# Effect of Autocorrelation on Applying Central Limit Theorem to Air Pollutant Concentration Time Series

Chung-Kung Lee , Ding-Shun Ho, Chung-Chin Yu, Cheng-Cai Wang, Yun-Hua Hsiao

• Department of Environmental Engineering, Van-Nung Institute of Technology, Chungli 320, Taiwan, ROC

Revised: May 31, 2002
Accepted: May 31, 2002

Lee, C.K., Ho, D.S., Yu, C.C., Wang, C.C. and Hsiao, Y.H. (2002). Effect of Autocorrelation on Applying Central Limit Theorem to Air Pollutant Concentration Time Series. Aerosol Air Qual. Res. 2: 87-92. https://doi.org/10.4209/aaqr.2002.06.0009

## ABSTRACT

One-year of hourly average air pollutant concentration (APC) observations, including CO, NO, NO2, O3, PM10, and SO2 was used to examine the effects of autocorrelation on the assumption of Central Limit Theorem (CLT) by calculating the confidence intervals of the data that were known to be dependent. Monte Carlo sampling was used to draw random samples of various sizes from the population (1000 groups of each size), and the sample means and standard deviation of these observed means were then evaluated. Even with small sample sizes, the average of all the means in each group and the observed standard deviation of the means were found to closely approximate the means of the overall population and the standard deviation predicted by CLT, respectively. Moreover, the above consistency was closely related to coefficient of variation of the population rather than to the degree of long-range-dependence. These results were used to interpret why the right-skewed frequency distribution observed in the mutually dependent air quality data could be accurately described using the lognormal model derived from the CLT. The link between the lognormality and multifractality characteristics in APC time series was also discussed.

Keywords: Long-range dependence; Central Limit Theorem; Coefficient of variation; Lognormality; Multifractality