The paper aims at demonstrating the application of the Akaike information criterion to determine the order of two state Markov chain for studying the pattern of occurrence of wet and dry days during the rainy season (April to September) in North-East India. For each station, each day is classified as dry day if the amount of rainfall is less than 3 mm and wet day if the amount of rainfall is greater than or equal to 3 mm. We apply Markov chain of order up to three to the sequences of wet and dry days observed at seven distantly located stations in North East region of India. The Markov chain model of appropriate order for analyzing wet and dry days is determined. This is done using the Akaike Information Criterion (AIC) by checking the minimum of AIC estimate. Markov chain of order one is found to be superior to the majority of the stations in comparison to the other order Markov chains. More precisely, first order Markov chain model is an adequate model for the stations North Bank, Tocklai, Silcoorie, Mohanbari and Guwahati. Further, it is observed that second order and third order Markov chains are competing with first order in the stations Cherrapunji and Imphal, respectively. A fore-knowledge of rainfall pattern is of immense help not only to farmers, but also to the authorities concerned with planning of irrigation schemes. The outcomes are useful for taking decisions well in advance for transplanting of rice as well as for other input management and farm activities during different stages of the crop growing season.
Akaike Information Criterion, Markov chain, North East India, Rainfall
Akaike, H. (1976). Canonical Correlation Analysis of time Series and the use of an Information Criterion, Systems Identification: Advances and Case Studies, Ed. R. K. Mehra & D. G. Lainiotie, New York Academic Press, USA, 27-96.
ASDMR (2015)). Assam State Disaster Management Authority report (ASDMR) in collaboration with North Eastern Application Centre. Flood early warning system, http://www.asdma.gov.in /pdf/publication FLEWS.pdf
Basak, P. (2014). On the Markov chain models for monsoonal rainfall occurrence in different zones of West Bengal, Indian Journal of Radio & Space Physics, 43:349-354.
Bhargava, P. N., Narain, P., Aneja, K. G. and Asha, P. (1972). A study of the occurrence of rainfall in Raipur District with the help of Markov chain model, Journal of Indian Society of Agricultural statistics, 24:197-204.
Deka, S, Borah, M. and Kakaty, S. C. (2011). Statistical analysis of annual maximum rainfall in North-East India: an application of LH-moments, Theoretical and Applied Climatology, 104, 111-122.
Deka, R. L. (2013). Climate change in the Brahmaputra valley and impact on rice and tea productivity, Ph.D thesis submitted to Indian Institute of Technology Guwahati, http://gyan.iitg.ernet.in/handle/123456789/416.
Dash, P. R. (2012). A Markov chain modelling of daily precipitation occurrences of Odisha, Int. Jour. Adv. Comp. Math. Sci., 3:482-486.
Fisher, F.A. (1925). The influence of rainfall on the yield of wheat at Rothamsted, Phil. Trans. Roy. Soc., London, B, 213:89-142.
Gabriel, K. R. and Neumann, J. (1962). A Markov chain model for daily occurrence at Tel Aviv, Quart. J. R. met. Soc. 88:90-95.
Gabriel, K. R. and Neumann J. (1972). On a distribution of weather cycles by length, Quart. J. R. Met. Soc. 83:375-380.
Gates, P. and Tong, H. (1976). On Markov chain modeling to some weather data, J. App. Meteorol. 15:1145-1151.
Ghosh, K., Singh, A., Mohanty, U. C., Acharya, N., Pal, R. K., Singh, K. K. and Pasupalak, S. (2015). Development of a rice yield prediction system over Bhubaneswar, India: combination of extended range forecast and CERES-rice model, Meteorol. Appl., 22:525–533.
Good I. J. (1953). The serial test for sampling numbers and other tests for randomness, Proc. Camb. Phil. Soc. 49:276-284.
Gore, P.G. and Thapliyal, V. (2000). Occurrence of dry and wet weeks over Maharastra, Mausam, 51:24-38
Katz, R. W. (1981). On some criteria for estimating the order of a Markov chain, Technometrics, 23:243-249
Kitagawa, G. (1979). On the use of AIC for the detection of outliers, Technometrics, 21:193-199
Medhi, J. (1976). A Markov chain for the occurrence of wet and dry days, Ind. J. Met. Hydro.& Geophys. 27:431-435
Medhi, J. (1999). Stochastic Processes, 2nd edition, New Age International Publishers, New Delhi.
Otomo, T. Nakagawa, T. and Akaike, H. (1972). Statistical approach to computer control of cement rotary kiln, Automatica, 8:35-48.
Otsu, K., Horigome, M. and Kitagawa, G. (1976). On the prediction and stochastic control of ship's motion, Proc. 2nd. IFAC/IFIP Sympos., Ed. M. Pitkin, J. J. Roche & T. J. Williams, Washington, DC, USA, 69-76.
Prabhu, A., Oh. J., Kim, I, Kripalani, R. H., Mitra, A. K. and Pandithurai, G. (2016). Summer monsoon rainfall variability over North East regions of India and its association with Eurasian snow, Atlantic Sea Surface temperature and Arctic Oscillation, Climate Dynamics, DOI 10.1007/s00382-016-3445-4
Raheem, M. A., Yahya, W. B. and Obisesan, K. O. (2015). A Markov chain approach on pattern of rainfall distribution, Journal of Environmental Statistics, 7:1-13.
Sakamoto, Y. and Akaike, H. (1978). Analysis of cross classified data by AIC, Ann. Inst. Statist. Math., B 30:85-197.
Salas, J. P., Delluer, J. W., Yevjevich, V. and Lane, W. L. (1980). Applied Modelling of Hydrologie Time Series, Water Resources Publication, Fort Collins, Colorado, USA.
Singh, B., Arya, C. K., Singh, J. and Mourya, K. K. (2014). Analysis of rainfall data for storage and irrigation planning in humid south-eastern plain of Rajasthan in India, Journal of Applied and Natural Sciences, 6:14-219.
Snipes, M. and Taylor, D. C. (2014). Model selection and Akaike Information Criteria: An example from wine ratings and prices, Wine Economics and Policy, 3:3-9.
Sørup, H. J. D., Madsen, H. and Nielsen, K. A. (2011). Markov chain modeling of precipitation time series: Modeling waiting times between tipping bucket rain gauge tips, paper presented at 12th International Conference on Urban Drainage, Porto Alegre/Brazil, 11-16.
Tong, H. (1975). Determination of the order of a Markov chain by Akaike's Information Criterion, Journal of Applied Probability 12:488-497.
Zhao, L. C., Dorea, C. and Goncalves, C. R. (2001). On determination of the order of a Markov chain, Statist. Inferen. Stoch. Proc. 4:273-282.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
This work is licensed under Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) © Author (s)