Monte-Carlo multi-step ahead forecasting for nonlinear time series

非线性时间序列的蒙特卡洛多步超前预测

• 批准号: 0405330
• 负责人: Lijian Yang
• 金额: $ 19.21万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-15 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0405330&HistoricalAwards=false
• 关键词: Monte; Carlo; multi; step; ahead

ABSTRACTPI: Lijian YangPROPOSAL : 0405330This research develops multi-step ahead forecasting methods fornonlinear time series using a Monte-Carlo procedure. The focus is ontaking advantage of three types of simplifying structures in nonparametricauotoregression time series models: small number of significant lags,additive model, and additive coefficient model. For time series datagenerated according to one of these structures, plug-in type predictorsare developed by estimating the data generating process (DGP) andthen using the estimated DGP to generate realizations. By employing localpolynomial and polynomial spline techniques for the regression structureand kernel density estimation for the noise distribution, the empiricaldistribution of these generated realizations approximates the theoreticaldistribution of the time series at rates much faster than that of generalmultivariate function smoothing. Hence, the proposed forecasts are muchmore accurate than those made with many existing methods. Multi-step aheadforecasting of time series generated by either multiple index or partiallylinear autoregression are also studied, for which the forecastingaccuracy is improved significantly as well. Besides beingtheoretically justified, the proposed forecasting methods are expected tobe computationally expedient and should be easily accessible topractitioners working with time series data.Time series data appear in many scientific disciplines in the form ofsequences of numbers observed over fixed time period. Economic time seriesinclude leading indicators such as inflation index, oil price, real GNP,unemployment rate, etc., observed monthly or quarterly. Climatologystudies the trend and variation over time of humidity, precipitation,temperature, etc, while geographers collect daily measurements of suchvariables as leaf area index, soil adjusted vegetation index, soilmoisture index and investigate relationships that exist among them andwith other indices. Of central importance in the analysis of time seriesis the understanding of the hidden mechanism that generate the datasequentially, and the use of such knowledge to predict what the next oneor few numbers will be. These are one- and multi-step ahead forecasting.The statistical tools developed through this research significantlyenhance the capability to forecast macro-economic time series data severalquarters, even years, ahead. Advanced forecasts of this kind can greatlyhelp the making of macro-economic decisions. These forecasting methodshave strong impact in multiple disciplines beyond macroeconomics, forinstance, in the study of interaction between climate change and thevarious geographic indices.

本文研究了一种基于蒙特卡罗方法的非线性时间序列多步预测方法。重点研究了非参数自回归时间序列模型的三种简化结构：少量显著滞后、可加性模型和可加性系数模型。对于根据这些结构之一生成的时间序列数据，通过估计数据生成过程（DGP）然后使用估计的DGP生成实现来开发插件类型预测器。通过采用局部多项式和多项式样条技术进行回归结构和核密度估计噪声分布，这些生成的实现的经验分布以比一般多元函数平滑更快的速度近似时间序列的理论分布。因此，所提出的预测比许多现有方法所作的预测要准确得多。本文还研究了多指标或部分线性自回归生成的时间序列的多步预测，其预测精度也得到了显著提高。除了在理论上是合理的之外，所提出的预测方法预计在计算上是方便的，并且对于处理时间序列数据的从业者来说应该是容易访问的。时间序列数据以固定时间内观察到的数字序列的形式出现在许多科学学科中。经济时间序列包括领先指标，如通货膨胀指数，石油价格，实际国民生产总值，失业率等，观察每月或每季度。气候学研究湿度、降水、温度等的趋势和随时间的变化，地理学家收集诸如叶面积指数、土壤调整植被指数、土壤湿度指数等变量的日常测量数据，并研究它们之间以及与其他指数之间的关系。在时间序列分析中，最重要的是理解生成数据的隐藏机制，并利用这些知识来预测下一个或几个数字将是什么。这些都是提前一步和多步预测。通过本研究开发的统计工具显著提高了预测未来几个季度甚至几年宏观经济时间序列数据的能力。这种先进的预测可以极大地帮助制定宏观经济决策。这些预测方法在宏观经济学以外的多个学科中都有很强的影响，例如，在研究气候变化与各种地理指数之间的相互作用方面。