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

Michigan State University, East Lansing MI

Investigators

Abstract

ABSTRACT PI: Lijian Yang PROPOSAL : 0405330 This research develops multi-step ahead forecasting methods for nonlinear time series using a Monte-Carlo procedure. The focus is on taking advantage of three types of simplifying structures in nonparametric auotoregression time series models: small number of significant lags, additive model, and additive coefficient model. For time series data generated according to one of these structures, plug-in type predictors are developed by estimating the data generating process (DGP) and then using the estimated DGP to generate realizations. By employing local polynomial and polynomial spline techniques for the regression structure and kernel density estimation for the noise distribution, the empirical distribution of these generated realizations approximates the theoretical distribution of the time series at rates much faster than that of general multivariate function smoothing. Hence, the proposed forecasts are much more accurate than those made with many existing methods. Multi-step ahead forecasting of time series generated by either multiple index or partially linear autoregression are also studied, for which the forecasting accuracy is improved significantly as well. Besides being theoretically justified, the proposed forecasting methods are expected to be computationally expedient and should be easily accessible to practitioners working with time series data. Time series data appear in many scientific disciplines in the form of sequences of numbers observed over fixed time period. Economic time series include leading indicators such as inflation index, oil price, real GNP, unemployment rate, etc., observed monthly or quarterly. Climatology studies the trend and variation over time of humidity, precipitation, temperature, etc, while geographers collect daily measurements of such variables as leaf area index, soil adjusted vegetation index, soil moisture index and investigate relationships that exist among them and with other indices. Of central importance in the analysis of time series is the understanding of the hidden mechanism that generate the data sequentially, and the use of such knowledge to predict what the next one or few numbers will be. These are one- and multi-step ahead forecasting. The statistical tools developed through this research significantly enhance the capability to forecast macro-economic time series data several quarters, even years, ahead. Advanced forecasts of this kind can greatly help the making of macro-economic decisions. These forecasting methods have strong impact in multiple disciplines beyond macroeconomics, for instance, in the study of interaction between climate change and the various geographic indices.