Pure and Applied Geophysics

, Volume 176, Issue 1, pp 463–482 | Cite as

Unobservable Components Modelling of Monthly Average Maximum and Minimum Temperature Patterns in India 1981–2015

  • Narasimha Murthy Kaipa ViswanathEmail author
  • Saravana Ramachandran


The paper deals with modelling and forecasting the behaviour of monthly average maximum and minimum temperature patterns through unobservable components model (UCM) for the period, 1981–2015 in India. The monthly average spatial surface air temperature data was provided by India Meteorological Department (IMD), India using daily gridded temperature data with 395 stations spread over the country. The temperature series is modelled and analyzed separately because the time series plot indicates that the maximum temperature series has sharp peaks in almost all the years, whereas the minimum temperature series has no sharp peaks for all the years. The basic structure model with deterministic level, fixed slope and deterministic dummy seasonal and stochastic auto regressive component for cycle is selected for maximum and minimum temperatures from the parsimonious models of UCM based on Akaike’s Information Criteria, Bayesian Information Criteria and significant tests. The model parameters are obtained using method of maximum likelihood estimation, the suitability of the selected model are determined with residuals diagnostics. The forecast of monthly maximum and minimum temperature patterns in India for the 3 years has been presented. It is noticed that there is a 0.002 °C increase in monthly maximum temperature and 0.0019 °C increase in monthly minimum temperature over the years. Further the forecast results indicate that the average maximum temperature increases by 0.1 °C in the months of January and May and the average minimum temperature increases by 0.1 °C in the December for the years 2016, 2017 and 2018.


Temperature UCM model AIC normal Q–Q plot LJung–Box test statistic 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Narasimha Murthy Kaipa Viswanath
    • 1
    Email author
  • Saravana Ramachandran
    • 1
  1. 1.Department of MathematicsMadanapalle Institute of Technology and ScienceMadanapalleIndia

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