Structural time-series modelling for seasonal surface air temperature patterns in India 1951-2016

To investigate variability patterns, to predict short-term and long-term changes of weather, time-series data analysis is considered to be a valuable tool. The paper presents modelling and forecasting the seasonal surface air temperature patterns in India for the period 1951-2016 using the structural time-series modelling. The structural time-series model (STSM) with the hidden components of deterministic linear time trend, trigonometric seasonal, and stochastic autoregression for cycle is selected from the parsimonious models. The model selection can be done based on Bayesian Information Criteria (BIC), significant tests, and statistical fit. The model parameters of the noise terms and the damping coefficient in the autoregression are determined using maximizing the likelihood function. The diagnostics of the selected STSM is determined with normal diagnostics checked by examining the histogram and Q-Q plot of residuals; the whiteness checked by autocorrelation function (ACF), partial autocorrelation function (PACF), and p values of LJung-Box portmanteau test of residuals. Furthermore, the forecast of seasonal surface air temperature patterns in India during the years 2017-2019 has been forecasted from the selected STSM. Statistically significant increase is noticed in annual average surface air temperature over India. The increase in surface temperature is about 0.0132 degrees C per year for the period 1951-2016. The study also showed slow and steady increase in the mean surface air temperature over India during the recent years.