How to identify cross correlations: a statistical test with time lag and its application on air-pollutant time series


Gergely Tóth, Institute of Chemistry, Loránd Eötvös University, Pázmány sétány 1/a, Budapest, H-1117, Hungary.



We developed a method to detect time-lag-dependent cross-correlation effects in time series. The method is a statistical test based on ANOVA with resampling, but the simple plot of the p-values in respect to the time lag provides an intuitive recognition of cross correlations as well. It is applied on meteorological and air-pollutant data measured in Budapest. We detected periodic and odd cross-correlation effects easily on the graphs, for example, the effect of weekend/weekdays on pollutants, an odd effect of solar radiation on humidity in the fourth quarter of the year, an opposite effect of solar radiation and height of mixing layer on CO at the same day opposite to the following days, and the prompt resuspension of PM10 caused by solar radiation in the fourth quarter of the year. We estimated the length of the cross-correlation effects on the air pollutants: 2–3 days of precipitation depending on the solubility of the pollutants, 3–4 days of wind, and 2–5 days for the cross reactions of NO2 and O3. We found that yearlong time domain provides different correlation effects than seasonal ones for the same daily time lags. The visual comparison of the curves also helps to identify the time domains, which can be modeled similarly. Our method is an efficient tool to identify cross-correlation effects before modeling, because it enlarges the correlations undetectable in cross-correlation functions. Copyright © 2012 John Wiley & Sons, Ltd.