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Single‐Index Additive Vector Autoregressive Time Series Models
Author(s) -
LI YEHUA,
GENTON MARC G.
Publication year - 2009
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.1467-9469.2009.00641.x
Subject(s) - autoregressive model , mathematics , series (stratigraphy) , smoothing , model selection , vector autoregression , econometrics , nonlinear system , time series , autoregressive integrated moving average , star model , index (typography) , statistics , computer science , paleontology , physics , quantum mechanics , biology , world wide web
. We study a new class of nonlinear autoregressive models for vector time series, where the current vector depends on single‐indexes defined on the past lags and the effects of different lags have an additive form. A sufficient condition is provided for stationarity of such models. We also study estimation of the proposed model using P‐splines, hypothesis testing, asymptotics, selection of the order of the autoregression and of the smoothing parameters and nonlinear forecasting. We perform simulation experiments to evaluate our model in various settings. We illustrate our methodology on a climate data set and show that our model provides more accurate yearly forecasts of the El Niño phenomenon, the unusual warming of water in the Pacific Ocean.