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Meteorolojik Zaman Serilerinde Kayıp Veri Tahmin Yöntemlerinin Başarımlarının Korelasyon Boyutu Analiziyle Karşılaştırılması

Year 2011, Volume: 8 Issue: 2, 55 - 67, 17.10.2011

Abstract

Bu çalışmada, meteorolojik zaman serilerinde kayıp veri tahmin yöntemlerinin başarımları doğrusal olmayan dinamik zaman serileri analizinde sıklıkla kullanılan korelasyon boyutu belirleme yöntemiyle karşılaştırılmıştır. Bu amaçla, 1965-2006 periyodunda, eksik veri içermeyen aylık meteorolojik zaman serilerinde farklı oranlarda yapay kayıp veriler oluşturulmuş ve oluşturulan yapay kayıp veriler tahmin yöntemleriyle tamamlanarak bu serilerin korelasyon boyutları orijinal serilerden elde edilen korelasyon boyutlarıyla karşılaştırılmıştır. Elde edilen bulgular doğrultusunda, karekök hata kareler ortalaması gibi sadece merkezi eğilimleri dikkate alan doğruluk ölçüm yöntemleri yanında serilerin alansal ve zamansal özelliklerine hassas bağımlı olan korelasyon boyutu belirleme yönteminin de kullanılmasının zaman serilerinde kayıp veri tahmin yöntemlerinin başarımlarının karşılaştırılmasını daha güvenilir düzeye taşıyacağı gözlenmiştir.

References

  • Aly, A., Pathak, C., Teegavarapu, R. S. V., Ahlquist, J., Fuelberg, H., 2009. Evaluation of Improvised Spatial Interpolation Methods For Infilling Missing Precipitation Records. Paper presented at the Proceedings of World Environmental and Water Resources Congress, 342 5914-5923.
  • Asar, Ö., Kartal, E., Aslan, S., Öztürk, M.Z., Yozgatlıgil, C., Çınar, İ., Batmaz, İ., Köksal, G., Türkeş, M., Tatlı, H., 2010. Descriptive Analysis of Turkish Precipitation data with Data Mining Methods. Presented at the 7th National Symposium of Statistics Days, Ankara, Middle East Technical University.
  • Bishop, C. M., 1995. Neural Networks for Pattern Recognition. Oxford University Press, New York, USA.
  • Cano, S., Andreu, J., 2010. Using Multiple Imputation To Simulate Time Series: A Proposal To Solve The Distance Effect. WSEAS Transactions on Computers, 9(7), 768-777.
  • Coulibaly P., Evora N.D., 2007. Comparison of Neural Network Methods For Infilling Missing Daily Weather Records. Journal of Hydrology, Vol. 341, pp. 27-41.
  • Demirtas, H., Freels, S.A., Yucel, R.M., 2008. Plausibility of Multivariate Normality Assumption When Multiply Imputing Non-Gaussian Continuous Outcomes: A Simulation Assessment. Journal of Statistical Computation and Simulation, 78 (1), pp. 69-84.
  • Dempster A.P., Laird N.M., Rubin D.B., 1977. Maximum Likelihood From Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society .B., 39, pp. 1-38.
  • Fraser, A. M. ve Swinney, H. L. 1986. Independent Coordinates for Strange Attractors from Mutual Information. Phys. Rev. A, 33, 1134.
  • Gardner, M. W., Dorling, S. R., 1998. Artificial Neural Networks (The Multiplayer Perceptron)--A Review of Applications in The Atmospheric Sciences. Atmospheric Environment, 32, 2627-2636.
  • Grassberger, P., Procaccia, I., 1983. Measuring The Strangeness of Strange Attractors. Physica D, 9,189-208.
  • Haykin, S., 1999. Neural Networks: A Comprehensive Foundation. 2nd Edition, Prentice-Hall.
  • Hyndman, R. J., Koehler, A. B., 2006. Another Look at Measures of Forecast Accuracy. International Journal of Forecasting, 22 (4), 679-688.
  • Junninen, H., Niska, H., Tuppurainen, K., Ruuskanen, J., Kolehmainen, M., 2004. Methods For Imputation of Missing Values in Air Quality Data Sets. Atmospheric Environment, 38(18), 2895-2907.
  • Kalteh, A. M., Berndtsson, R., 2007. Interpolating Monthly Precipitation By Self-Organizing Map (SOM) And Multilayer Perceptron (MLP). Hydrological Sciences Journal, 52(2), 305-317.
  • Kalteh, A. M., Hjorth, P., 2009. Imputation of Missing Values in a Precipitation-Runoff Process Database. Hydrology Research, 40(4), 420-432.
  • Kantz, H., Schriber, T., 2003. Nonlinear Time Series Analysis. Cambridge University Press, Cambridge UK. 2nd Edition.
  • Kennel, M. B., Brown, R., Abarbanel, H. D. I., 1992. Determining Embedding Dimension For Phase-Space Reconstruction Using A Geometrical Construction. Phys. Rev. A, 45, 3403. Reprinted in Ott et al. (1994).
  • Little, R. J. A., Rubin, D. B., 2002. Statistical Analysis with Missing Data. 2nd Edition. Chichester: Wiley.
  • Lo Presti, R., Barca, E., Passarella, G., 2010. A Methodology For Treating Missing Data Applied To Daily Rainfall Data in The Candelaro River Basin (Italy). Environmental Monitoring and Assessment, 160 (1-4), pp. 1-22.
  • Makhuvha, T., Pegram, G., Sparks, R., Zucchini, W., 1997. Patching Rainfall Data Using Regression Methods. 2. Comparisons of Accuracy, Bias And Efficiency. Journal of Hydrology, 198(1-4), 308-318.
  • Paulhus, J. L. H., Kohler, M. A., 1952. Interpolation of Missing Precipitation Records. Mon. Weather Rev. 80, pp. 129-133.
  • Schafer, J. L., 1997. Analysis of Incomplete Multivariate Data. London: Chapman and Hall / CRC Press.
  • Schneider, T., 2001. Analysis of Incomplete Climate Data: Estimation of Mean Values and Covariance Matrices and Imputation of Missing Values. Journal of Climate, Vol. 14, pp. 853-871.
  • Sivakumar, B., 2004. Chaos Theory in Geopyhsics: Past, Present and Future. Chaos, Solitons and Fractals. No:19, Sh. 441-462.
  • Sivakumar, B., Wallender, W. W., Horwath, W. R., Mitchell, J. P., Prentice, S. E., Joyce, B. A., 2006. Nonlinear Analysis of Rainfall Dynamics in California's Sacramento Valley. Hydrological Processes, No:20 (8), Sh. 1723-1736.
  • Small, M., 2005. Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance. Nonlinear Science Series A, World Scientific.vol 52.
  • Takens, F., 1981. Detecting Strange Attractors in Turbulence. Lecture Notes in Math. Vol. 898, Springer, New York.
  • Toth, E., Brath, A., Montanari, A., 2000. Comparison of Short-Term Rainfall Prediction Models For Real-Time Flood Forecasting. Journal of Hydrology, 239(1-4), 132-147.
  • Xia Y., Fabian P., Stohl A., Winterhalter M., 1999a. Forest Climatology: Estimation of Missing Values For Bavaria Germany. Agricultural and Forest Meteorology, Vol. 96 (1-3), pp. 131-144.
  • Xia, Y., Fabian, P., Stohl, A., Winterhalter, M., 1999b. Forest Climatology: Reconstruction of Mean Climatological Data for Bavaria, Germany. Agricultural and Forest Meteorology, 96(1-3), 117-129.
  • Young, K.C., 1992. A Three-Way Model For Interpolating For Monthly Precipitation Values. Monthly Weather Review,Vol. 120., pp. 2562-2569.

Comparison of Missing Data Imputation Methods for Meteorological Time Series Data Via Correlation Dimension Technique

Year 2011, Volume: 8 Issue: 2, 55 - 67, 17.10.2011

Abstract

In this study, the performances of missing value imputation methods for meteorological data are compared by Correlation Dimension Technique, which is frequently used in nonlinear dynamic time series analysis. For this purpose, artificial missing data sets are created with different missing data ratios from complete monthly meteorological time series in the spanning period of 1965-2006. Comparisons were made between original Correlation Dimensions which are calculated by using complete time series and with Correlation Dimensions calculated on re-estimated time series. Since the Correlation Dimension is highly dependent on auto-correlation structures of time series and according to our findings using Correlation Dimension, besides central tendency measures, will make comparisons more appropriate and reliable.

References

  • Aly, A., Pathak, C., Teegavarapu, R. S. V., Ahlquist, J., Fuelberg, H., 2009. Evaluation of Improvised Spatial Interpolation Methods For Infilling Missing Precipitation Records. Paper presented at the Proceedings of World Environmental and Water Resources Congress, 342 5914-5923.
  • Asar, Ö., Kartal, E., Aslan, S., Öztürk, M.Z., Yozgatlıgil, C., Çınar, İ., Batmaz, İ., Köksal, G., Türkeş, M., Tatlı, H., 2010. Descriptive Analysis of Turkish Precipitation data with Data Mining Methods. Presented at the 7th National Symposium of Statistics Days, Ankara, Middle East Technical University.
  • Bishop, C. M., 1995. Neural Networks for Pattern Recognition. Oxford University Press, New York, USA.
  • Cano, S., Andreu, J., 2010. Using Multiple Imputation To Simulate Time Series: A Proposal To Solve The Distance Effect. WSEAS Transactions on Computers, 9(7), 768-777.
  • Coulibaly P., Evora N.D., 2007. Comparison of Neural Network Methods For Infilling Missing Daily Weather Records. Journal of Hydrology, Vol. 341, pp. 27-41.
  • Demirtas, H., Freels, S.A., Yucel, R.M., 2008. Plausibility of Multivariate Normality Assumption When Multiply Imputing Non-Gaussian Continuous Outcomes: A Simulation Assessment. Journal of Statistical Computation and Simulation, 78 (1), pp. 69-84.
  • Dempster A.P., Laird N.M., Rubin D.B., 1977. Maximum Likelihood From Incomplete Data via the EM Algorithm. Journal of the Royal Statistical Society .B., 39, pp. 1-38.
  • Fraser, A. M. ve Swinney, H. L. 1986. Independent Coordinates for Strange Attractors from Mutual Information. Phys. Rev. A, 33, 1134.
  • Gardner, M. W., Dorling, S. R., 1998. Artificial Neural Networks (The Multiplayer Perceptron)--A Review of Applications in The Atmospheric Sciences. Atmospheric Environment, 32, 2627-2636.
  • Grassberger, P., Procaccia, I., 1983. Measuring The Strangeness of Strange Attractors. Physica D, 9,189-208.
  • Haykin, S., 1999. Neural Networks: A Comprehensive Foundation. 2nd Edition, Prentice-Hall.
  • Hyndman, R. J., Koehler, A. B., 2006. Another Look at Measures of Forecast Accuracy. International Journal of Forecasting, 22 (4), 679-688.
  • Junninen, H., Niska, H., Tuppurainen, K., Ruuskanen, J., Kolehmainen, M., 2004. Methods For Imputation of Missing Values in Air Quality Data Sets. Atmospheric Environment, 38(18), 2895-2907.
  • Kalteh, A. M., Berndtsson, R., 2007. Interpolating Monthly Precipitation By Self-Organizing Map (SOM) And Multilayer Perceptron (MLP). Hydrological Sciences Journal, 52(2), 305-317.
  • Kalteh, A. M., Hjorth, P., 2009. Imputation of Missing Values in a Precipitation-Runoff Process Database. Hydrology Research, 40(4), 420-432.
  • Kantz, H., Schriber, T., 2003. Nonlinear Time Series Analysis. Cambridge University Press, Cambridge UK. 2nd Edition.
  • Kennel, M. B., Brown, R., Abarbanel, H. D. I., 1992. Determining Embedding Dimension For Phase-Space Reconstruction Using A Geometrical Construction. Phys. Rev. A, 45, 3403. Reprinted in Ott et al. (1994).
  • Little, R. J. A., Rubin, D. B., 2002. Statistical Analysis with Missing Data. 2nd Edition. Chichester: Wiley.
  • Lo Presti, R., Barca, E., Passarella, G., 2010. A Methodology For Treating Missing Data Applied To Daily Rainfall Data in The Candelaro River Basin (Italy). Environmental Monitoring and Assessment, 160 (1-4), pp. 1-22.
  • Makhuvha, T., Pegram, G., Sparks, R., Zucchini, W., 1997. Patching Rainfall Data Using Regression Methods. 2. Comparisons of Accuracy, Bias And Efficiency. Journal of Hydrology, 198(1-4), 308-318.
  • Paulhus, J. L. H., Kohler, M. A., 1952. Interpolation of Missing Precipitation Records. Mon. Weather Rev. 80, pp. 129-133.
  • Schafer, J. L., 1997. Analysis of Incomplete Multivariate Data. London: Chapman and Hall / CRC Press.
  • Schneider, T., 2001. Analysis of Incomplete Climate Data: Estimation of Mean Values and Covariance Matrices and Imputation of Missing Values. Journal of Climate, Vol. 14, pp. 853-871.
  • Sivakumar, B., 2004. Chaos Theory in Geopyhsics: Past, Present and Future. Chaos, Solitons and Fractals. No:19, Sh. 441-462.
  • Sivakumar, B., Wallender, W. W., Horwath, W. R., Mitchell, J. P., Prentice, S. E., Joyce, B. A., 2006. Nonlinear Analysis of Rainfall Dynamics in California's Sacramento Valley. Hydrological Processes, No:20 (8), Sh. 1723-1736.
  • Small, M., 2005. Applied Nonlinear Time Series Analysis: Applications in Physics, Physiology and Finance. Nonlinear Science Series A, World Scientific.vol 52.
  • Takens, F., 1981. Detecting Strange Attractors in Turbulence. Lecture Notes in Math. Vol. 898, Springer, New York.
  • Toth, E., Brath, A., Montanari, A., 2000. Comparison of Short-Term Rainfall Prediction Models For Real-Time Flood Forecasting. Journal of Hydrology, 239(1-4), 132-147.
  • Xia Y., Fabian P., Stohl A., Winterhalter M., 1999a. Forest Climatology: Estimation of Missing Values For Bavaria Germany. Agricultural and Forest Meteorology, Vol. 96 (1-3), pp. 131-144.
  • Xia, Y., Fabian, P., Stohl, A., Winterhalter, M., 1999b. Forest Climatology: Reconstruction of Mean Climatological Data for Bavaria, Germany. Agricultural and Forest Meteorology, 96(1-3), 117-129.
  • Young, K.C., 1992. A Three-Way Model For Interpolating For Monthly Precipitation Values. Monthly Weather Review,Vol. 120., pp. 2562-2569.
There are 31 citations in total.

Details

Primary Language Turkish
Subjects Statistical Analysis
Journal Section Research Articles
Authors

Sipan Aslan This is me

Ceylan Yozgatlıgil

Cem İyigün

İnci Batmaz

Hasan Tatlı

Publication Date October 17, 2011
Published in Issue Year 2011 Volume: 8 Issue: 2

Cite

APA Aslan, S., Yozgatlıgil, C., İyigün, C., Batmaz, İ., et al. (2011). Meteorolojik Zaman Serilerinde Kayıp Veri Tahmin Yöntemlerinin Başarımlarının Korelasyon Boyutu Analiziyle Karşılaştırılması. İstatistik Araştırma Dergisi, 8(2), 55-67.