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New models and methods for time series analysis in big data era.

机译：大数据时代的时间序列分析的新模型和新方法。

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摘要

In big data era, available information becomes massive and complex and is often observed over time. Conventional time series models are limited in capability of dealing with these type of data. This dissertation focuses on developing new statistical models, along with their associated estimation procedures, to analyze time series data in functional form, and in high dimension, with linear or nonlinear dynamics, which can be broadly applicable to finance, environment, engineering, biological and medical sciences.;Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. Motivated by Bosq (2000), who worst introduced the functional autoregressive (FAR) models, we propose a convolutional functional autoregressive (CFAR) model, where the function at time t is a result of the sum of convolutions of the past functions with a set of convolution functions, plus a noise process, mimicking the autoregressive process. It provides an intuitive and direct interpretation of the dynamics of a stochastic process. We adopt a sieve estimation procedure based on the B-spline approximation of the convolution functions. We establish convergence rate of the proposed estimator, and investigate its theoretical properties. The model building, model validation, and prediction procedures are also developed.;As for high-dimensional time series data, dimension reduction is an important issue and can be effectively performed by factor analysis. Considering the factor impacts may vary under different conditions, we propose a factor model with regime-switching mechanism, allowing loadings to change across regimes, and combined eigendecomposition and Viterbi algorithm for estimation. We discover that, with multiple states of different 'strength', the convergence rate of loading matrix estimator for strong states is the same as the one-regime case, while the rate improves for weak states, gaining extra information from strong states. The theoretical properties of the procedure are investigated as well.;In addition, we propose a new class of nonparametric seasonal time series models under the framework of the functional coefficient model. The coefficients in the proposed model change over time and consist of the trend and seasonal components to characterize seasonality. A local linear approach is developed to estimate the nonparametric trend and seasonal effect functions. The proposed methodologies are illustrated by two simulated examples and the model is applied to characterizing the seasonality of the monthly number of tourists visiting Hawaii.
机译：在大数据时代，可用信息变得庞大而复杂，并且经常随着时间的推移而被观察。常规时间序列模型在处理这些类型的数据的能力上受到限制。本文致力于开发新的统计模型及其相关的估算程序，以线性或非线性动力学的形式分析高维时间序列数据，可广泛应用于金融，环境，工程，生物和金融等领域。功能数据分析已成为统计研究中越来越流行的一类问题。然而，随着时间的流逝，具有序列依赖性的功能数据仍然是研究较少的领域。受Bosq（2000）的启发，他最差地介绍了函数自回归（FAR）模型，我们提出了卷积函数自回归（CFAR）模型，其中时间t处的函数是过去函数与一个集合的卷积之和的结果卷积函数，加上一个噪声过程，模仿了自回归过程。它提供了对随机过程动力学的直观，直接解释。我们采用基于卷积函数的B样条近似的筛估计程序。我们建立拟议估计量的收敛速度，并研究其理论性质。还开发了模型建立，模型验证和预测程序。对于高维时间序列数据，降维是一个重要问题，可以通过因子分析有效地进行。考虑到因素影响在不同条件下可能会有所不同，我们提出了一种具有状态切换机制的因素模型，允许负荷随状态变化，并结合了特征分解和维特比算法进行估计。我们发现，在具有不同“强度”的多个状态下，强状态的负载矩阵估计的收敛速度与单态情况相同，而弱状态的速度提高，并且从强状态获得了更多信息。还研究了该程序的理论特性。此外，我们在函数系数模型的框架下提出了一类新的非参数季节时间序列模型。所提出的模型中的系数随时间变化，由趋势和季节成分组成以表征季节性。开发了一种局部线性方法来估计非参数趋势和季节效应函数。通过两个模拟示例说明了所提出的方法，并将该模型应用于表征访问夏威夷的每月游客人数的季节性。

著录项

  • 作者

    Liu, Xialu.;

  • 作者单位

    Rutgers The State University of New Jersey - New Brunswick.;

  • 授予单位 Rutgers The State University of New Jersey - New Brunswick.;
  • 学科 Biostatistics.
  • 学位 Ph.D.
  • 年度 2015
  • 页码 138 p.
  • 总页数 138
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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