The incidence of respiratory infections in the population is related to many factors, among which environmental factors such as air quality, temperature, and humidity have attracted much attention. In particular, air pollution has caused widespread discomfort and concern in developing countries. Although the correlation between respiratory infections and air pollution is well known, establishing causality between them remains elusive. In this study, by conducting theoretical analysis, we updated the procedure of performing the extended convergent cross-mapping (CCM, a method of causal inference) to infer the causality between periodic variables. Consistently, we validated this new procedure on the synthetic data generated by a mathematical model. For real data in Shaanxi province of China in the period of 1 January 2010 to 15 November 2016, we first confirmed that the refined method is applicable by investigating the periodicity of influenza-like illness cases, an air quality index, temperature, and humidity through wavelet analysis. We next illustrated that air quality (quantified by AQI), temperature, and humidity affect the daily influenza-like illness cases, and, in particular, the respiratory infection cases increased progressively with increased AQI with a time delay of 11 days.