Compositional time series analysis for Air Pollution Index data

The increasing importance of understanding the structure of Air Pollution Index (API) makes it necessary to come out with a compositional of API based on its pollutants. This will be more comprehensible for the public and easier to cooperate with authorities in reducing the causes of air pollution. Since five pollutants contribute in determining the API values, API can be shown as a compositional data. This study is conducted based on the data of API and its pollutants collected from Klang city in Malaysia for the period of January 2005 to December 2014. The proportion of each pollutant in API is considered as a component with five components in a compositional API. The existence of zero components in some pollutants, that have no effect on API, is a serious problem that prevents the application of log-ratio transformation. Thus, the approach of amalgamation has been used to combine the components with zero in order to reduce the number of zeros. Also, a multiplicative replacement has been utilized to eliminate the zero components and replace them with a small value that maintains the ratios of nonzero components. Transforming the compositional data to log-ratio coordinates has been done using the additive log ratio transformation, and the transformed series is then modeled by using a VAR model. Four criteria are used to determine the number of lags p of VAR(p) and these are: the Akaike Information, the Schwartz, the Hannan–Quinn and the Final Prediction Error criteria. Based on the results, A VAR (1) model with no constants or trend is considered as the best fitted model and it is used to forecast 12 months ahead. In addition, API values are mainly determined by PM₁₀ that has a proportion close to one most of the time during study period. Therefore, authorities and researchers need to study the sources of PM₁₀ and provide the public with useful information and alternatives in term of reducing the air pollution.