Systematic Approach to Determining True Long Memory on PM10 Data

Abstract

Abstract Particulate matter pollutants are common atmospheric air pollutants in Malaysia which have numerous harmful effects on the environment, the flora and fauna, as well as human health. Long memory process may spuriously be detected due to presence of break in the time series data since a short memory process with occasional structural break can show a slower rate of decay in the autocorrelation function and other properties of fractionally integrated \(I\left(d\right)\) process. Numerous research around the globe confirmed evidence of long memory on particulate matter pollutant, but few or none in Malaysia have tested for it and investigated whether the persistence (if evident) is truly detected or merely spurious due to presence of neglected structural breaks. In this paper, we examined the statistical properties of daily PM10 emission in fourteen Malaysian air quality stations over the period 1 January 2011 through 31 December 2020 by applying a fractional integration framework on both the original and partitioned series that encountered structural break as confirmed by the OLS-based CUSUM test. Both the original and sub-series (before and after the break regime) are found to be characterized by long memory with orders of integration within the range \(\left(0, 1\right)\) implying the evidence of mean reversion form of long memory. Thus, this evidence confirms the presence of true long memory not due to structural break. We also obtained higher values for Kurtosis statistic implying that the emission fluctuates significantly.