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Stochastic simulation model for nonstationary time series using an autoregressive wavelet decomposition: Applications to rainfall and temperature
Author(s) -
Kwon HyunHan,
Lall Upmanu,
Khalil Abedalrazq F.
Publication year - 2007
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2006wr005258
Subject(s) - autoregressive model , series (stratigraphy) , star model , wavelet , time series , nonlinear autoregressive exogenous model , mathematics , setar , wavelet transform , econometrics , statistics , climatology , autoregressive integrated moving average , computer science , geology , artificial intelligence , paleontology
A time series simulation scheme based on wavelet decomposition coupled to an autoregressive model is presented for hydroclimatic series that exhibit band‐limited low‐frequency variability. Many nonlinear dynamical systems generate time series that appear to have amplitude‐ and frequency‐modulated oscillations that may correspond to the recurrence of different solution regimes. The use of wavelet decomposition followed by an autoregressive model of each leading component is explored as a model for such time series. The first example considered is the Lorenz‐84 low‐order model of extratropical circulation, which has been used to illustrate how chaos and intransitivity (multiple stable solutions) can lead to low‐frequency variability. The central England temperature (CET) time series, the NINO3.4 series that is a surrogate for El Nino–Southern Oscillation, and seasonal rainfall from Everglades National Park, Florida, are then modeled with this approach. The proposed simulation model yields better results than a traditional linear autoregressive (AR) time series model in terms of reproducing the time‐frequency properties of the observed rainfall, while preserving the statistics usually reproduced by the AR models.