REGRESSION MODELS FOR NON-STATIONARY CATEGORICAL TIME SERIES

Abstract. Categorical time series often exhibit non-stationary behaviour, due to the influence of exogenous variables. A parsimonious and flexible class of models is proposed for the statistical analysis of such data. These models are extensions of regression models for stochastically independent observations. Statistical inference can be based on asymptotic properties of the maximum likelihood estimator and of test statistics for linear hypotheses. Weak conditions assuring these properties are stated. Some tests which are of special interest in the time series situation are treated in more detail, for example tests of stationarity or independence of parallel time series.     

地震动非平稳性对深覆盖场地地震反应的影响

以上海某深覆盖场地为背景,分别选用普通El-Centro波和长周期HKD123波作为输入,采用正交化HHT方法探讨地震动非平稳性对深覆盖场地地震反应的影响。首先,采用正交化HHT方法分析El-Centro波和HKD123波的局部功率谱,比较这两条波的能量分布情况。然后,采用等效线性波动法求取深覆盖场地的地表反应,并采用正交化HHT法对其进行时频特性分析,比较不同强度的不同类型地震波作用下深覆盖场地的反应差异,以及能量分布的变化情况。结果表明,地震动的非平稳性对深覆盖场地非线性地震反应的影响不容忽视。     

Testing for long-range dependence in the presence of shifting means or a slowly declining trend, using a variance-type estimator

In this paper we examine the effects of certain types of non- stationarity on the detection of long-range dependence and on the estimation of the Hurst parameter H , when using a variance-type estimator. The resulting estimate of H can be misleading when the series has either a jump in the mean or a slow trend. In such a case, plotting the logarithm of the variance versus the logarithm of the level of aggregation gives a curve which is quite different from a straight line. A method for distinguishing between the effects of long-range dependence and these types of non-stationarity is developed.     

Second-order-based blind signal separation in reverberant environments

The aim of this paper was to provide a derivation to explain the performance of the second-order-based blind signal separation (BSS) in reverberant environments. In particular, the second-order-based BSS algorithm, which exploits non-stationarity of the input signals, is investigated. The derivation provides a quantitative link between the reverberation parameter of the environment with the cost function of the BSS. Importantly, the theoretical finding complements existing literature on the interpretation of BSS and provides incremental insight to its performance.     

Time-dependent spectral analysis of epidemiological time-series with wavelets.

In the current context of global infectious disease risks, a better understanding of the dynamics of major epidemics is urgently needed. Time-series analysis has appeared as an interesting approach to explore the dynamics of numerous diseases. Classical time-series methods can only be used for stationary time-series (in which the statistical properties do not vary with time). However, epidemiological time-series are typically noisy, complex and strongly non-stationary. Given this specific nature, wavelet analysis appears particularly attractive because it is well suited to the analysis of non-stationary signals. Here, we review the basic properties of the wavelet approach as an appropriate and elegant method for time-series analysis in epidemiological studies. The wavelet decomposition offers several advantages that are discussed in this paper based on epidemiological examples. In particular, the wavelet approach permits analysis of transient relationships between two signals and is especially suitable for gradual change in force by exogenous variables.     

非稳态条件下的中长期径流耦合预报方法

气候变化会导致水文序列的非稳态性,从而给水文预报带来新的挑战。以疏勒河上游为例,提出了一种适于非稳态条件下的新的中长期径流预报方法。根据疏勒河径流的补给来源及其受气候变化的影响,按照时间序列模型的思路,依次提取趋势项和周期项,对剩余的随机项采用基于水文-气象遥相关模型,构建了时间序列与水文-气象遥相关的耦合模型。对比分析时间序列法、水文-气象遥相关法和耦合预报法对昌马堡站径流预报的结果,发现耦合预报方法不仅精度最高、模型可信度最高,而且可以描述非稳态的趋势性变化。     

无线局域网聚集业务流非平稳性检验*

无线网络业务特性分析是网络性能评价、规划、设计、管理和控制的基础。分析了真实无线局域网业务流的基本统计特性,并应用单位根检验方法检验无线局域网中的聚集业务流的非平稳性。实验结果表明,不论是下行的还是上行的聚集流在不同显著水平上存在非平稳性;同时对这些聚集业务流的一阶差分序列进行检验,结果表明差分序列都是平稳的,这说明下行和上行的聚集业务流均是含有一个单位根的非平稳序列,这为无线网络业务流的进一步建模提供了指导。     

长江流域极端降水与当地平均气温的响应关系分析

研究极端降水的非平稳性及对气温的响应有助于应对相关灾害事件带来的消极影响。基于长江流域1961-2020年降水和气温格点数据,建立广义极值模型以确定当日(T₀)和前1～9 d(T_1-9)当地平均气温是否会引起极端降水的非平稳性,然后通过等样本箱元法、分段线性回归法和指数回归法探讨极端降水对T₀和T_1-9的响应。结果表明：长江流域99.7%格点的极端降水是非平稳的,T₀和T_1-9共驱动74.4%格点的极端降水向非平稳演变,且T_1-9对极端降水的影响更大。流域极端降水随T₀升高主要呈低温时增加而高温时减少的峰值型结构,且峰值点气温以青藏高原东缘为界西低而东高并分别集中于9℃和24℃左右;同时,极端降水随T₀的变化率介于(-12.3%～53.6%)/℃之间,并以四川盆地为中心向四周呈超CC(Clausius-Clapeyron)、类CC和次CC变率的分布格局。极端降水随T_1-9     

基于局部相似度的非稳态相位校正方法

针对常规的常相位校正方法无法满足非稳态相位校正的精度要求,滑动时窗常相位校正方法虽然可以在一定程度上考虑相位的非稳态特性,但是其前提是相位变化分段平稳,因此该方法的精度有限,而且难以控制时窗大小,容易产生不稳定等问题。本文将相位估计看成最小二乘反演问题,在局部地震属性的框架下,根据最大方差模和相似系数的概念,利用零相位判别准则,实现了一种基于局部相似系数的非稳态相位校正方法。相对于滑动时窗常相位校正方法,本文方法精度更高、稳定性更好。理论模型和实际资料处理表明,本文方法可以有效实现信号的零相位化,改善叠加效果,提高地震资料的分辨率。     

考虑水位过程变异的非一致性最低通航水位设计方法

在河道断面水位年际变异和年内分配变异的综合作用下,基于历史资料的最低通航水位设计值已无法反映真实的水位变化规律,导致船舶的通航安全面临威胁。为设计出合理的最低通航水位,本文结合分解合成思想和二阶矩变异概念,提出了考虑水位过程变异(即不同时间尺度下水位特征值的年际变异和水位过程的年内分配变异)的非一致性最低通航水位设计方法——频率-保证率法。该方法不仅符合工程水文学中关于设计水文过程的定义,兼顾了年保证率和频率的概念,而且综合考虑了水位年际和年内分配的双重变异,可为其它工程水文设计提供参考。本文将该设计方法应用于澜沧江允景洪水文站,并将设计结果与均值变异条件下采用频率-保证率法、方差变异条件下采用综合历时曲线法的设计结果作比较,对本方法的优势进行了验证和讨论。