A time-varying autoregressive model for groundwater depth prediction

Abstract

The nonstationarity of hydrological variables makes the application of autoregressive (AR) models challenging. Therefore, this study introduces a new time-varying AR (TVAR) model in the field of hydrology. Specifically, in this study, we focus the parameter estimation of the TVAR model and exploring the model’s performance for predicting groundwater depth. We demonstrate the application of the model to the monthly groundwater depth series obtained on the Guanzhong Plain, China. We summarize the process of parameter estimation of the TVAR model. First, the TVAR model is transformed into the time-invariance regression problem by expanding the time-varying coefficients into a set of Fourier or Legendre basis functions. Then, a fading memory recursive least squares (FMRLS) algorithm is used to estimate the parameters of the regression problem. In this process, the model order and dimension of the basis function are determined by minimizing our proposed improved Bayesian information criterion (IBIC) with a range of dimensions greater than 0. To further demonstrate the effectiveness of the parameter estimation method and the generalizable performance of the model, the method is applied to nonstationary series simulated in statistical experiments. The study results indicate that the TVAR model based on such a parameter estimation process exhibits better prediction performance, lower model complexity and more straight-forward application compared with the autoregressive integrated (ARI) and seasonal ARI (SARI) models. In conclusion, using the TVAR model as an alternative to the time-invariance ARI and SARI models results in a model that is more flexible and suitable for nonstationary groundwater depth prediction.