Explosive Behavior Detection of PM2.5 During Wildfire Period Based on BSADF Test

Abstract

Time series is a type of data that is popular in statistical analysis. Explosive behavior, which is an immediately skyrocketing time series, is one of the important behaviors of time series that is often used in many tasks. In addition, a particular tool that has been used frequently in the last few years is the Backward Supremum Augmented Dickey-Fuller Test (BSADF Test). BSADF is developed for mainly use in the stock market, but when it is used with PM 2.5 data in which wildfires occurred, it is observed that BSADF cannot detect the explosive behavior in a short time series of the data. This problem leads to the development of a method based on BSADF to detect explosive behavior in a short period of a time series, so this new method can face various types of data. From investigating the BSADF test by using different sizes of windows in synthetic data that was generated by the ARMA process, it has been noticed that decreasing of windows will affect the BSADF test by increasing the BSADF value a little in the explosive behavior period, whereas other periods have been increased numerously. So, by using the difference in the amount of gap of the BSADF value in different sizes of windows, it led to a new test statistic. The new test statistic is outperformed compared to the BSADF test both in synthetic and real data, it could detect explosive behavior in a short period of time series when wildfire occurred and not over-detect explosive behavior in other periods.