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

摘要：杨立坚提案：0405330本研究利用蒙特-卡罗程序发展非线性时间序列的多步预测方法。重点讨论了非参数自回归时间序列模型的三种简化结构：少量显著滞后模型、加性模型和加性系数模型。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型预测器。通过采用局部多项式和多项式样条技术的回归结构和核密度估计的噪声分布，这些生成的实现的概率分布近似的theoricaldistribution的时间序列的速率比generalmultivariate函数平滑。因此，建议的预测比许多现有的方法更准确。本文还研究了多指标时间序列和部分线性自回归时间序列的多步超前预测问题，其预测精度也得到了显著提高。除了在理论上是合理的，所提出的预测方法预计是计算上方便，应该很容易获得的操作员与时间序列数据。时间序列数据出现在许多科学学科的形式观察到的数字序列在固定的时间段。经济时间序列包括通货膨胀指数、油价、真实的GNP、失业率等先行指标，每月或每季度观察。气候学研究湿度、降水、温度等随时间的趋势和变化，而地理学家收集叶面积指数、土壤调整植被指数、土壤湿度指数等变量的每日测量值，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，最重要的是理解按顺序产生时间序列的隐藏机制，并利用这些知识来预测下一个或几个数字是什么。通过本研究开发的统计工具显著提高了预测几个季度甚至几年宏观经济时间序列数据的能力。这种超前的预测对宏观经济决策有很大的帮助。这些预测方法在宏观经济学之外的多个学科中具有强大的影响力，例如，在研究气候变化和各种地理指数之间的相互作用方面。

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.