Stochastic simulation model for nonstationary time series using an autoregressive wavelet decomposition: Applications to rainfall and temperature

[1] 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.