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Vector Autoregression (VAR) Modeling and Forecasting of Temperature, Humidity, and Cloud Coverage

  • Md. Abu ShahinEmail author
  • Md. Ayub Ali
  • A. B. M. Shawkat Ali
Chapter
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Abstract

Climate change is a global phenomenon but its implications are distinctively local. The climatic variables include temperature, rainfall, humidity, wind speed, cloud coverage, and bright sunshine. The study of behavior of the climatic variables is very important for understanding the future changes among the climatic variables and implementing important policies. The problem is how to study the past, present, and future behaviors of the climatic variables. The purpose of the present study was to develop an appropriate vector autoregression (VAR) model for forecasting monthly temperature, humidity, and cloud coverage of Rajshahi district in Bangladesh. The test for stationarity of the time series variables has been confirmed with augmented Dickey–Fuller, Phillips–Perron, and Kwiatkowski–Phillips–Schmidt–Shin tests. The endogenity among the variables was examined by F-statistic proposed by C.W.J. Granger. The order of the VAR model was selected using Akaike information criterion, Schwarz information criteria, Hannan–Quinn information criteria, final prediction error, and likelihood ratio test. The ordinary least square method was used to estimate the parameters of the model. The VAR(8) model was found to be the best. Structural analyses were performed using forecast error variance decomposition and impulse response function. These structural analyses divulged that the temperature, humidity, and cloud coverage would be interrelated and endogenous in future. Finally, temperature, humidity, and cloud coverage were forecasted from January 2011 to December 2016 using the best selected model VAR(8). The forecasted values showed an upward trend in temperature and humidity and downward trend in cloud coverage. Therefore, we must show our friendly behavior to the environment to control such trends.

Keywords

Forecast error variance (FEV) decomposition Granger causality test Impulse response function (IRF) Unit root Vector autoregression (VAR) 
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Notes

Acknowledgments

We would like to express our gratitude to Professor Dr. Mohammed Nasser, Chairman, Department of Statistics, University of Rajshahi, Bangladesh, for giving us the opportunity to present this paper in the International Conference and Publish in Conference Proceedings. Very special thanks go to Dr. Tanvir Islam, Department of Civil Engineering, University of Bristol, and his honorable team for publishing this manuscript with a revised version again as a book chapter of Springer Publication.

References

  1. Adenomon MO, Ojehomon VET, Oyejola BA (2013) Modelling the dynamic relationship between rainfall and temperature time series data in Niger State, Nigeria. Math Theory Model 3(4):53–71Google Scholar
  2. Akaike H (1969) Fitting autoregressive models for prediction. Ann Inst Stat Math 21:243–247CrossRefGoogle Scholar
  3. Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19:716–723CrossRefGoogle Scholar
  4. Altaf MZ, Arshad IA, Ilys MR (2012) Vector autoregression application on macroeconomic variables of Pakistan’s economic growth. Sindh Univ Res J 44(2):267–272Google Scholar
  5. Awokuse OT, Bessler DA (2003) Vector autoregressions, policy analysis and directed acyclic graphs: an application to the U.S. economy. J Appl Econ 6(1):1–24Google Scholar
  6. Canova F (1995) VAR models: specification, estimation, inference and forecasting. In: Pesaran H, Wickens M (eds) Handbook of applied econometrics. Blackwell, Oxford, EnglandGoogle Scholar
  7. Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74:427–431Google Scholar
  8. Durban M, Glasbey CA (2001) Weather modelling using a multivariate latent Gaussian model. Agr Forest Meteorol 109:187–201CrossRefGoogle Scholar
  9. Durbin J, Watson GS (1951) Testing for serial correlation in least squares regression. Biometrika 38:159–171CrossRefGoogle Scholar
  10. Ferdous MG, Baten MA (2011) Climatic variables of 50 years and their trends over Rajshahi and Rampur division. J Environ Sci Nat Resour 4(2):147–150Google Scholar
  11. Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:424–438CrossRefGoogle Scholar
  12. Gujarati DN (1993) Basic econometrics, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  13. Hamilton DJ (1994) Time series analysis. Princeton University Press, Princeton, NJGoogle Scholar
  14. Hannan EJ, Quinn BG (1979) The determination of the order of an autoregression. J R Stat Soc B 41:190–195Google Scholar
  15. Hatanaka M (1996) Time series based econometrics: unit roots and co-integration. Oxford University Press, OxfordCrossRefGoogle Scholar
  16. Ivanov V, Kilian L (2001) A practitioner’s guide to lag-order selection for vector autoregressions. CEPR discussion paper no. 2685. Centre for Economic Policy Research, LondonGoogle Scholar
  17. Janjua PZ, Samad G, Khan NU (2010) Impact of climate change on wheat production: a case study of Pakistan. Pak Dev Rev 49(4):799–821Google Scholar
  18. Johansen S (1995) Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, OxfordCrossRefGoogle Scholar
  19. Khan MZS, Hossain MI (2010) Democracy and trade balance: a vector autoregressive analysis. Bangladesh Dev Stud 33(4):23–37Google Scholar
  20. Kleiber W, Katz RW, Rajagopalan B (2013) Daily minimum and maximum temperature simulation over complex terrain. Ann Appl Stat 7(1):588–612CrossRefGoogle Scholar
  21. Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationary against the alternative of a unit root. J Econom 54:159–178CrossRefGoogle Scholar
  22. Litterman RB (1986) Forecasting with Bayesian vector autoregression: five years of experience. J Bus Econ Stat 4:25–38Google Scholar
  23. Liu P, Theodoridis K (2012) DSGE model restrictions for structural VAR identification. Int J Cent Bank 8(4):61–95Google Scholar
  24. Liu X, Lindquist E, Vedlitz A (2011) Explaining media and congressional attention to global climate change, 1969–2005: an empirical test of agenda-setting theory. Polit Res Q 64(2):405–419CrossRefGoogle Scholar
  25. Lütkepohl H (1991) Introduction to multiple time series analysis. Springer, BerlinCrossRefGoogle Scholar
  26. Lütkepohl H (2005) New introduction to multiple time series analysis. Springer, BerlinCrossRefGoogle Scholar
  27. Lütkepohl H, Krätzig M (2004) Applied time series econometrics. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  28. Moneta A, Chlab N, Entner D, Hoyer P (2011) Causal search in structural vector autoregressive models. Workshop Conf Proc 12:95–118Google Scholar
  29. Mosedale TJ, Stephenson DB, Collins M, Mills TC (2006) Granger causality of coupled climate processes: ocean feedback on the North Atlantic oscillation. J Clim 19:1182–1194CrossRefGoogle Scholar
  30. Ni S, Sun D (2005) Bayesian estimates for vector autoregressive models. J Bus Econ Stat 23(1):105–117CrossRefGoogle Scholar
  31. Pankratz A (1991) Forecasting with dynamic regression models. Wiley, New YorkCrossRefGoogle Scholar
  32. Phillips PCB, Perron P (1988) Testing for a unit root in time series regression. Biometrika 75:335–346CrossRefGoogle Scholar
  33. Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464CrossRefGoogle Scholar
  34. Shamsnia SA, Shahidi N, Liaghat A, Sarraf A, Vahdat SF (2011) Modeling of weather parameters using stochastic methods (ARIMA model) (case study: Abadeh region, Iran). International conference on environment and industrial innovation IPCBEE. IACSIT Press, SingaporeGoogle Scholar
  35. Sims CA (1972) Money, income and causality. Am Econ Rev 62:540–552Google Scholar
  36. Sims CA (1980) Macroeconomics and reality. Econometrica 48(1):1–48CrossRefGoogle Scholar
  37. Stergiou KI, Christou ED, Petrakis G (1997) Modelling and forecasting monthly fisheries catches: comparison of regression, univariate and multivariate time series methods. Fish Res 29(1):55–95CrossRefGoogle Scholar
  38. Stevens J (1996) Applied multivariate statistics for the social sciences. Lawrence Erlbaum, Mahwah, NJGoogle Scholar
  39. Sun D, Ni S (2004) Bayesian analysis of vector-autoregressive models with non-informative priors. J Stat Plan Inference 121:291–309CrossRefGoogle Scholar
  40. Wang W, Niu Z (2009) VAR model of PM2.5, weather and traffic in Los Angeles-long beach area. International conference on environmental science and information application technology, 4–5 July 2009, Wuhan, 3:66–69, ISBN: 978-0-7695-3682-8. DOI:  10.1109/ESIAT.2009.226

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Md. Abu Shahin
    • 1
    Email author
  • Md. Ayub Ali
    • 1
  • A. B. M. Shawkat Ali
    • 2
  1. 1.Department of StatisticsUniversity of RajshahiRajshahiBangladesh
  2. 2.School of Engineering and TechnologyCentral Queensland UniversityNorth RockhamptonAustralia

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