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

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Computational Intelligence Techniques in Earth and Environmental Sciences

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.

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References

  • 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):53–71

    Google Scholar 

  • Akaike H (1969) Fitting autoregressive models for prediction. Ann Inst Stat Math 21:243–247

    Article  Google Scholar 

  • Akaike H (1974) A new look at the statistical model identification. IEEE Trans Automat Contr 19:716–723

    Article  Google Scholar 

  • Altaf MZ, Arshad IA, Ilys MR (2012) Vector autoregression application on macroeconomic variables of Pakistan’s economic growth. Sindh Univ Res J 44(2):267–272

    Google Scholar 

  • 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):1–24

    Google Scholar 

  • Canova F (1995) VAR models: specification, estimation, inference and forecasting. In: Pesaran H, Wickens M (eds) Handbook of applied econometrics. Blackwell, Oxford, England

    Google Scholar 

  • Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74:427–431

    Google Scholar 

  • Durban M, Glasbey CA (2001) Weather modelling using a multivariate latent Gaussian model. Agr Forest Meteorol 109:187–201

    Article  Google Scholar 

  • Durbin J, Watson GS (1951) Testing for serial correlation in least squares regression. Biometrika 38:159–171

    Article  CAS  Google Scholar 

  • 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):147–150

    Google Scholar 

  • Granger CWJ (1969) Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37:424–438

    Article  Google Scholar 

  • Gujarati DN (1993) Basic econometrics, 3rd edn. McGraw-Hill, New York

    Google Scholar 

  • Hamilton DJ (1994) Time series analysis. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Hannan EJ, Quinn BG (1979) The determination of the order of an autoregression. J R Stat Soc B 41:190–195

    Google Scholar 

  • Hatanaka M (1996) Time series based econometrics: unit roots and co-integration. Oxford University Press, Oxford

    Book  Google Scholar 

  • 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, London

    Google Scholar 

  • Janjua PZ, Samad G, Khan NU (2010) Impact of climate change on wheat production: a case study of Pakistan. Pak Dev Rev 49(4):799–821

    Google Scholar 

  • Johansen S (1995) Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, Oxford

    Book  Google Scholar 

  • Khan MZS, Hossain MI (2010) Democracy and trade balance: a vector autoregressive analysis. Bangladesh Dev Stud 33(4):23–37

    Google Scholar 

  • Kleiber W, Katz RW, Rajagopalan B (2013) Daily minimum and maximum temperature simulation over complex terrain. Ann Appl Stat 7(1):588–612

    Article  Google Scholar 

  • Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationary against the alternative of a unit root. J Econom 54:159–178

    Article  Google Scholar 

  • Litterman RB (1986) Forecasting with Bayesian vector autoregression: five years of experience. J Bus Econ Stat 4:25–38

    Google Scholar 

  • Liu P, Theodoridis K (2012) DSGE model restrictions for structural VAR identification. Int J Cent Bank 8(4):61–95

    Google Scholar 

  • 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):405–419

    Article  Google Scholar 

  • Lütkepohl H (1991) Introduction to multiple time series analysis. Springer, Berlin

    Book  Google Scholar 

  • Lütkepohl H (2005) New introduction to multiple time series analysis. Springer, Berlin

    Book  Google Scholar 

  • Lütkepohl H, Krätzig M (2004) Applied time series econometrics. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Moneta A, Chlab N, Entner D, Hoyer P (2011) Causal search in structural vector autoregressive models. Workshop Conf Proc 12:95–118

    Google Scholar 

  • Mosedale TJ, Stephenson DB, Collins M, Mills TC (2006) Granger causality of coupled climate processes: ocean feedback on the North Atlantic oscillation. J Clim 19:1182–1194

    Article  Google Scholar 

  • Ni S, Sun D (2005) Bayesian estimates for vector autoregressive models. J Bus Econ Stat 23(1):105–117

    Article  Google Scholar 

  • Pankratz A (1991) Forecasting with dynamic regression models. Wiley, New York

    Book  Google Scholar 

  • Phillips PCB, Perron P (1988) Testing for a unit root in time series regression. Biometrika 75:335–346

    Article  Google Scholar 

  • Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464

    Article  Google Scholar 

  • 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, Singapore

    Google Scholar 

  • Sims CA (1972) Money, income and causality. Am Econ Rev 62:540–552

    Google Scholar 

  • Sims CA (1980) Macroeconomics and reality. Econometrica 48(1):1–48

    Article  Google Scholar 

  • 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):55–95

    Article  Google Scholar 

  • Stevens J (1996) Applied multivariate statistics for the social sciences. Lawrence Erlbaum, Mahwah, NJ

    Google Scholar 

  • Sun D, Ni S (2004) Bayesian analysis of vector-autoregressive models with non-informative priors. J Stat Plan Inference 121:291–309

    Article  Google Scholar 

  • 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

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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.

Author information

Authors and Affiliations

  1. Department of Statistics, University of Rajshahi, Rajshahi, 6205, Bangladesh

    Md. Abu Shahin & Md. Ayub Ali

  2. School of Engineering and Technology, Central Queensland University, North Rockhampton, QLD, 4702, Australia

    A. B. M. Shawkat Ali

Authors
  1. Md. Abu Shahin
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  2. Md. Ayub Ali
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  3. A. B. M. Shawkat Ali
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Corresponding author

Correspondence to Md. Abu Shahin .

Editor information

Editors and Affiliations

  1. Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, CO, USA, NOAA/NESDIS Center for Satellite Applications and Research, College Park, MD, USA, Fort Collins, CO, USA

    Tanvir Islam

  2. NASA Goddard Space Flight Center, Greenbelt & ESSIC, University of Maryland College Park, MD, USA, Greenbelt, Maryland, USA

    Prashant K. Srivastava

  3. Department of Civil Engineering, IIT Delhi, Delhi, India

    Manika Gupta

  4. School of Geog. and Env. Sciences, Monash University, Melbourne, Australia

    Xuan Zhu

  5. School of Environmental Sciences Remote Sensing, Jawaharlal Nehru University, New Delhi, India

    Saumitra Mukherjee

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Shahin, M.A., Ali, M.A., Ali, A.B.M.S. (2014). Vector Autoregression (VAR) Modeling and Forecasting of Temperature, Humidity, and Cloud Coverage. In: Islam, T., Srivastava, P., Gupta, M., Zhu, X., Mukherjee, S. (eds) Computational Intelligence Techniques in Earth and Environmental Sciences. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8642-3_2

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