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Modelling High Dimensional Paddy Production Data using Copulas

Nuranisyha Mohd Roslan, Wendy Ling Shinyie and Sim Siew Ling

Pertanika Journal of Science & Technology, Volume 29, Issue 1, January 2021

DOI: https://doi.org/10.47836/pjst.29.1.15

Keywords: Archimedean copula family, dependence structure, elliptical copula family, paddy production

Published on: 22 January 2021

As the climate change is likely to be adversely affecting the yield of paddy production, thence it has brought a limelight of the probable challenges on human particularly regional food security issues. This paper aims to fit multivariate time series of paddy production variables using copula functions and predicts the next year event based on the data of five countries in southeast Asia. In particular, the most appropriate marginal distribution for each univariate time series was first identified using maximum likelihood parameter estimation method. Next, we performed multivariate copula fitting using two types of copula families, namely, elliptical copula family and Archimedean copula family. Elliptical copula family studied are normal and t copula, while Archimedean copula family considered are Joe, Clayton and Gumbel copulas. The performance of marginal distribution and copula fitting was examined using Akaike information criterion (AIC) values. Finally, we used the best fitted copula model to forecast the succeeding event. In order to assess the performance of copula function, we computed the forecast means and estimation errors of copula function with a generalized autoregressive conditional heteroskedasticity model as reference group. Based on the smallest AIC, the majority of the data favoured the Gumbel copula, which belongs to Archimedean copula family as well as extreme value copula family. Likewise, applying the historical data to forecast the future trends may assist all relevant stakeholders, for instance government, NGO agencies, and professional practitioners in making informed decisions without compromising the environmental as well as economical sustainability in the region.

  • Ariff, N. M., Jemain, A. A., Ibrahim, K., & Zin, W. Z. W. (2012). IDF relationships using bivariate copula for storm events in peninsular Malaysia. Journal of Hydrology, 470, 158-171. doi: https://doi.org/10.1016/j.jhydrol.2012.08.045

  • ASEAN Food Security Information System. (2019). ASEAN Agricultural Commodity Outlook, No. 22, June 2019. Retrieved July 11, 2020, from http://www.aptfsis.org/uploads/normal/ ACO%20Report%2022/ACO%20Report22.pdf

  • Bandumula, N. (2017). Rice production in Asia: Key to global food security. In Proceedings of the Natural Academy of Sciences, India, Section B: Biological Sciences, 88(4), 1323-1328. doi: https://doi.org/10.1007/s40011-017-0867-7

  • Cherubini, U., & Luciano, E. (2002). Bivariate option pricing with copulas. Applied Mathematical Finance, 9(2), 69-86.

  • Clayton, D. G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65(1), 141-151. doi: https://doi.org/10.1093/biomet/65.1.141

  • Cook, R. D., & Johnson, M. E. (1981). A family of distributions for modeling nonelliptically symmetric multivariate data. Journal of the Royal Statistical Society: Series B, 4(2)3, 210-218.­ doi: https://doi.org/10.1111/j.2517-6161.1981.tb01173.x

  • Food and Agriculture Organization of the United Nations. (2019). Macroeconomic statistics: Global trends in GDP, agriculture value added, and food-processing value added (1970-2017). Retrieved June 28, 2020, from http://www.fao.org/economic/ess/ess-economic/ gdpagriculture/en/

  • Fouque, J. P., & Zhou, X. (2008). Perturbed gaussian copula. In J. P. Fouque, T. B. Fomby & K. Solna (Eds.), Econometrics and risk management (pp. 103-121). Bingley, England: Emerald Group Publishing Limited. doi: https://doi.org/10.1016/S0731-9053(08)22005-0

  • Gumbel, E. J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 55(292), 698-707.

  • Hsiang, S., Kopp, R., Jina, A., Rising, J., Delgado, M., Mohan, S., … & Oppenheimer, M. (2017). Estimating economic damage from climate change in the United States. Science, 356(6345), 1362-1369. doi: 10.1126/science.aal4369

  • IPCC. (2019). Summary for policymakers. In Global Warming of 1.5°C. An IPCC Special Report on the impacts of global warming of 1.5°C above pre-industrial levels and related global greenhouse gas emission pathways, in the context of strengthening the global response to the threat of climate change, sustainable development, and efforts to eradicate poverty. Intergovernmental Panel on Climate Change (IPCC), Geneva, Switzerland. Retrieved June 28, 2020, from https://www.ipcc.ch/site/assets/uploads/sites/2/2019/06/ SR15_Full_Report _High_Res.pdf

  • Joe, H. (1997). Multivariate models and dependence concepts. London, UK: Chapman and Hall.

  • Khazanah Research Institute. (2019). The status of the paddy and rice industry in Malaysia. Retrieved July 11, 2020, from http://www.krinstitute.org/assets/contentMS/img/template/ editor/20190409_RiceReport_Full%20Report_Final.pdf

  • Luo, X., & Shevchenko, P. V. (2012). Bayesian model choice of grouped t-copula. Methodology and Computing in Applied Probability, 14(4), 1097-1119. doi: https://doi.org/10.1007/s11009-011-9220-4

  • Muhammad, M., & Abdullah, M. H. H. (2013). Modelling and forecasting on paddy production in Kelantan under the implementation of system of rice intensification (SRI). Academic Journal of Agricultural Research, 1(7), 106-113. doi: http://dx.doi.org/10.15413/ajar.2013.0112

  • Moore, M. (2020). Rice paddy production in the Asia Pacific region in 2018, by country. Retrieved July 11, 2020, from https://www.statista.com/statistics/681740/asia-pacific-rice-paddy-production-by-country/#statisticContainer

  • Mutert, E., & Fairhurst, T. H. (2002). Developments in rice production in Southeast Asia. Better Crops International, 15(Suppl), 12-17.

  • Nyang’au, W., Mati, B., Kalamwa, K., Wanjogu, R., & Kiplagat, L. (2014). Estimating rice yield under changing weather conditions in Kenya using CERES rice model. International Journal of Agronomy, 2014, 1-12. doi: https://doi.org/10.1155/2014/849496

  • Oakes, D. (1982). A model for association in bivariate survival data. Journal of the Royal Statistical Society: Series B, 44(3), 414-422. doi: https://doi.org/10.1111/j.2517-6161.1982.tb01222.x

  • OECD. (2018). Joint working party on agriculture and trade. ASEAN rice market integration: Findings from a feasible study. Organisation for Economic Co-operation and Development. Retrieved July 11, 2020, from http://www.oecd.org/officialdocuments/publicdisplay documentpdf/? cote=TAD/TC/CA/WP(2018)7/FINAL&docLanguage=En

  • OECD. (2020). OECD-FAO agricultural outlook 2019 – 2028: OECD-FAO agricultural outlook 1990-2028, by country. Retrieved July 7, 2020, from https://stats.oecd.org/

  • Okhrin, O., Ristig, A., & Xu, X. F. (2017). Copulae in high dimensions: An introduction. In W. Härdle, C. H. Chen & L. Overbeck (Eds.), Applied quantitative finance, statistics and computing. Heidelberg, Germany: Springer. doi: https://doi.org/10.1007/978-3-662-54486-0_13

  • Putri, R. E., Yahya, A., Adam, N. M., & Aziz, S. A. (2019). Rice yield prediction model with respect to crop healthiness and soil fertility. Food Research, 3(2), 174-180. doi: http://doi.org/10.26656/fr.2017.3(2).117

  • Simard, C., & Rémillard, B. (2015). Forecasting time series with multivariate copulas. Dependence Modeling, 3, 59-82.

  • Singh, B., & Singh, V. K. (2017). Fertilizer management in rice. In B. Chauhan, K. Jabran & G. Mahajan (Eds.), Rice production worldwide (pp. 217-253). Cham, Switzerland: Springer. doi: https://doi.org/10.1007/978-3-319-47516-5_10

  • Sørensen, M. (2011). Estimating functions for diffusion-type processes. In M. Kessler, A. Lindner & M. Sørensen (Eds.), Statistical methods for stochastic differential equations. London, UK: Chapman & Hall.

  • United Nations. (2019). World Population Prospects 2019: Highlights. Department of Economic and Social Affairs, Population Division. Retrieved June 28, 2020, from https://population.un.org/wpp/Publications/Files/WPP2019_Highlights.pdf

  • USDA. (2015). Southeast Asia: 2015/16 rice production outlook at record levels. Commodity Intelligence Report. United State Department of Agriculture.

  • Xie, K., Li, Y., & Li, W. (2012). Modelling wind speed dependence in system reliability assessment using copulas. IET Renewable Power Generation, 6(6), 392-399.

  • Zhang, L., & Singh, V. P. (2007). Bivariate rainfall frequency distributions using Archimedean copulas. Journal of Hydrology, 332, 93-109. doi: https://doi.org/10.1016/j.jhydrol.2006.06.033

  • Zhang, L., & Singh, V. P. (2012). Bivariate rainfall and runoff analysis using entropy and copula theories. Entropy, 14, 1784-1812. doi: https://doi.org/10.3390/e14091784

  • Zhang, L., Yang, B., Guo, A., Huang, D., & Huo, Z. (2018). Multivariate probabilistic estimates of heat stress for rice across China. Stochastic Environmental Research and Risk Assessment, 32, 3137-3150. doi: https://doi.org/10.1007/s00477-018-1572-7

ISSN 0128-7680

e-ISSN 2231-8526

Article ID

JST-2206-2020

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