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References on Long memory and parametric models in environmental time series


This page is managed by Marcella Corduas (Università degli Studi di Napoli Federico II).

I update March, 2012 (... references) thanks to Marcella Corduas, Salvatore Grimaldi, and.......


References with *star are the last update

Before 2004

Anh JV., K. Lunney, S. Peiris (1997) Stochastic models for characterisation and prediction of time series with long-range dependence and fractality, Environmental Modelling & Software, Volume 12, Issue 1, Pages 67-73

Montanari A., Rosso R. and Taqqu M.S. (1997). Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation, and simulation. Water Resources Research, 33(5),

Gordon R. Richards (1997) Interpolating a palaeoclimatic time series: nonlinearity, persistence and trending in the Cenozoic Palaeogeography, Palaeoclimatology, Palaeoecology, Volume 128, Issues 1–4,  Pages 17-27

Ramachandra Rao A., D. Bhattacharya (1999) Hypothesis testing for long-term memory in hydrologic series, Journal of Hydrology, Volume 216, Issues 3–4,  Pages 183-196

Montanari, A., Taqqu, M.S., Teverovsky, V. (1999), Estimating long-range dependence in the presence of periodicity: an empirical study, Mathematical and Computer Modeling, 29, 217-228, Elsevier, Stati Uniti.

Montanari A., Rosso R. and Taqqu M.S. (2000). A seasonal fractional ARIMA model applied to the Nile River monthly at Aswan. Water Resources Research, 36, 1249-1259.

Ooms M.,  Franses P.H. (2001) A seasonal periodic long memory model for monthly river flows, Environmental Modelling & Software, Volume 16, 6, Pages 559-569

Pagano T.C., Q.J. Wang, P. Hapuarachchi, D. Robertson (2001) A dual-pass error-correction technique for forecasting streamflow ,Journal of Hydrology, Volume 405, Issues 3–4,  Pages 367-381

Baillie RT, Chung S-K (2002) Modeling and forecasting from trend-stationary long memory models with applications to climatology, Int J Forecast 18:215–226

Grimaldi S., (2004) Linear parametric models applied on daily hydrological series, Journal of Hydrologic Engineering, 9 (5), pp. 383-391.




 Gil-Alana, Luis A., (2005) Statistical Modeling of the Temperatures in the Northern Hemisphere, Using Fractional Integration Techniques. J. Climate, 18, 5357–5369. doi:




Corduas M., D. Piccolo (2006) Short and Long Memory Unobserved Components in Hydrological Time Series, Physics and Chemistry of the Earth, 31, 1099-1106, ISSN 1474-7085

Kantelhardt, J. W., E. Koscielny-Bunde, D. Rybski, P. Braun, A. Bunde, and S. Havlin (2006),  Long-term persistence and multifractality of precipitation and river runoff records, J. Geophys. Res., 111, D01106, doi:10.1029/2005JD005881.




Mills T (2007), Time series modelling of two millenia of northern hemispere temperatures: long memory or shifting trends?, J R Stat Soc Ser A 170:83–94

Gilbert C.S. Lui, W.K. Li, Kenneth M.Y. Leung, Joseph H.W. Lee, A.W. Jayawardena (2007) Modelling algal blooms using vector autoregressive model with exogenous variables and long memory filter, Ecological Modelling, Volume 200, Issues 1–2, Pages 130-138




Jeh-Nan Pan,  Su-Tsu Chen (2008) Monitoring long-memory air quality data using ARFIMA model, Environmetrics 2008; 19: 209–219

Gil-Alana, Luis A. (2008) Time trend estimation with breaks in temperature time series. Climatic Change 89:3-4, 325-337

Gil-Alana, Luis A., (2008) Warming Break Trends and Fractional Integration in the Northern, Southern, and Global Temperature Anomaly Series, J. Atmos. Oceanic Technol., 25, 570–578. doi:




Gil-Alana, Luis A. (2009) Persistence and Time Trends in the Temperatures in Spain. Advances in Meteorology 2009, 1-9

Gil-Alana, Luis A., (2009) Modelling Australian annual mean rainfall data: a new approach based on fractional integration, Australian Meteorological and Oceanographic Journal, 58, 119-128




Koutsoyiannis, D., Paschalis, A., Theodoratos, N. (2011) Two-dimensional Hurst-Kolmogorov process and its application to rainfall fields, Journal of Hydrology, 398 (1-2), pp. 91-100.

Poveda, G. (2011) Mixed memory, (non) Hurst effect, and maximum entropy of rainfall in the tropical Andes, Advances in Water Resources, 34 (2), pp. 243-256.

Rea W., Reale M., Brown J. (2011) Long memory in temperature reconstructions, Climatic Change Volume 107, Numbers 3-4, 247-265, DOI: 10.1007/s10584-011-0068-y

Tabari, H., Marofi, S. (2011) "Changes of pan evaporation in the west of Iran". Water Resources Management, 25:97-111.

Tabari, H., Marofi, S., Ahmadi, M. (2011) "Long-term variations of water quality parameters in the Maroon River, Iran". Environmental Monitoring and Assessment, 177:273-2871.

Tabari, H., Marofi, S., Aeini, A., Hosseinzadeh Talaee, P., Mohammadi, K. (2011) "Trend analysis of reference evapotranspiration in the western half of Iran". Agricultural and Forest Meteorology, 151:128-1361.

Tabari, H., Shifteh Somee, B., Rezaeian Zadeh, M. (2011) "Testing for long-term trends in climatic variables in Iran". Atmospheric Research, 100:132-140.

Tabari, H., Hosseinzadeh Talaee, P. (2011) "Recent trends of mean maximum and minimum air temperatures in the western half of Iran". Meteorology and Atmospheric Physics, 111:121-131.

Tyralis, H., Koutsoyiannis, D. (2011) Simultaneous estimation of the parameters of the Hurst-Kolmogorov stochastic process, Stochastic Environmental Research and Risk Assessment, 25 (1), pp. 21-33.




Gil-Alana, Luis A., (2012) Long memory, seasonality and time trends in the average monthly temperatures in Alaska. Theoretical and Applied Climatology

R. Maheswaran, Rakesh Khosa (2012) Comparative study of different wavelets for hydrologic forecasting, Computers & Geosciences,

Lombardo, F., E. Volpi, and D. Koutsoyiannis (2012), Rainfall downscaling in time: Theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades, Hydrological Science Journal,  doi:10.1080/02626667.2012.695872, 2012.

Lombardo, F., E. Volpi, and D. Koutsoyiannis, Rainfall downscaling in time: Theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades, Hydrological Sciences Journal, 57 (6), 1052-1066, 2012.

Tabari, H., Nikbakht, J., Shifteh Some'e, B. (2012) "Investigation of groundwater level fluctuations in the north of Iran". Environmental Earth Science, 66:231-243.




Koutsoyiannis, D., Hydrology and Change, Hydrological Sciences Journal, 58 (6), 1177-1197, 2013.

Markonis, Y., and D. Koutsoyiannis, Climatic variability over time scales spanning nine orders of magnitude: Connecting Milankovitch cycles with Hurst-Kolmogorov dynamics, Surveys in Geophysics, 34 (2), 181-207, 2013.




Tsekouras, G., and D. Koutsoyiannis, Stochastic analysis and simulation of hydrometeorological processes associated with wind and solar energy, Renewable Energy, 63, 624-633, 2014.




Müller, H., Haberlandt, U. (2015): Temporal rainfall disaggregation with a cascade model: from single-station disaggregation to spatial rainfall - Journal of Hydrologic Engineering, 20 (11), 04015026,

Müller, H., Haberlandt, U. (2016): Temporal rainfall disaggregation using a multiplicative cascade model for spatial application in urban hydrology - Journal of Hydrology (SI "Measuring & Modeling Rain"), in press,






Ministero dell'Ambiente e della Tutela del Territorio e del Mare

Institute for Environmental Protection and Research

 Honors Center of Italian Universities - H2CU 
Sapienza University of Rome

University of Tuscia,
Viterbo, Italy


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