Time series has fundamental importance in various practical domains in the world, more so in modeling and forecasting. Many important models have been proposed to improve the accuracy of their prediction. Global warming has been a big challenge to the world in affecting economic and Agricultural activities. It causes drastic weather changes, which are characterized by precipitation and temperature. Rainfall prediction is one of the most important and challenging tasks in today’s world. The objective of this study was to conducted a diagnostic analyzes of weather variables which were used to model the rainfall patterns by use of Bayesian Vector Autoregressive (BVAR). The diagnostic analyzes was done after the normalization of the data. The data was found to be stable after first differencing and it was tested using Augmented Dicker Fuller (ADF) and Phillips-Perron (PP) test. The tests were found to have the P-values that were statistically significant. The Granger Causality test was also conducted and found to be statistically significant. The Ljung-Box test of residuals, shows that the graphs of these residuals produced, appeared to explain all the available information in the forecasted model. The mean of the residuals was near to zero and therefore no significant correlation was witnessed. The time plot shows that the variation of the residuals remains much the same across the historical data, apart from the two values that were beyond 0.2 or -0.2 in Zone Two, and therefore the residual variance was treated as constant. The histogram shows that the residuals were normally distributed, which represented gaussian behavior. The ACF graph, shows that the spikes were within the required limits, so the conclusion was that the residuals had no autocorrelation of the residuals. The Ljung-Box test shows that the developed model was good for forecasting. Finally, the researcher recommends application of other techniques like Random Forest and Bootstrapping technique to check whether the accuracy may further be improved from other models.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 10, Issue 6) |
| DOI | 10.11648/j.ajtas.20211006.14 |
| Page(s) | 249-256 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Global Warming, Bayesian, Diagnostic Analyzes, Vector Autoregressive
| [1] | Mary Kilavi, Dave M, Maurine A and Joanne R. (2018). Extreme Rainfall and Flooding over Central Kenya Including Nairobi City during the Long-Rains Season. |
| [2] | Otiende P, & Brian M. (2009). The economic impacts of climate change in Kenya: Riparian flood impacts and cost of adaptation. |
| [3] | Linacre, E and Geerts, B. (2016). Climates and Weather Explained Routledge London, pp. 321 – 345. |
| [4] | Lutgens, F. K. and TarBuck, E. J. (2016). The Atmosphere: An Introduction to Meteorology, Fourth edition. Prentice Hall, New Jersey, pp. 299 – 331. |
| [5] | Bauer P., A. Thopre and G. Brunet, 2015: The quiet revolution of numerical weather prediction. Nature, 525: 47–55. |
| [6] | Stockdale, T. N., D. L. T. Anderson, J. O. S. Alves, and M. A. Balmaseda, 2010: Global seasonal rainfall forecasts using a coupled ocean-atmosphere model. Nature, 392: 371–373. |
| [7] | Blunden, J., D. S. Arndt, and G. Hartfield (eds.), 2018: State of the Climate in 2017. Bull. Amer. Meteor. Soc., 99: 8, Si–S310, doi: 10.1175/2018BAMSStateoftheClimate.1. |
| [8] | Ji, M., A. Kumar and A. Leetmaa (2018): A multiseason climate forecast system at the National Meteorological Center. Bull. Amer. Meteo. Soc., 75: 569–577. |
| [9] | Coumou, D. and S. Rahmstorf, 2012: A decade of weather extremes. Nature Climate Change, 2: 491–49. |
| [10] | Giannone D, Lenza M, Primiceri GE (2015). “Prior Selection for Vector Autoregressions.” Review of Economics and Statistics, 97 (2), 436–451. |
| [11] | Verbeek, Marno. (2008) A guide to modern econometrics. 3rd ed. Chichester, England ; Hoboken, NJ: John Wiley & Sons. |
| [12] | Stock, J. H., & Watson, M. W. (2015). Generalized shrinkage methods for forecasting using many predictors. Journal of Business & Economic Statistics, 30 (4), 481-493. |
| [13] | Asteriou, Dimitrios, och Stephen G. Hall. Applied Econometrics: A Modern Approach Using EViews and Microfit. Rev. ed. Basingstoke: Palgrave Macmillan, 2021. |
| [14] | Ratsimalahelo, Z. (2017) Generalised Wald Type Test of Nonlinear Restrictions. Open Access Library Journal, 4, 1-8. doi: 10.4236/oalib.1103923. |
| [15] | Subba Rao and J. Yang. Reconciling the Gaussian and Whittle likelihood with an application to estimation in the frequency domain. arXiv preprint arXiv: 2001.06966, 2020. |
| [16] | Sumitra Iyer, Alka Mahajan. “Predicting total electron content in ionosphere using vector autoregression model during geomagnetic storm”, Journal of Applied Geodesy, 2021. |
| [17] | Korobilis, D and Pettenuzzo, D (2016) Adaptive Minnesota Prior for High= D imensional Vector Autoregressions. Working paper Essex Finance Centre working paper, Colchest. |
| [18] | Lütkepohl, H. (2005). New introduction to multiple time series analysis. Springer Science & Business Media. |
| [19] | Chan, Joshua C. C and Chan, Joshua. C. Large Bayesian Vector Autoregressions (February 14, 2019) CAMA working paper No 19/2019, Available at SSRN. |
APA Style
Gitonga Harun Mwangi, Joseph Koske, Mathew Kosgei. (2021). Diagnostic Analysis of Weather Variables for Forecasting Rainfall Patterns in Kenya Using Bayesian Vector Autoregressive Model. American Journal of Theoretical and Applied Statistics, 10(6), 249-256. https://doi.org/10.11648/j.ajtas.20211006.14
ACS Style
Gitonga Harun Mwangi; Joseph Koske; Mathew Kosgei. Diagnostic Analysis of Weather Variables for Forecasting Rainfall Patterns in Kenya Using Bayesian Vector Autoregressive Model. Am. J. Theor. Appl. Stat. 2021, 10(6), 249-256. doi: 10.11648/j.ajtas.20211006.14
AMA Style
Gitonga Harun Mwangi, Joseph Koske, Mathew Kosgei. Diagnostic Analysis of Weather Variables for Forecasting Rainfall Patterns in Kenya Using Bayesian Vector Autoregressive Model. Am J Theor Appl Stat. 2021;10(6):249-256. doi: 10.11648/j.ajtas.20211006.14
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajtas.20211006.14,
author = {Gitonga Harun Mwangi and Joseph Koske and Mathew Kosgei},
title = {Diagnostic Analysis of Weather Variables for Forecasting Rainfall Patterns in Kenya Using Bayesian Vector Autoregressive Model},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {10},
number = {6},
pages = {249-256},
doi = {10.11648/j.ajtas.20211006.14},
url = {https://doi.org/10.11648/j.ajtas.20211006.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20211006.14},
abstract = {Time series has fundamental importance in various practical domains in the world, more so in modeling and forecasting. Many important models have been proposed to improve the accuracy of their prediction. Global warming has been a big challenge to the world in affecting economic and Agricultural activities. It causes drastic weather changes, which are characterized by precipitation and temperature. Rainfall prediction is one of the most important and challenging tasks in today’s world. The objective of this study was to conducted a diagnostic analyzes of weather variables which were used to model the rainfall patterns by use of Bayesian Vector Autoregressive (BVAR). The diagnostic analyzes was done after the normalization of the data. The data was found to be stable after first differencing and it was tested using Augmented Dicker Fuller (ADF) and Phillips-Perron (PP) test. The tests were found to have the P-values that were statistically significant. The Granger Causality test was also conducted and found to be statistically significant. The Ljung-Box test of residuals, shows that the graphs of these residuals produced, appeared to explain all the available information in the forecasted model. The mean of the residuals was near to zero and therefore no significant correlation was witnessed. The time plot shows that the variation of the residuals remains much the same across the historical data, apart from the two values that were beyond 0.2 or -0.2 in Zone Two, and therefore the residual variance was treated as constant. The histogram shows that the residuals were normally distributed, which represented gaussian behavior. The ACF graph, shows that the spikes were within the required limits, so the conclusion was that the residuals had no autocorrelation of the residuals. The Ljung-Box test shows that the developed model was good for forecasting. Finally, the researcher recommends application of other techniques like Random Forest and Bootstrapping technique to check whether the accuracy may further be improved from other models.},
year = {2021}
}
TY - JOUR T1 - Diagnostic Analysis of Weather Variables for Forecasting Rainfall Patterns in Kenya Using Bayesian Vector Autoregressive Model AU - Gitonga Harun Mwangi AU - Joseph Koske AU - Mathew Kosgei Y1 - 2021/12/09 PY - 2021 N1 - https://doi.org/10.11648/j.ajtas.20211006.14 DO - 10.11648/j.ajtas.20211006.14 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 249 EP - 256 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20211006.14 AB - Time series has fundamental importance in various practical domains in the world, more so in modeling and forecasting. Many important models have been proposed to improve the accuracy of their prediction. Global warming has been a big challenge to the world in affecting economic and Agricultural activities. It causes drastic weather changes, which are characterized by precipitation and temperature. Rainfall prediction is one of the most important and challenging tasks in today’s world. The objective of this study was to conducted a diagnostic analyzes of weather variables which were used to model the rainfall patterns by use of Bayesian Vector Autoregressive (BVAR). The diagnostic analyzes was done after the normalization of the data. The data was found to be stable after first differencing and it was tested using Augmented Dicker Fuller (ADF) and Phillips-Perron (PP) test. The tests were found to have the P-values that were statistically significant. The Granger Causality test was also conducted and found to be statistically significant. The Ljung-Box test of residuals, shows that the graphs of these residuals produced, appeared to explain all the available information in the forecasted model. The mean of the residuals was near to zero and therefore no significant correlation was witnessed. The time plot shows that the variation of the residuals remains much the same across the historical data, apart from the two values that were beyond 0.2 or -0.2 in Zone Two, and therefore the residual variance was treated as constant. The histogram shows that the residuals were normally distributed, which represented gaussian behavior. The ACF graph, shows that the spikes were within the required limits, so the conclusion was that the residuals had no autocorrelation of the residuals. The Ljung-Box test shows that the developed model was good for forecasting. Finally, the researcher recommends application of other techniques like Random Forest and Bootstrapping technique to check whether the accuracy may further be improved from other models. VL - 10 IS - 6 ER -
Email: