construct a new process based on a different overdisperse count model, namely, the generalized Waring (GW) distribution. While comparably tractable and flexible to negative binomial processes, the GW process is shown to possess all required properties and additionally span the negative binomial and Poisson processes as limiting cases. In this sense, the GW process provides an approximate resolution to the conundrum highlighted by Diggle and Milne.     

The Robustness of Trend Stationarity: An Illustration with the Extended Nelson-Plosser Dataset

We re-evaluate Andreu and Spanos's findings in favour of trend stationarity by considering the extended Nelson-Plosser data set. This expanded (to 1988) data set includes a period of rather different behaviour compared with the original Nelson-Plosser data used by Andreou and Spanos. We find that Andreou and Spanos's models (with only minor adjustments) exhibit remarable stability over this extended period, and indicate that their conclusions are more robust than they have shown.     

Efficient Estimation of a Distribution Function under Quadrant Dependence

LetX₁,X₂, ..., be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being either pairwise positively quadrant dependent or pairwise negatively quadrant dependent. LetF^ be the marginal distribution function of theX_ips, which is estimated by the empirical distribution functionF_n and also by a smooth kernel-type estimateF_n, by means of the segmentX₁, ...,X_n. These estimates are compared on the basis of their mean squared errors (MSE). The main results of this paper are the following. Under certain regularity conditions, the optimal bandwidth (in the MSE sense) is determined, and is found to be the same as that in the independent identically distributed case. It is also shown thatn MSE(F_n(t)) andnMSE (F^_n(t)) tend to the same constant, asn→∞ so that one can not discriminate be tween the two estimates on the basis of the MSE. Next, ifi(n) = min {k∈{1, 2, ...}; MSE (F_k(t)) ≤ MSE (F_n(t))}, then it is proved thati(n)/n tends to 1, asn→∞. Thus, once again, one can not choose one estimate over the other in terms of their asymptotic relative efficiency. If, however, the squared bias ofF^_n(t) tends to 0 sufficiently fast, or equivalently, the bandwidthh_n satisfies the requirement thatnh³_n→ 0, asn→∞, it is shown that, for a suitable choice of the kernel, (i(n) ?n)/(nh_n) tends to a positive number, asn→∞ It follows that the deficiency ofF_n(t) with respect toF^_n(t),i(n) ?n, is substantial, and, actually, tends to ∞, asn→∞. In terms of deficiency, the smooth estimateF^_n(t) is preferable to the empirical distribution functionF_n(t)     

A股价格波动真的非平稳？ ——大数据背景下个股数据的全样本实证

传统研究对股票市场平稳性分析中大多采用市场指数抽样方式,分析方法和数据采样的差异一定程度上解析了现有研究结论中的不一致性。从市场指数构建原理入手可探究抽样分析的局限,作为系列个股的加权值,市场指数无法精确刻画市场所有个股的波动情况。实证时采用A股市场所有个股数据开展全样本分析,这更符合大数据分析理念,统计出个股分析结果继而对A股市场波动进行判定将更加系统和可靠。在不考虑结构突变的情形下,分别计算出ADF检验、KPSS检验和PP检验三种方法的结果;全样本分析结果表明A股市场年度股价数据更多地呈现出平稳性特点,而且,个股数据检验结果与市场指数检验结果存在显著差异。     

Piecewise FARIMA models for long-memory time series

We consider the problem of modelling a long-memory time series using piecewise fractional autoregressive integrated moving average processes. The number as well as the locations of structural break points (BPs) and the parameters of each regime are assumed to be unknown. A four-step procedure is proposed to find out the BPs and to estimate the parameters of each regime. Its effectiveness is shown by Monte Carlo simulations and an application to real traffic data modelling is considered.     

A note on mixingale limit theorems and stable convergence in law

A gap in the proof of a non stationary mixingale invariance principle is identified and fixed by introducing a skipped subsampling of a partial sum process and letting the skipped interval vanish asymptotically at an appropriate rate as the sample size increases. The corrected proof produces a mixingale limit theorem in the form of a mixing convergence in law, occurring jointly with the stable convergence in law for the same σ-field relative to which they are stable and mixing. The applicability of established results to a high-frequency estimation of the quadratic variation of financial price process is discussed.     

时间序列平稳性分类识别研究

平稳性检验是时间序列回归分析的一个关键问题,已有的检验方法在处理海量时间序列数据时显得乏力,检验准确率有待提高。采用分类技术建立平稳性检验的新方法,可以有效地处理海量时间序列数据。首先计算时间序列自相关函数,构建一个充分非必要的判定准则;然后建立序列收敛的量化分析方法,研究收敛参数的最优取值,并提取平稳性特征向量;最后采用k-means聚类建立平稳性分类识别方法。采用一组模拟数据和股票数据进行分析,将ADF检验、PP检验、KPSS检验进行对比,实证结果表明新方法的准确率较高。