Time series analysis of aerosol optical depth over New Delhi using Box–Jenkins ARIMA modeling approach

The present study focuses on the application of stochastic modeling technique in analyzing the future trends of aerosol optical properties. For this, the Box–Jenkins ARIMA (Autoregressive Integrated Moving Average) model has been used for simulating the monthly average Aerosol Optical Depth (AOD550 nm) retrieved from Terra MODIS (Moderate Resolution Imaging Spectroradiometer) over New Delhi, the urban capital of India. The satellite dataset has been collected for a period of ten years from 2004 to 2014. The analysis of autocorrelation function indicates existence of seasonality in the AOD time series. Several seasonal ARIMA models have been generated and their validation has been verified by assessing various estimation parameters, using the Statistical Package for the Social Sciences (SPSS, version 20). After rigorous evaluation of the selected models, the ARIMA (1,0,0)x(0,1,2)12 is identified as the best fit model w.r.t. measures of goodness-of-fit like Stationary R-square (0.530), R-square (0.674), Root Mean Squared Error (0.128); Mean Absolute Error (0.095); Mean Absolute Percentage Error (16.942); and normalized Bayesian Information Criteria (−3.941). The selected models have been further used to forecast AOD values for the year 2014 at 95% level of confidence. However, the ARIMA (1,0,0)x(2,1,1)12 model is found to have minimum forecasting error, calculated as Mean Percentage Error (0.220). As the difference in BIC of both the models is minimal (0.046), so both the models have been considered as best fit models and utilized for prediction of AOD. Satisfactory results have been obtained using the selected ARIMA models, suggesting that a simplistic modeling technique for determining the future values of AOD is feasible.