Andel, J., 1986: Long memory time series models. Kybernetika, 22, 105–123.
Arneodo, A., Y. d’Auberton-Carafa, E. Bacry, P. V. Graves, J. F. Muzy, C. Thermes, 1996: Wavelet based fractal analysis of DNA sequences. Physica D, 96, 291–320.
Ashley, R., 1998: A new technique for postsample model selection and validation. J. Econ. Dyn. Control, 22, 647–665.
Beaulieu, J. J., and A. Miron, 1993: Seasonal unit roots in aggregate U.S. data. J. Econom., 55, 305–328.
Bloomfield, P., 1992: Trends in global temperatures. Climatic Change, 21, 275–287.
Booy, C., and L. M. Lye, 1989: A new look at flood risk determination. Water Resour. Bull., 25, 933–943.
Bras, R. L., and I. Rodriguez-Iturbe, 1985: Random Functions in Hydrology. Addison-Wesley, 559 pp.
Brath, A., A. Castellarin, and A. Montanari, 2001: At site and regional assessment of the possible presence of non-stationarity in extreme rainfall in Northern Italy. Phys. Chem. Earth, 26, 705–710.
Brockwell, A. E., and N. H. Chan, 2006: Long memory dynamic Tobit model. J. Forecasting, 25, 351–367.
Bunde, A., J. Eichner, R. Govindan, S. Havlin, E. Koscielny-Bunde, D. Rybski, and D. Vjushin, 2003a: Power-law persistence in the atmosphere: Analysis and application. Nonextensive Entropy—Interdisciplinary Applications, M. Gell-Mann and C. Tsallis, Eds., Oxford University Press, 207–220.
Bunde, A., J. Eichner, S. Havlin, and J. W. Kantelhardt, 2003b: The effect of long term correlations on the statistics of rare events. Physica A, 330, 1–7.
Burlando, P., A. Montanari, and R. Rosso, 1996: Modelling hydrological data with and without long memory. Mecanica, 31, 87–101.
Camuffo, D., 1984: Analysis of the series of precipitation at Padova, Italy. Climatic Change, 5, 55–77.
Castañeda, E., and V. Barros, 1994: Las tendencias de la precipitación en el cono sur de América al este de los Andes (The precipitation tendencies in the southern cone of America to the east of the Andes). Meteorológica, 19, 23–32.
Chung, C.-F., 1996a: A generalized fractionally integrated autoregressive moving-average process. J. Time Ser. Anal., 17, 111–140.
Chung, C.-F., 1996b: Estimating a generalized long memory process. J. Econom., 73, 237–259.
Corduas, M., and D. Piccolo, 2006: Short and long memory unobserved components in hydrological time series. Phys. Chem. Earth, 31, 1099–1106.
Dahlhaus, R., 1989: Efficient parameter estimation for self-similar process. Ann. Stat., 17, 1749–1766.
Dalla, V., and J. Hidalgo, 2005: A parametric bootstrap test for cycles. J. Econom., 129, 219–261.
Delleur, J. W., P. C. Tao, and M. L. Kavass, 1976: An evaluation of practicality and complexity of some rainfall and runoff time series models. Water Resour. Res., 12, 953–970.
Dickey, D. A., and W. A. Fuller, 1979: Distributions of the estimators for autoregressive time series with a unit root. J. Amer. Stat. Assoc., 74, 427–431.
Dickey, D. A., D. P. Hasza, and W. A. Fuller, 1984: Testing for unit roots in seasonal time series. J. Amer. Stat. Assoc., 79, 355–367.
Diebold, F. X., and R. S. Mariano, 1995: Comparing predictive accuracy. J. Bus. Econ. Stat., 13, 253–263.
Elliot, G., T. Rothenberg, and J. H. Stock, 1996: Efficient tests for an autoregressive unit root. Econometrica, 64, 813–836.
Gil-Alana, L. A., 2001: Testing stochastic cycles in macroeconomic time series. J. Time Ser. Anal., 22, 411–430.
Gil-Alana, L. A., 2003: An application of fractional integration to a long temperature time series. Int. J. Climatol., 23, 1699–1710.
Gil-Alana, L. A., 2004: A fractionally integrated model for some Indian monthly rainfall data. J. Indian Inst. Sci., 84, 1–20.
Gil-Alana, L. A., 2005: Statistical model of the temperatures in the Northern Hemisphere using fractional integration techniques. J. Climate, 18, 5357–5369.
Gil-Alana, L. A., 2009: Modelling Australian annual mean rainfall data: A new approach based on fractional integration. Aust. Meteor. Ocean. J., 58, 119–128.
Gil-Alana, L. A., and P. M. Robinson, 1997: Testing of unit roots and other nonstationary hypotheses in macroeconomic time series. J. Econom., 80, 241–268.
Gil-Alana, L. A., and P. M. Robinson, 2001: Testing of seasonal fractional integration in the UK and Japanese consumption and income. J. Appl. Econ., 16, 95–114.
Granger, C. W. J., 1980: Long memory relationships and the aggregation of dynamic models. J. Econom., 14, 227–238.
Granger, C. W. J., 1981: Some properties of time series data and their use in econometric model specification. J. Econom., 16, 121–130.
Gray, H. L., N. Zhang, and W. A. Woodward, 1989: On generalized fractional processes. J. Time Ser. Anal., 10, 233–257.
Gray, H. L., N. Zhang, and W. A. Woodward, 1994: On generalized fractional processes—A correction. J. Time Ser. Anal., 15, 561–562.
Harvey, D. I., S. J. Leybourne, and P. Newbold, 1997: Testing the equality of prediction mean squared errors. Int. J. Forecasting, 13, 281–291.
Hipel, K. W., and A. E. McLeod, 1994: Time Series Modelling of Water Resources and Environmental Systems. Elsevier, 1013 pp.
Hosking, J. R. M., 1981: Fractional differencing. Biometrika, 68, 168–176.
Hurst, H. E., 1951: Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civil, 116, 770–779.
Hylleberg, S., R. F. Engle, C. W. J. Granger, and B. S. Yoo, 1990: Seasonal integration and cointegration. J. Econom., 44, 215–238.
Kantelhardt, J. W., E. Koscielny-Bunde, D. Rybski, P. Braun, A. Bunde, and S. Haulin, 2006: Long-term persistence and multifractality of precipitation and river runoff records. J. Geophys. Res., 111, D01106, doi:10.1029/2005JD005881.
Karl, T. R., R. W. Knight, and B. Baker, 2000: The record breaking global temperatures of 1997 and 1998. Evidence for an increase in the rate of global warming? Geophys. Res. Lett., 27, 719–722.
Koutsoyiannis, D., and A. Montanari, 2007: Statistical analysis of hydroclimatic time series: Uncertainty and insights. Water Resour. Res., 43, W05429, doi:10.1029/2006WR005592.
Lewis, P. A. W., and B. K. Ray, 1997: Modelling long-range dependence, nonlinearity and periodic phenomena in sea surface temperatures using TSMARS. J. Amer. Stat. Assoc., 92, 881–893.
Magnus, W., F. Oberhettinger, and R. P. Soni, 1966: Formulas and Theorems for the Special Functions of Mathematical Physics. Springer, 508 pp.
Maraun, D., H. W. Rust, and H. Timmer, 2004: Tempting long memory on the interpretation of DFA results. Nonlinear Processes Geophys., 11, 495–503.
Minetti, J. L., W. M. Vargas, A. G. Poblete, L. R. Acuña, and G. Casagrande, 2003: Non-linear trends and low frequency oscillations in annual precipitation over Argentina and Chile, 1931–1999. Atmósfera, 16, 119–135.
Montanari, A., and R. Rosso, 1997: Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation and simulation. Water Resour. Res., 33, 1035–1044.
Montanari, A., R. Rosso, and M. Taqqu, 1996: Some long-run properties of rainfall records in Italy. J. Geophys. Res., 101, 431–438.
Ng, S., and P. Perron, 2001: Lag length selection and the construction of unit root tests with good size and power. Econometrica, 69, 1519–1554.
Pelletier, J. D., and D. L. Turcotte, 1997: Long range persistence in climatological and hydrological time series: Analysis, modelling and applications to drought hazard assessment. J. Hydrol., 203, 198–208.
Phillips, P. C. B., and P. Perron, 1988: Testing for a unit root in a time series regression. Biometrika, 75, 335–346.
Porter-Hudak, S., 1990: An application of the seasonal fractionally differenced model to the monetary aggregate. J. Amer. Stat. Assoc., 85, 338–344.
Rainville, E. D., 1960: Special Functions. MacMillan, 365 pp.
Ray, B. K., 1993: Long range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model. Int. J. Forecasting, 9, 255–269.
Robinson, P. M., 1978: Statistical inference for a random coefficient autoregressive model. Scand. J. Stat., 5, 163–168.
Robinson, P. M., 1994: Efficient tests of nonstationary hypotheses. J. Amer. Stat. Assoc., 89, 1420–1437.
Salas, J. D., 1993: Analysis and modelling of hydrological time series. Handbook of Hydrology, D. R. Maidment, Ed., McGraw Hill, 19.1–19.72.
Salas, J. D., J. W. Delleur, V. M. Yevjevich, and M. L. Lane, 1980: Applied Modeling of Hydrologic Time Series. Water Resources Publications, 484 pp.
Smith, R. L., 1993: Long-range dependence and global warming. Statistics for the Environment, V. Barnett, and K. F. Turkman, Eds., J. Wiley, 141–161.
Sutcliffe, A., 1994: Time series forecasting using fractional differencing. J. Forecasting, 13, 383–393.
Trömel, S., and C. D. Schönwiese, 2008: Robust trend estimation of observed German precipitation. Theor. Appl. Climatol., 93 (1–2), 107–115.
Yazdani, M. R., K. D. Javad, M. Mohammad, and S. Ashish, 2011: Trend detection of the rainfall and air temperature data in the Zayandehrud Basin. J. Appl. Sci., 11, 2125–2134.
Yue, J., Y. Zhao, and P. Shang, 2010: Effects of trends in detrended fluctuation analysis of precipitation series. Math. Probl. Eng., 2010, 749894, doi:10.1155/2010/749894.
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Displayed acceptance dates for articles published prior to 2023 are approximate to within a week. If needed, exact acceptance dates can be obtained by emailing amsjol@ametsoc.org.
This paper looks at the analysis of U.K. monthly rainfall data from a long-term persistence viewpoint. Different modeling approaches are considered, taking into account the strong dependence and the seasonality in the data. The results indicate that the most appropriate model is the one that presents cyclical long-run dependence with the order of integration being positive though small, and the cycles having a periodicity of about a year.
This paper looks at the analysis of U.K. monthly rainfall data from a long-term persistence viewpoint. Different modeling approaches are considered, taking into account the strong dependence and the seasonality in the data. The results indicate that the most appropriate model is the one that presents cyclical long-run dependence with the order of integration being positive though small, and the cycles having a periodicity of about a year.
Andel, J., 1986: Long memory time series models. Kybernetika, 22, 105–123.
Arneodo, A., Y. d’Auberton-Carafa, E. Bacry, P. V. Graves, J. F. Muzy, C. Thermes, 1996: Wavelet based fractal analysis of DNA sequences. Physica D, 96, 291–320.
Ashley, R., 1998: A new technique for postsample model selection and validation. J. Econ. Dyn. Control, 22, 647–665.
Beaulieu, J. J., and A. Miron, 1993: Seasonal unit roots in aggregate U.S. data. J. Econom., 55, 305–328.
Bloomfield, P., 1992: Trends in global temperatures. Climatic Change, 21, 275–287.
Booy, C., and L. M. Lye, 1989: A new look at flood risk determination. Water Resour. Bull., 25, 933–943.
Bras, R. L., and I. Rodriguez-Iturbe, 1985: Random Functions in Hydrology. Addison-Wesley, 559 pp.
Brath, A., A. Castellarin, and A. Montanari, 2001: At site and regional assessment of the possible presence of non-stationarity in extreme rainfall in Northern Italy. Phys. Chem. Earth, 26, 705–710.
Brockwell, A. E., and N. H. Chan, 2006: Long memory dynamic Tobit model. J. Forecasting, 25, 351–367.
Bunde, A., J. Eichner, R. Govindan, S. Havlin, E. Koscielny-Bunde, D. Rybski, and D. Vjushin, 2003a: Power-law persistence in the atmosphere: Analysis and application. Nonextensive Entropy—Interdisciplinary Applications, M. Gell-Mann and C. Tsallis, Eds., Oxford University Press, 207–220.
Bunde, A., J. Eichner, S. Havlin, and J. W. Kantelhardt, 2003b: The effect of long term correlations on the statistics of rare events. Physica A, 330, 1–7.
Burlando, P., A. Montanari, and R. Rosso, 1996: Modelling hydrological data with and without long memory. Mecanica, 31, 87–101.
Camuffo, D., 1984: Analysis of the series of precipitation at Padova, Italy. Climatic Change, 5, 55–77.
Castañeda, E., and V. Barros, 1994: Las tendencias de la precipitación en el cono sur de América al este de los Andes (The precipitation tendencies in the southern cone of America to the east of the Andes). Meteorológica, 19, 23–32.
Chung, C.-F., 1996a: A generalized fractionally integrated autoregressive moving-average process. J. Time Ser. Anal., 17, 111–140.
Chung, C.-F., 1996b: Estimating a generalized long memory process. J. Econom., 73, 237–259.
Corduas, M., and D. Piccolo, 2006: Short and long memory unobserved components in hydrological time series. Phys. Chem. Earth, 31, 1099–1106.
Dahlhaus, R., 1989: Efficient parameter estimation for self-similar process. Ann. Stat., 17, 1749–1766.
Dalla, V., and J. Hidalgo, 2005: A parametric bootstrap test for cycles. J. Econom., 129, 219–261.
Delleur, J. W., P. C. Tao, and M. L. Kavass, 1976: An evaluation of practicality and complexity of some rainfall and runoff time series models. Water Resour. Res., 12, 953–970.
Dickey, D. A., and W. A. Fuller, 1979: Distributions of the estimators for autoregressive time series with a unit root. J. Amer. Stat. Assoc., 74, 427–431.
Dickey, D. A., D. P. Hasza, and W. A. Fuller, 1984: Testing for unit roots in seasonal time series. J. Amer. Stat. Assoc., 79, 355–367.
Diebold, F. X., and R. S. Mariano, 1995: Comparing predictive accuracy. J. Bus. Econ. Stat., 13, 253–263.
Elliot, G., T. Rothenberg, and J. H. Stock, 1996: Efficient tests for an autoregressive unit root. Econometrica, 64, 813–836.
Gil-Alana, L. A., 2001: Testing stochastic cycles in macroeconomic time series. J. Time Ser. Anal., 22, 411–430.
Gil-Alana, L. A., 2003: An application of fractional integration to a long temperature time series. Int. J. Climatol., 23, 1699–1710.
Gil-Alana, L. A., 2004: A fractionally integrated model for some Indian monthly rainfall data. J. Indian Inst. Sci., 84, 1–20.
Gil-Alana, L. A., 2005: Statistical model of the temperatures in the Northern Hemisphere using fractional integration techniques. J. Climate, 18, 5357–5369.
Gil-Alana, L. A., 2009: Modelling Australian annual mean rainfall data: A new approach based on fractional integration. Aust. Meteor. Ocean. J., 58, 119–128.
Gil-Alana, L. A., and P. M. Robinson, 1997: Testing of unit roots and other nonstationary hypotheses in macroeconomic time series. J. Econom., 80, 241–268.
Gil-Alana, L. A., and P. M. Robinson, 2001: Testing of seasonal fractional integration in the UK and Japanese consumption and income. J. Appl. Econ., 16, 95–114.
Granger, C. W. J., 1980: Long memory relationships and the aggregation of dynamic models. J. Econom., 14, 227–238.
Granger, C. W. J., 1981: Some properties of time series data and their use in econometric model specification. J. Econom., 16, 121–130.
Gray, H. L., N. Zhang, and W. A. Woodward, 1989: On generalized fractional processes. J. Time Ser. Anal., 10, 233–257.
Gray, H. L., N. Zhang, and W. A. Woodward, 1994: On generalized fractional processes—A correction. J. Time Ser. Anal., 15, 561–562.
Harvey, D. I., S. J. Leybourne, and P. Newbold, 1997: Testing the equality of prediction mean squared errors. Int. J. Forecasting, 13, 281–291.
Hipel, K. W., and A. E. McLeod, 1994: Time Series Modelling of Water Resources and Environmental Systems. Elsevier, 1013 pp.
Hosking, J. R. M., 1981: Fractional differencing. Biometrika, 68, 168–176.
Hurst, H. E., 1951: Long-term storage capacity of reservoirs. Trans. Amer. Soc. Civil, 116, 770–779.
Hylleberg, S., R. F. Engle, C. W. J. Granger, and B. S. Yoo, 1990: Seasonal integration and cointegration. J. Econom., 44, 215–238.
Kantelhardt, J. W., E. Koscielny-Bunde, D. Rybski, P. Braun, A. Bunde, and S. Haulin, 2006: Long-term persistence and multifractality of precipitation and river runoff records. J. Geophys. Res., 111, D01106, doi:10.1029/2005JD005881.
Karl, T. R., R. W. Knight, and B. Baker, 2000: The record breaking global temperatures of 1997 and 1998. Evidence for an increase in the rate of global warming? Geophys. Res. Lett., 27, 719–722.
Koutsoyiannis, D., and A. Montanari, 2007: Statistical analysis of hydroclimatic time series: Uncertainty and insights. Water Resour. Res., 43, W05429, doi:10.1029/2006WR005592.
Lewis, P. A. W., and B. K. Ray, 1997: Modelling long-range dependence, nonlinearity and periodic phenomena in sea surface temperatures using TSMARS. J. Amer. Stat. Assoc., 92, 881–893.
Magnus, W., F. Oberhettinger, and R. P. Soni, 1966: Formulas and Theorems for the Special Functions of Mathematical Physics. Springer, 508 pp.
Maraun, D., H. W. Rust, and H. Timmer, 2004: Tempting long memory on the interpretation of DFA results. Nonlinear Processes Geophys., 11, 495–503.
Minetti, J. L., W. M. Vargas, A. G. Poblete, L. R. Acuña, and G. Casagrande, 2003: Non-linear trends and low frequency oscillations in annual precipitation over Argentina and Chile, 1931–1999. Atmósfera, 16, 119–135.
Montanari, A., and R. Rosso, 1997: Fractionally differenced ARIMA models applied to hydrologic time series: Identification, estimation and simulation. Water Resour. Res., 33, 1035–1044.
Montanari, A., R. Rosso, and M. Taqqu, 1996: Some long-run properties of rainfall records in Italy. J. Geophys. Res., 101, 431–438.
Ng, S., and P. Perron, 2001: Lag length selection and the construction of unit root tests with good size and power. Econometrica, 69, 1519–1554.
Pelletier, J. D., and D. L. Turcotte, 1997: Long range persistence in climatological and hydrological time series: Analysis, modelling and applications to drought hazard assessment. J. Hydrol., 203, 198–208.
Phillips, P. C. B., and P. Perron, 1988: Testing for a unit root in a time series regression. Biometrika, 75, 335–346.
Porter-Hudak, S., 1990: An application of the seasonal fractionally differenced model to the monetary aggregate. J. Amer. Stat. Assoc., 85, 338–344.
Rainville, E. D., 1960: Special Functions. MacMillan, 365 pp.
Ray, B. K., 1993: Long range forecasting of IBM product revenues using a seasonal fractionally differenced ARMA model. Int. J. Forecasting, 9, 255–269.
Robinson, P. M., 1978: Statistical inference for a random coefficient autoregressive model. Scand. J. Stat., 5, 163–168.
Robinson, P. M., 1994: Efficient tests of nonstationary hypotheses. J. Amer. Stat. Assoc., 89, 1420–1437.
Salas, J. D., 1993: Analysis and modelling of hydrological time series. Handbook of Hydrology, D. R. Maidment, Ed., McGraw Hill, 19.1–19.72.
Salas, J. D., J. W. Delleur, V. M. Yevjevich, and M. L. Lane, 1980: Applied Modeling of Hydrologic Time Series. Water Resources Publications, 484 pp.
Smith, R. L., 1993: Long-range dependence and global warming. Statistics for the Environment, V. Barnett, and K. F. Turkman, Eds., J. Wiley, 141–161.
Sutcliffe, A., 1994: Time series forecasting using fractional differencing. J. Forecasting, 13, 383–393.
Trömel, S., and C. D. Schönwiese, 2008: Robust trend estimation of observed German precipitation. Theor. Appl. Climatol., 93 (1–2), 107–115.
Yazdani, M. R., K. D. Javad, M. Mohammad, and S. Ashish, 2011: Trend detection of the rainfall and air temperature data in the Zayandehrud Basin. J. Appl. Sci., 11, 2125–2134.
Yue, J., Y. Zhao, and P. Shang, 2010: Effects of trends in detrended fluctuation analysis of precipitation series. Math. Probl. Eng., 2010, 749894, doi:10.1155/2010/749894.
| All Time | Past Year | Past 30 Days | |
|---|---|---|---|
| Abstract Views | 0 | 0 | 0 |
| Full Text Views | 222 | 57 | 1 |
| PDF Downloads | 316 | 30 | 2 |
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