Long-range correlations in the air quality index (AQI) are analysed using rescaled range analysis (R/S), detrended fluctuation analysis (DFA) and power spectral density analysis. Air quality index in five cities of India is considered for this purpose. Statistical transformations such as differencing and shuffling have been carried out to examine the effect of temporal correlations on long-range correlation property of the time series. All three methods indicated the presence of persistence in original AQI time series. After differencing, long-range correlation property is, however, observed to be distorted. R/S analysis did not show the similar results as DFA and power spectral density analysis. Shuffled time series is shown to possess persistence as in the original one by using R/S analysis, whereas other two methods showed random behaviour at most of the locations. This suggests that the persistence property is largely influenced by short-range correlations in the AQI time series. The incorporation of this information can enhance the performance of the models to forecast the air quality. The similarity in the results of DFA and power spectral density analysis suggests that both methods can be relied more than R/S analysis in studying the persistence property of the time series.