Time series aggregation, disaggregation and long memory

Aggregation and long memory: recent developments

It is well-known that the aggregated time series might have very different properties from those of the individual series, in particular, long memory. At the present time, aggregation has become one of the main tools for modelling of long memory processes. We review recent work on contemporaneous aggregation of random-coefficient AR(1) and related models, with particular focus on various long memory properties of the aggregated process.

tempdisagg：时间序列数据时间分解的Python框架

tempdisagg: A Python Framework for Temporal Disaggregation of Time Series Data

tempdisagg是一个Python框架，通过多种计量方法和增强功能实现时间序列的时间分解，提供模块化API支持生产环境使用。

Asymptotic normality of the mixture density estimator in a disaggregation scheme

The paper concerns the asymptotic distribution of the mixture density estimator, proposed by Oppenheim et al 2006, in the aggregation/disaggregation problem of random parameter AR(1) process. We prove that, under mild conditions on the (semiparametric) form of the mixture density, the estimator is asymptotically normal. The proof is based on the limit theory for the quadratic form in linear random variables developed by Bhansali et al 2007. The moving average representation of the aggregated process is investigated. A small simulation study illustrates the result.

Long-memory process and aggregation of AR(1) stochastic processes: A new characterization

Contemporaneous aggregation of individual AR(1) random processes might lead to different properties of the limit aggregated time series, in particular, long memory (Granger, 1980). We provide a new characterization of the series of autoregressive coefficients, which is defined from the Wold representation of the limit of the aggregate stochastic process, in the presence of long-memory features. Especially the infinite autoregressive stochastic process defined by the almost sure representation of the aggregate process has a unit root in the presence of the long-memory property. Finally we discu…

Disaggregation of Long Memory Processes on C^{\infty} Class

We prove that a large set of long memory (LM) processes (including classical LM processes and all processes whose spectral densities have a countable number of singularities controlled by exponential functions) are obtained by an aggregation procedure involving short memory (SM) processes whose spectral densities are infinitely differentiable (C^{infty}). We show that the C^{infty} class of spectral densities is the optimal class to get a general result for disaggregation of LM processes in SM processes, in the sense that the result given in C^{infty} class cannot be improved taking for instan…

整合时间 disaggregation（时间分解）与分布滞后非线性模型，用于结合高分辨率环境暴露的贝叶斯时空疾病制图

Integrating Temporal Disaggregation and Distributed Lag Nonlinear Models for Bayesian Spatio-Temporal Disease Mapping with High-Resolution Environmental Exposures

该研究提出整合时间分解与分布滞后非线性模型的贝叶斯时空框架，结合高分辨率环境暴露开展疟疾制图，在莫桑比克数据上验证其提升了预测精度，可用于研究环境延迟效应并扩展至多类疾病。