Wavelet based deseasonalization for modelling and forecasting of daily discharge series considering long range dependence

Adamowski, J.F., 2008. Development of a short-term river flood forecasting method for snowmelt driven floods based on wavelet and cross-wavelet analysis. J. Hydrol., 353, 247-266.10.1016/j.jhydrol.2008.02.013Search in Google Scholar

Andreo, B., 2006. Climatic and hydrological variations during the last 117-166 years in the south of the Iberian Peninsula, from spectral and correlation analyses and continuous wavelet analyses. J. Hydrol., 324, 24-39.10.1016/j.jhydrol.2005.09.010Search in Google Scholar

Beran, J., 1994. Statistics for long - memory processes. Chapman and Hall, New York.Search in Google Scholar

Blöschl, G., Reszler, C., omma, J., 007. A spatially distributed flash flood forecasting model. Environ. Modell. Softw., 23, 464-478.10.1016/j.envsoft.2007.06.010Search in Google Scholar

Box, G.E.P., Jenkins, G.M., 1976. Time series analysis forecasting and control. Holden-Day, San Francisco, USA.Search in Google Scholar

Brockwell, P., Davis, R.A., 2002. Introduction to time Series and forecasting. Springer Verlag, New York, USA.10.1007/b97391Search in Google Scholar

Burlando, P., Rosso, R., Cadavid, L.G., Salas, J.D., 1993. Forecasting of short-term rainfall using ARMA models. J. Hydrol., 144, 193-211.10.1016/0022-1694(93)90172-6Search in Google Scholar

Daubechies, I., 1992. Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, Philadephia, USA.10.1137/1.9781611970104Search in Google Scholar

Crato, N., Ray, B.K., 1998. Model selection and forecasting for long-range dependent processes. Journal of Forecasting, 15, 107-125.10.1002/(SICI)1099-131X(199603)15:2<107::AID-FOR612>3.0.CO;2-DSearch in Google Scholar

Diebold, F.X., Mariano, R.S., 1995. Comparing predictive accuracy. Journal of Business and Economic Statistics, 13, 253-263.10.1080/07350015.1995.10524599Search in Google Scholar

Harvey, D.I., Leybourne, S.J., Newbold, P., 1997. Testing the equality of prediction mean squared errors. International Journal of Forecasting, 13, 281-291.10.1016/S0169-2070(96)00719-4Search in Google Scholar

Dou, H., Chan, Y.Q., 1998. Optimal Features Extraction of Noisy Sinusoidal Signals Using Two-Stage Linear Least Squares Fitting. Technical report, Mechatronics and Automation Laboratory, National University of Singapore.Search in Google Scholar

Ehsanzadeh, E., Adamowski, K., 2010. Trends in timing of low stream flows in Canada: impact of autocorrelation and long - term persistence. Hydrol. Process., 24, 970-980.10.1002/hyp.7533Search in Google Scholar

Doukhan, P., Oppenheim, G., Taqqu, M. S., 2003. Long-range dependence. Birkhäuser, Boston, USA.Search in Google Scholar

Engle, R.F., 1982. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 50, 987-1008.10.2307/1912773Search in Google Scholar

Gencay, R., Selcuk, F., Whitcher, B., 2001. Differentiating intraday seasonalities through wavelet multi - scaling. Physica A, 289, 543 - 556.10.1016/S0378-4371(00)00463-5Search in Google Scholar

Grinsted, A., Moore, J.C., Jevrejeva, S., 2004. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Proc. Geoph., 11, 561-566.10.5194/npg-11-561-2004Search in Google Scholar

Hipel, K.W., McLeod, A.I., 1994. Time Series Modelling of Water Resources and Environmental Systems. Elsevier, Amsterdam.Search in Google Scholar

Jain, S.K., Sudheer, K.P., 2012. Fitting of hydrologic models: a close look at the nash-sutcliffe index. J. Hydrol. Eng., 13, 981-986. 10.1061/(ASCE)1084-0699(2008)13:10(981)Search in Google Scholar

Jomorn k, J., omorn ková, M., Mesiar, R., Szökeová, D., Szolgay, J., 2006. Comparison of forecasting performance of nonlinear models of hydrological time series. Phys. Chem.10.1016/j.pce.2006.05.006Search in Google Scholar

Earth, 18, 1127-1145. omorn ková, M., Szolgay, J., Svetl ková, D., Szökeová, D., Jurčák, S., 2008. A hybrid modelling framework for forecasting monthly reservior inflows. J. Hydrol. Hydromech., 56, 145-162.Search in Google Scholar

Koop, G., Ley, E., Osiewalski, J., Steel, M.F.J., 1997. Bayesian analysis of long memory and persistence using ARFIMA models. J. Econometrics, 76, 149-169.10.1016/0304-4076(95)01787-9Search in Google Scholar

Koscielny-Bunde, E., Kantelhardt, J.W., Braun, P., Bunde, A., Havlin, S., 2006. Long - term persistence and multifractality of river runoff records: Detrended fluctuation studies. J. Hydrol., 322, 120-137.10.1016/j.jhydrol.2005.03.004Search in Google Scholar

Lohre, M., Sibbertsen, P., önning, T., 2003. Modeling water flow of the Rhine River using seasonal long memory. Water Resour. Res., 39, 1132.10.1029/2002WR001697Search in Google Scholar

Lye, L.M., Lin, Y., 1994. Long - term dependence in annual peak flows of Canadian rivers. J. Hydrol., 160, 89-103.10.1016/0022-1694(94)90035-3Search in Google Scholar

Maier, H.R., Dandy, G.C., 2000. Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environ. Modell. Softw., 15, 101-124 .10.1016/S1364-8152(99)00007-9Search in Google Scholar

Mallat, S., 1998. A Wavelet Tour of Signal Processing Academic Press, New York.10.1016/B978-012466606-1/50008-8Search in Google Scholar

Nelson, M., ill, T., Remus, W., O’Connor, M., 1999. Time series forecasting using neural networks: Should the data be deseasonalized first? Journal of Forecasting, 18, 359-367.10.1002/(SICI)1099-131X(199909)18:5<359::AID-FOR746>3.0.CO;2-PSearch in Google Scholar

Modarres, R., Ouarda, T.B.M.J., 2012. Generalized autoregressive conditional heteroscedasticity modelling of hydrologic time series. Hydrol. Process., 27, 22, 3174-3191.10.1002/hyp.9452Search in Google Scholar

Montanari, A., Rosso, R., Taqqu, M. S., 1997. Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation. Water Resour. Res., 33, 1035-1044.10.1029/97WR00043Search in Google Scholar

Montanari, A., Taqqu, M., Teverovski, V., 1999. Estimating long-range dependence in the presence of periodicity: an empirical study. Math. Comput. Model., 29, 217-228.10.1016/S0895-7177(99)00104-1Search in Google Scholar

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I - A discussion of principles. J. Hydrol., 10, 282-290.10.1016/0022-1694(70)90255-6Search in Google Scholar

Ooms, M., Franses, P.H., 2001. A seasonal periodic long memory model for monthly river flows. Environ. Modell. Softw., 16, 559-569.10.1016/S1364-8152(01)00025-1Search in Google Scholar

Pasquini, A.I., Depetris, P.J., 2010. ENSO - triggered exceptional flooding in the Parana River: Where is the excess water coming from? J. Hydrol., 383, 186-193.10.1016/j.jhydrol.2009.12.035Search in Google Scholar

Patassiová, M., lementová, E., Litschmann, T., Čistý, M., 2002. Analysis of the drought and influence of the precipitation on its occurrence during spring months. Acta Hydrologica Slovaca, 3, 94-101. (In Slovak.) Search in Google Scholar

Pelletier, J.D., Turcotte, D.L., 1997. Long-range persistance in climatological and hydro- logical time series: analysis, modeling and application to drought hazard assessment. J. Hydrol., 203, 198-208.10.1016/S0022-1694(97)00102-9Search in Google Scholar

Pekárová, P., almová, D., Bačová Mitková, V., Miklánek, P., Pekár, J., Škoda, P., 013. istoric flood marks and flood frequency analysis of the Danube River at Bratislava, Slovakia. J. Hydrol. Hydromech., 61, 326-333.10.2478/johh-2013-0041Search in Google Scholar

Prass, T.S., Bravo, J.M., Clarke, R.T., Collischonn, W., Lopes, S.R.C., 2012. Comparison of forecasts of mean monthly water level in the Paraguay River, Brazil, from two fractionally differenced models. Water Resour. Res., 48, W05502.10.1029/2011WR011358Search in Google Scholar

Quimpo, R.G., 1969. Reduction of serially correlated hydrologic data. Bulletin of the International Association of Scientific Hydrology, 4, 111-118.10.1080/02626666909493758Search in Google Scholar

Renaud, O., Starck, J., Murtagh, F., 2003. Prediction based on multiscale decomposition. Int. J. Wavelets Multi., 1, 217-232.10.1142/S0219691303000153Search in Google Scholar

Reszler, C., Blöschl, G., omma, J., 2008. Identifying runoff routing parameters for operational flood forecasting in small to medium sized catchments. Hydrological Sciences Journal, 53, 112-129.10.1623/hysj.53.1.112Search in Google Scholar

Shensa, M.J., 1992. Discrete wavelet transforms: Wedding the trous and Mallat algorithms. In: IEEE Transactions on Signal Processing, 40, 2464-2482.Search in Google Scholar

Starck, J.L., Murtagh, F., Bijaoui, A., 1998. Image processing and data analysis: The multiscale approach. Cambridge University Press, Cambridge, United Kingdom.10.1017/CBO9780511564352Search in Google Scholar

Teverovsky, V., Taqqu, M. S., Willinger, W., 1995. Estimator for long-range dependence: an empirical study. Fractals, 3, 785-798.10.1142/S0218348X95000692Search in Google Scholar

Theil, H., 1958. Economic Forecasting and Policy. North Holland, Amsterdam.Search in Google Scholar

Thuillard, M., 2002. A review of wavelet networks, wavenets, fuzzy wavenets and their applications. Advances in computational intelligence and learning, 18, 43-60.10.1007/978-94-010-0324-7_3Search in Google Scholar

Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analysis. B. Am. Meteorol. Soc., 78, 61-78.10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2Search in Google Scholar

Torrence, C., Webster, P.J., 1999. Interdecadal Changes in the ENSO-Monsoon System. J. Climate, 12, 2679-2690.10.1175/1520-0442(1999)012<2679:ICITEM>2.0.CO;2Search in Google Scholar

Yousefi, S., Weinreich, I., Reinarz, D., 2005. Wavelet-based prediction of oil prices. Chaos Soliton. Fract., 25, 265-275.10.1016/j.chaos.2004.11.015Search in Google Scholar

Wei, S., Song, J., Khan, N.I., 2012. Simulating and predicting river discharge time series using a wavelet-neural network hybrid modelling approach. Hydrol. Process., 26, 28-296.10.1002/hyp.8227Search in Google Scholar

Zealand, C.M., Burn, D.H., Simonovic, S.P., 1999. Short term streamflow forecasting using artificial neural networks. J. Hydrol., 214, 32-48. 10.1016/S0022-1694(98)00242-XSearch in Google Scholar