Atmospheric Environment 40 (2006) 1774–1780 Air quality forecasting using a hybrid autoregressive and nonlinear model Asha B. Chelani à , S. Devotta National Environmental Engineering Research Institute, Nagpur 440 020, India Received 10 October 2005; received in revised form 27 October 2005; accepted 9 November 2005 Abstract The usual practices of air quality time-series forecasting are based on applying the models that deal with either the linear or nonlinear patterns. As the linear or nonlinear behavior of the time series is not known in advance, one applies the number of models and finally selects the one, which provides the most accurate results. The air pollutant concentration time series contain patterns that are not purely linear or nonlinear and applying either technique may give inadequate results. This study aims to develop a hybrid methodology that can deal with both the linear and nonlinear structure of the time series. The hybrid model is developed using the combination of autoregressive integrated moving average model, which deals with linear patterns and nonlinear dynamical model. To demonstrate the utility of the proposed technique, nitrogen dioxide concentration observed at a site in Delhi during 1999 to 2003 was utilized. The individual linear and nonlinear models were also applied in order to examine the performance of the hybrid model. The performance is compared for one-step and multi-step ahead forecasts using the error statistics such as mean absolute percentage error and relative error. It is observed that hybrid model outperforms the individual linear and nonlinear models. The exploitation of unique features of linear and nonlinear models makes it a powerful technique to predict the air pollutant concentrations. r 2005 Elsevier Ltd. All rights reserved. Keywords: Time-series forecasting; ARIMA; Nonlinear dynamics; Hybrid model 1. Introduction In the air quality literature, time-series analysis is generally carried out to understand the cause and effect relationships, which in turn helps in forecast- ing the future concentrations. In this direction, a class of techniques including autoregressive inte- grated moving average (ARIMA) or Box–Jenkins models (Shi and Harrison, 1997; Milionis and Davies, 1994; Zennetti, 1990) and structural models (Schlink et al., 1997) have been applied to analyze air pollutant concentrations. These approaches are widely applied in the air-quality literature due to the lack of data on emissions of air pollutants. Although these models are quite flexible as they can represent several different types of time series, their major limitation is the pre-assumed linear form of the model. The approximation of linear models to real-world problems is not always satisfactory. For example, the air pollutant concentrations are influenced by several factors in the atmosphere and prediction using linear models may not always give reasonable results (Benarie, 1987). As an ARTICLE IN PRESS www.elsevier.com/locate/atmosenv 1352-2310/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.atmosenv.2005.11.019 à Corresponding author. E-mail address: ashachelani@rediffmail.com (A.B. Chelani).