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Functional Coefficient Regression Models for Non‐linear Time Series: A Polynomial Spline Approach
Author(s) -
Huang Jianhua Z.,
Shen Haipeng
Publication year - 2004
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2004.00404.x
Subject(s) - mathematics , smoothing spline , polynomial regression , spline (mechanical) , consistency (knowledge bases) , series (stratigraphy) , polynomial , linear regression , smoothing , convergence (economics) , rate of convergence , statistics , spline interpolation , computer science , mathematical analysis , paleontology , channel (broadcasting) , geometry , computer network , structural engineering , economic growth , engineering , economics , bilinear interpolation , biology
. We propose a global smoothing method based on polynomial splines for the estimation of functional coefficient regression models for non‐linear time series. Consistency and rate of convergence results are given to support the proposed estimation method. Methods for automatic selection of the threshold variable and significant variables (or lags) are discussed. The estimated model is used to produce multi‐step‐ahead forecasts, including interval forecasts and density forecasts. The methodology is illustrated by simulations and two real data examples.