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

本研究采用蒙特卡罗方法对非线性时间序列进行多步超前预测。重点是利用非参数自回归时间序列模型中的三种简化结构：小显著滞后模型、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来生成实现，从而开发出插件式预测器。通过对回归结构使用局部多项式和多项式样条技术，以及对噪声分布进行核密度估计，这些生成的实现的经验分布以比一般多元函数平滑快得多的速度逼近时间序列的理论分布。因此，建议的预测比许多现有方法所做的预测准确得多。对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也进行了研究，预测精度也得到了显著提高。除了理论上的合理性，所提出的预测方法在计算上应该是方便的，而且对于使用时间序列数据的实践者来说应该很容易获得。时间序列数据以固定时间段内观察到的数字序列的形式出现在许多科学学科中。经济时间序列包括按月或按季观察的领先指标，如通胀指数、油价、实际国民生产总值、失业率等。气候学研究湿度、降水、温度等的趋势和随时间的变化，而地理学家收集叶面积指数、土壤调整植被指数、土壤水分指数等变量的每日测量数据，并调查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数据的隐藏机制，并使用这种知识来预测下一个或几个数字将是什么。这些都是超前一步和多步预测。通过本研究开发的统计工具，显著提高了对未来几个季度甚至几年宏观经济时间序列数据的预测能力。这种超前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强大的影响，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。

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.