Multi-step SETARMA predictors in the analysis of hydrological time series

Abstract The performance of the self-exciting threshold autoregressive moving average model in forecasting river flow data is investigated. Multi-step forecasts of two daily time series are generated through three different nonlinear predictors. The model adequacy to capture the main features of the data under study and its forecasting performance are analysed and discussed.

[1]  B. LeBaron,et al.  A test for independence based on the correlation dimension , 1996 .

[2]  Richard L. Tweedie,et al.  ON THE EXISTENCE OF STATIONARY THRESHOLD AUTOREGRESSIVE MOVING‐AVERAGE PROCESSES , 1992 .

[3]  F. Diebold,et al.  Comparing Predictive Accuracy , 1994, Business Cycles.

[4]  Anil K. Bera,et al.  Efficient tests for normality, homoscedasticity and serial independence of regression residuals , 1980 .

[5]  George E. P. Box,et al.  Time Series Analysis: Forecasting and Control , 1977 .

[6]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[7]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[8]  D. I. Steinberg.  Mathematical models for surface water hydrology : Edited by T. A. Ciriani, U. Maione and J. R. Wallis. Wiley Interscience, New York, 1977, 423 pp., $27.50 , 1978 .

[9]  Ruey S. Tsay,et al.  Testing and Modeling Threshold Autoregressive Processes , 1989 .

[10]  Hung Man Tong,et al.  Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21 , 1983 .

[11]  Howell Tong,et al.  TESTING FOR A LINEAR MA MODEL AGAINST THRESHOLD MA MODELS , 2005 .

[12]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[13]  Luca Ridolfi,et al.  Detecting determinism and nonlinearity in river-flow time series , 2003 .

[14]  Hirotugu Akaike,et al.  On the Likelihood of a Time Series Model , 1978 .

[15]  M. A. Kohler,et al.  Hydrology for engineers , 1958 .

[16]  On strict stationarity and ergodicity of a non-linear ARMA model , 1992 .

[17]  H. Tong,et al.  Threshold Autoregression, Limit Cycles and Cyclical Data , 1980 .

[18]  Marcella Niglio,et al.  The moments of SETARMA models , 2006 .

[19]  Luca Ridolfi,et al.  Nonlinear analysis of river flow time sequences , 1997 .

[20]  Wen Wang,et al.  Testing and modelling autoregressive conditional heteroskedasticity of streamflow processes , 2005 .

[21]  N. T. Kottegoda,et al.  Stochastic Modelling of Riverflow Time Series , 1977 .

[22]  R. Tsay.  Testing and modeling multivariate threshold models , 1998 .