On a General Class of Count Time Series Models

关于一类一般计数时间序列模型

• 批准号: 1407480
• 负责人: Robert Lund
• 金额: $ 15万
• 依托单位: Clemson University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1407480&HistoricalAwards=false
• 关键词: General; Class; Count; Time; Series

This research studies data recorded in time that is count-valued, e.g., the annual number of Californian wildfires, yearly Alaskan polar bear sightings, monthly flu deaths, annual North Atlantic severe hurricanes, etc. The data may be correlated in time, implying that counts observed today may be influenced by (correlated with) counts occurring in the immediate past. This work develops time series methods that take into account the particular type of distribution appropriate for the counts, e.g., Poisson, geometric, binomial, etc.. Using the correct distribution facilitates accurate forecasts and inferences. The models developed here allow both positive and negative correlations, a feature absent from current statistical count time series models. For example, annual Pacific and Atlantic hurricane counts are well described by a Poisson-type distribution, but are negatively correlated: when Atlantic hurricane counts are high, Pacific counts tend to be low (and vice versa). It is important to account for such correlations to make accurate climate change conclusions.On technical levels, a discrete-time renewal process is used as a general model for a binary (zero-one) series. The renewal process is rendered stationary by selecting a special initial renewal life length. Copies of the stationary binary sequence are then superimposed in various ways to build the marginal distribution sought. It is easy to construct stationary series with Poisson, geometric, and binomial marginal distributions. The methods easily generate stationary count series with negative correlations and/or long-memory --- aspects not achievable from classical integer autoregressive moving-average count techniques. Inference issues, covariates, and multivariate series are also considered.

这项研究研究的数据记录在时间是计数值，例如，加利福尼亚野火的年度数量、阿拉斯加北极熊的年度目击、每月流感死亡、每年北大西洋严重飓风等。数据可以在时间上相关，这意味着今天观察到的计数可能受到不久前发生的计数的影响（与之相关）。 这项工作开发了时间序列方法，该方法考虑了适合于计数的特定类型的分布，例如，泊松分布、几何分布、二项式分布等。使用正确的分布有助于准确的预测和推断。这里开发的模型允许正相关和负相关，这是当前统计计数时间序列模型中缺少的功能。 例如，太平洋和大西洋的飓风数量可以用泊松分布来描述，但两者之间存在负相关：当大西洋飓风数量高时，太平洋飓风数量往往较低（反之亦然）。 在技术层面上，离散时间更新过程被用作二进制（0 - 1）序列的一般模型。 通过选择一个特殊的初始更新生命长度，使得更新过程是平稳的。然后以各种方式叠加固定二进制序列的副本，以构建所寻求的边缘分布。 用泊松分布、几何分布和二项边缘分布构造平稳序列很容易。 该方法很容易生成静态计数系列与负相关和/或长记忆-方面无法实现从经典的整数自回归移动平均计数技术。 推理问题，协变量，和多变量系列也被认为是。

项目成果

CONVERGENCE RATES FOR SHADOWING MARKOV CHAINS

影子马尔可夫链的收敛率

• 发表时间: 2024
• 期刊: Journal of Applied Probability
• 影响因子: 1
• 作者: CHAN, FUN CHOI;KIESSLER, PETER;LUND, ROBERT
• 通讯作者: LUND, ROBERT