Markov Chain Modelling for Short-Term NDVI Time Series Forecasting
Abstract
In this paper, the NDVI time series forecasting model has been developed based on the use of discrete time, continuous state Markov chain of suitable order. The normalised difference vegetation index (NDVI) is an indicator that describes the amount of chlorophyll (the green mass) and shows the relative density and health of vegetation; therefore, it is an important variable for vegetation forecasting. A Markov chain is a stochastic process that consists of a state space. This stochastic process undergoes transitions from one state to another in the state space with some probabilities. A Markov chain forecast model is flexible in accommodating various forecast assumptions and structures. The present paper discusses the considerations and techniques in building a Markov chain forecast model at each step. Continuous state Markov chain model is analytically described. Finally, the application of the proposed Markov chain model is illustrated with reference to a set of NDVI time series data.
Keywords: |
Continuous state space; Markov chains; NDVI; short-term forecasting
|
Full Text: |
References
Y. Wang (Ed.), Remote Sensing of Coastal Environments (Remote Sensing Applications Series), CRC Press, 2009, p. 41. https://doi.org/10.1201/9781420094428
E. Sahebjalal and K. Dashtekian, “Analysis of land use-land covers changes using normalized difference vegetation index (NDVI) differencing and classification methods,” African Journal of Agricultural Research, vol. 8, no. 37, pp. 4614–4622, Sept. 2013. https://doi.org/10.5897/AJAR11.1825
A. Stepchenko and J. Chizhov, “Applying Markov Chains for NDVI Time Series Forecasting of Latvian Regions,” Information Technology and Management Science, vol. 8, no. 1, pp. 57–61, Dec. 2016. https://doi.org/10.1515/itms-2015-0009
D. R Anderson, D. J. Sweeney, T. A. Williams, J. D. Camm and J. J. Cochran, Quantitative Methods for Business, 13th ed. South-Western College Pub, 2015, p. 771.
Z. Peng, C. Bao, Y. Zhao, H. Yi, L. Xia, H. Shen and F. Chen, “Weighted Markov chains for forecasting and analysis in Incidence of infectious diseases in jiangsu Province, China,”, Journal of Biomedical Research, vol. 24, no. 3, pp. 207–214, May 2010. https://doi.org/10.1016/S1674-8301(10)60030-9
T. Liu, “Application of Markov Chains to Analyze and Predict the Time Series,” Modern Applied Science, vol. 4, no. 5, pp. 162–166, May 2010. https://doi.org/10.5539/mas.v4n5p162
University of Natural Resources and Life Sciences, Vienna. Data service platform for MODIS Vegetation Indices time series processing at BOKU, Vienna. [Online]. Available: http://ivfl-info.boku.ac.at/ [Accessed: Aug. 25, 2015].
F. Vuolo, M. Mattiuzzi, A. Klisch and C. Atzberger, “Data service platform for MODIS Vegetation Indices time series processing at BOKU Vienna: current status and future perspectives,” in Proc. SPIE 8538, Earth Resources and Environmental Remote Sensing/GIS Applications III, 85380A, 2012. https://doi.org/10.1117/12.974857
W. Watthayu, “Loopy Belief Propagation: Bayesian Networks for Multi- Criteria Decision Making (MCDM),” International Journal of Hybrid Information Technology, vol. 2, no. 2, Apr. 2009.
H. Kantz, D. Holstein, M. Ragwitz and N. K. Vitanov, “Markov chain model for turbulent wind speed data,” Physicsa A: Statistical Mechanics and its Applications, vol. 342, issue 1–2, pp. 315–321, Oct. 2004. https://doi.org/10.1016/S0378-4371(04)00488-1
V. Soloviev, V. Saptsin and D. Chabenko, “Markov Chains Application To The Financial-Economic Time Series Prediction,” Computer Modelling and New Technologies, vol. 14, no. 3, pp. 16–20, 2011.
B. Klikova and A. Raidl, “Reconstruction of Phase Space of Dynamical Systems Using Method of Time Delay,” WDS'11 Proceedings of Contributed Papers, Part III, pp. 83–87, 2011.
M. Templ, A. Kowarik and P. Filzmoser, “Iterative stepwise regression imputation using standard and robust methods,” Journal of Computational Statistics and Data Analysis, vol. 55, no. 10, pp. 2793– 2806, Oct. 2013. https://doi.org/10.1016/j.csda.2011.04.012
J. M. Saleh and B. S. Hoyle, “Improved Neural Network Performance Using Principal Component Analysis on Matlab,” International Journal of The Computer, the Internet and Management, vol. 16, no. 2, pp. 1–8, 2008.
P. Ng’andwe, J. Mwitwa and A. Muimba-Kankolongo, Forest Policy, Economics, and Markets in Zambia, Academic Press, 2015, pp. 6–7.
Refbacks
- There are currently no refbacks.
Copyright (c) 2016 Artūrs Stepčenko, Jurijs Čižovs
This work is licensed under a Creative Commons Attribution 4.0 International License.