Abstract
This paper points out two procedures for verifying the statistical independence between the historical and actual data series. They are based respectively on the computation of an empirical distance correlation coefficient, and the use of Hamming distance between binary encoded phase signals corresponding to Log-Gabor filtered time-series. Both procedures are applied to the monthly precipitation series recorded during 480 successive months at 49 meteorological stations in Dobrogea region (Romania) and on 4 and 5-valued fuzzified versions of the initial data represented using linguistic labels. The results show that the crisp data and their fuzzified versions cannot support the hypothesis of history-based predictability from their history. Hence, the two statistical independence tests are robust with respect to the k-means fuzzification of data and cross-validate each other, being applicable to any long-term analysis of precipitation series, to any other signals in general, and to their fuzzified versions, as well.
Similar content being viewed by others
References
Aksoy H, Dahamsheh A (2008) Artificial neural network models for forecasting monthly precipitation in Jordan. Stoch Environ Res Risk Assess 23(7):917–931
Bakirov NK, Rizzo ML, Székely GJ (2006) A multivariate nonparametric test for independence. J Multivar Anal 97(8):1742–1756. https://doi.org/10.1016/j.jmva.2005.10.005
Balas VE, Motoc IM, Barbulescu A (2013) Combined Haar-Hilbert and Log-Gabor based iris encoders. In: Balas VE, Fodor J, Varkonyi-Koczy AM (eds) New concepts and applications in soft computing, vol 417. Studies in computational intelligence. Springer, Berlin, pp 1–26
Barbulescu A (2016a) Modeling temperature evolution. Case study. Rom Rep Phys 68(2):788–798
Barbulescu A (2016b) Models for temperature evolution in Constanta area (Romania). Rom J Phys 68(3–4):676–686
Barbulescu A (2016c) Studies on time series. Applications in environmental sciences. Springer, Berlin
Barbulescu A (2016d) A new method for estimation the regional precipitation. Water Resour Manag 30(1):33–42. https://doi.org/10.1007/s1126
Barbulescu A, Deguenon J (2014a) Models for trend of precipitation in Dobrudja. Environ Eng Manag J 13(4):873–881
Barbulescu A, Deguenon J (2014b) Change point detection and models for precipitation evolution. Case study. Rom J Phys 59(5–6):590–600
Barbulescu A, Deguenon J, Teodorescu D (2011) Study on water resources in the Black Sea region. Nova Publishers, New York
Beran R, Bilodeau M, Lafaye de Micheaux P (2007) Nonparametric tests of independence between random vectors. J Multivar Anal 98(9):1805–1824. https://doi.org/10.1016/j.jmva.2007.01.009
Blum R, Kiefer J, Rosenblatt M (1961) Distribution free tests of independence based on the sample distribution function. Ann Math Sci 32(2):485–489
Boer GJ, Lambert SJ (2008) Multi-model decadal potential predictability of precipitation and temperature. Geophys Res Lett 35(50):L05706. https://doi.org/10.1029/2008GL033234
Boulanger JP, Martinez F, Penalba O, Segura EC (2007) Neural network based daily precipitation generator. Clim Dyn 28:307–324. https://doi.org/10.1007/s00382-006-0184-y
Cook TC, Campbell DT (1979) Quasi-experimentation. Houghton Mifflin, Boston
Daugman J (1994) Biometric personal identification system based on iris analysis. US Patent No. 5, 291, 560
Daugman J (2003) The importance of being random: statistical principles of iris recognition. Pattern Recogn 36:279–291. https://doi.org/10.1016/S0031-3203(02)00030-4
Daugman J (2004) How iris recognition works. IEEE Trans Circuits Syst Video 14(1):21–30
Delgado MA (1996) Testing the serial independence using the sample distribution function. J Time Ser Anal 17:271–285. https://doi.org/10.1111/j.1467-9892.1996.tb00276.x
Dionisio A (2006) Entropy-based independence test. Nonlinear Dyn 44:351–357. https://doi.org/10.1007/s11071-006-2019-0
Dunn JC (1973) A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters. J Cybern 3:32–57. https://doi.org/10.1080/01969727308546046
Ehrendorfer M (1994) The Liouville equation and its potential usefulness for the prediction of forecast skill. Part I: theory. Mon Weather Rev 122:703–713
García JE, González-López VA (2013) Independence tests for continuous random variables based on the longest increasing subsequence. J Multivar Anal 127:126–146. https://doi.org/10.1016/j.jmva.2014.02.010
Genest C, Nešlehová JG, Rémillard B (2013) On the estimation of Spearman’s rho and related tests of independence for possibly discontinuous multivariate data. J Multivar Anal 117:214–228. https://doi.org/10.1016/j.jmva.2013.02.007
Golubyatnikov LL (2004) Stochastic simulation of daily precipitation and daily mean temperatures. Izv Atmos Ocean Phys 40(5):595–606. https://doi.org/10.1029/WR017i001p00182
Heller R, Gorfine M, Heller Y (2012) A class of multivariate distribution-free tests of independence based on graphs. http://www.math.tau.ac.il/~ruheller/Papers/draftHGH.pdf. Accessed 25 Nov 2015
Higgins RW, Leetma A, Xue Y, Barnston A (2000) Dominant factors influencing the seasonal predictability of U.S. precipitation and surface air temperature. J Clim 13:3994–4017
Jarque CM, Bera AK (1981) Efficient tests for normality, homoskedasticity and serial independence of regression residuals: Monte Carlo evidence. Econ Lett 7(4):313–318. https://doi.org/10.1016/0165-1765(81)90035-5
Jo S, Lim Y, Lee J, Kang HS, Oh HS (2012) Bayesian regression model for seasonal forecast of precipitation over Korea. Asia Pac J Atmos Sci 48(3):205–212. https://doi.org/10.1007/s13143-012-0021-7
Katz RW (1983) Statistical procedures for making inferences about precipitation changes simulated by an atmospheric general circulation model. J Atmos Sci 40:2193–2201
Kim J, Ivanov VY, Fatichi S (2016) Climate change and uncertainty assessment over a hydroclimatic transect of Michigan. Stoch Environ Res Risk Assess 30(3):923–944
Koutsoyiannis D (2000) A generalized mathematical framework for stochastic simulation and forecast of hydrologic time series. Water Resour Res 36(6):1519–1533. https://doi.org/10.1029/2000WR900044
Koutsoyiannis D, Onof C (2001) Rainfall disaggregation using adjusting procedures on a Poisson cluster model. J Hydrol 246:109–122. https://doi.org/10.1016/S0022-1694(01)00363-8
Langousis A, Koutsoyiannis D (2006) A stochastic methodology for generation of seasonal time series reproducing overyear scaling behaviour. J Hydrol 322:138–154. https://doi.org/10.1016/j.jhydrol.2005.02.037
Lehmann EL (2006) Nonparametrics. Statistical methods based on ranks. Springer, Berlin
Levene H (1960) Robust tests for equality of variances. In: Olkin I et al (eds) Contributions to probability and statistics: essays in honor of Harold Hotelling. Stanford University Press, Palo Alto, pp 278–292
Lloyd SP (1982) Least square quantization in PCM. IEEE Trans Inf Theory 28(2):129–137. https://doi.org/10.1109/TIT.1982.1056489
Lorenz EN (1963) Deterministic non-periodic flow. J Atmos Sci 20:130–141
Luo L, Wood EF (2006) Assessing the idealized predictability of precipitation and temperature in the NCEP climate forecast system. Geophys Res Lett 33:L04708. https://doi.org/10.1029/2005GL025292
MacQueen JB (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of 5th Berkeley symposium on mathematical statistics and probability. University of California Press, pp 281–297
Madden RA, Shea DJ, Katz RW, Kidson JW (1999) The potential long-range predictability of precipitation over New Zealand. Int J Climatol 19(4):405–421. https://doi.org/10.1002/(SICI)1097-0088(19990330)19:4%3c405:AID-JOC355%3e3.0.CO;2-U
Masek L (2003) Recognition of human iris patterns for biometric identification. Ph.D. thesis, University of Western Australia. http://www.peterkovesi.com/studentprojects/libor/LiborMasekThesis.pdf. Accessed 23 June 2017
Matilla-Garcıa M, Ruiz M (2008) A nonparametric independence test using permutation entropy. J Econ 144:139–155. https://doi.org/10.1016/j.jeconom.2007.12.005
Matilla-Garcıa M, Rodriguez JM, Marin MR (2010) A symbolic test for testing independence between time series. J Time Ser Anal 31:76–85. https://doi.org/10.1111/j.1467-9892.2009.00645.x
Mehrotra R, Srikanthan R, Sharma A (2006) A comparison of three stochastic multi-site precipitation occurrence generators. J Hydrol 331:280–292. https://doi.org/10.1016/j.jhydrol.2006.05.016
Papacharalampous G, Tyralis H, Koutsoyiannis D (2019) Comparison of stochastic and machine learning methods for multi-step ahead forecasting of hydrological processes. Stoch Environ Res Risk Assess 33(2):481–514. https://doi.org/10.1007/s00477-018-1638-6
Pinkse J (1998) A consistent nonparametric test for serial independence. J Econ 84:205–231. https://doi.org/10.1016/S0304-4076(97)00084-5
Popescu-Bodorin N (2009a) Exploring new directions in iris recognition. In: Proceedings of 11th international symposium on symbolic and numeric algorithms for scientific computing. CPS-IEEE Computer Society, pp 384–391. https://doi.org/10.1109/synasc.2009.45
Popescu-Bodorin N (2009b) A fuzzy view on k-means based signal quantization with application in iris segmentation. In: 17th telecommunications forum, University of Belgrade, November 2009. https://arxiv.org/ftp/arxiv/papers/1107/1107.2693.pdf
Popescu-Bodorin N, Balas VE (2010) Comparing Haar-Hilbert and Log-Gabor based iris encoders on bath iris image database. In: 4th International workshop on soft computing applications, July 2010. IEEE Press, pp 191–196
Popescu-Bodorin N, Balas VE (2014) Fuzzy membership, possibility, probability and negation in biometrics. Acta Polytech Hung 11(4):79–100
Puri ML, Sen PK (1971) Nonparametric Methods in Multivariate Analysis. Wiley, New York
Radhakrishna B, Zawadzki I, Fabry F (2012) Predictability of precipitation from continental radar images. Part V: growth and decay. J Atmos Sci 69:3336–3349. https://doi.org/10.1175/JAS-D-12-029.1
Risso WA (2014) An independence test based on symbolic time series. Int J Stat Mech. Article ID 809383. https://doi.org/10.1155/2014/809383
Robinson PM (1991) Consistent nonparametric entropy-based testing. Rev Econ Stud 58:437–453
Rodgers JL, Nicewander WA (1988) Thirteen ways to look at the correlation coefficient. Am Stat 42(1):59–66
Shapiro SS, Wilk MB (1965) An analysis of variance test for normality (complete samples. Biometrika 52(3–4):591–611
Singh P, Borah B (2013) Indian summer monsoon rainfall prediction using artificial neural network. Stoch Environ Res Risk Assess 27(7):1585–1599. https://doi.org/10.1007/s00477-013-0695-0
Singh SV, Kripalani RH (1986) Potential predictability of lower-tropospheric monsoon circulation and rainfall over India. Mon Weather Rev 114:758–763. https://doi.org/10.1175/1520-0493(1986)114%3C0758:PPOLTM%3E2.0.CO;2
Skaug HJ, Tjøstheim D (1993) Nonparametric tests of serial independence. In: Subba Rao T (ed) Developments in time series analysis: the Priestley birthday volume. Chapman & Hall, London, pp 207–229
Sloughter JM, Raftery AE, Gneiting T, Fraley C (2007) Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Mon Weather Rev 135:3209–3220. https://doi.org/10.1175/MWR3441.1
Smirnov N (1948) Table for estimating the goodness of fit of empirical distributions. Ann Math Stat 19:279–281
Stockdale TN (2000) An overview of techniques for seasonal forecasting. Stoch Environ Res Risk Assess 14(4–5):305–318
Sugeno M, Yasukawa T (1993) A fuzzy-logic-based approach to qualitative modeling. IEEE Trans Fuzzy Syst 1(1):7–31
Szekely GJ, Rizzo ML (2013) The distance correlation t-test of independence in high dimension. J Multivar Anal 117:193–213. https://doi.org/10.1016/j.jmva.2013.02.012
Szekely GJ, Rizzo ML, Bakirov NK (2007) Measuring and testing dependence by correlation of distances. Ann Stat 35(6):2769–2794. https://doi.org/10.1214/009053607000000505
Tang W, Lin ZH, Luo LF (2013) Assessing the seasonal predictability of summer precipitation over the Huaihe River basin with multiple APCC models. Atmos Ocean Sci Lett 6(4):185–190
Urs G, Zawadzki I, Turner B (2006) Predictability of precipitation from continental radar images. Part IV: limits to prediction. J Atmos Sci 63:2092–2108. https://doi.org/10.1175/JAS3735.1
Wilks SS (1935) On the independence of k sets of normally distributed statistical variables. Econometrica 3:309–326
Wu L, Seo DJ, Demargne J, Brown JD, Conga S, Schiaake J (2011) Generation of ensemble precipitation forecast from single-valued quantitative precipitation forecast for hydrologic ensemble prediction. J Hydrol 399:281–298. https://doi.org/10.1016/j.jhydrol.2011.01.013
Yang C, Yan Z, Shao Y (2012) Probabilistic precipitation forecasting based on ensemble output using generalized additive models and bayesian model averaging. Acta Meteorol Sin 26(1):1–12. https://doi.org/10.1007/s13351-012-0101-8
Zadeh LA (2009) Toward extended fuzzy logic—a first step. Fuzzy Sets Syst 160:3175–3181. https://doi.org/10.1016/j.fss.2009.04.009
Zadeh LA (2010) Precisiation of meaning—toward computation with natural language. Summer School on Semantic Computing (SSSC), Computer Science Division, Department of EECS, UC Berkeley, July 26
Zawadzki I (1973) Statistical properties of precipitation patterns. J Appl Meteorol 12:459–472. https://doi.org/10.1175/1520-0450(1973)012%3c0459:SPOPP%3e2.0.CO;2
Zhai P (2005) Trends in total precipitation and frequency of daily precipitation extremes over China. J Clim 18:1096–1108. https://doi.org/10.1175/JCLI-3318.1
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Barbulescu, A., Popescu-Bodorin, N. Assessing the history-based predictability of regional monthly precipitation data using statistical and fuzzy methods. Stoch Environ Res Risk Assess 33, 1435–1451 (2019). https://doi.org/10.1007/s00477-019-01702-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00477-019-01702-1