Existence of long memory in ozone time series

Abstract

Long-memory is often observed in time series data. The existence of long-memory in a data set implies that the successive data points are strongly correlated i.e. they remain persistent for quite some time. A commonly used approach in modelling the time series data such as the Box and Jenkins models are no longer appropriate since the assumption of stationary is not satisfied. Thus, the scaling analysis is particularly suitable to be used for identifying the existence of long-memory as well as the extent of persistent data. In this study, an analysis was carried out on the observed daily mean per hour of ozone concentration that were available at six monitoring stations located in the urban areas of Peninsular Malaysia from 1998 to 2006. In order to investigate the existence of long-memory, a preliminary analysis was done based on plots of autocorrelation function (ACF) of the observed data. Scaling analysis involving five methods which included rescaled range, rescaled variance, dispersional, linear and bridge detrending techniques of scaled windowed variance were applied to estimate the Hurst coefficient (H) at each station. The results revealed that the ACF plots indicated a slow decay as the number lag increased. Based on the scaling analysis, the estimated H values lay within 0.7 and 0.9, indicating the existence of long-memory in the ozone time series data. In addition, it was also found that the data were persistent for the period of up to 150 days.