# Prediction of Air Quality Combining Wavelet Transform, DCCA Correlation Analysis and LSTM Model
###### Abstract  
In the context of global climate change, air quality prediction work has a substantial impact on humans' daily lives. The current extensive usage of machine learning models for air quality forecasting has resulted in significant improvements to the sector. The long short-term memory network is a deep learning prediction model, which adds a forgetting layer to a recurrent neural network and has several applications in air quality prediction. The experimental data presented in this research include air pollution data (SO2, NO2, PM10, PM2.5, O3, and CO) and meteorological data (temperature, barometric pressure, humidity, and wind speed). Initially, using air pollution data to calculate the air pollution index (AQI) and the wavelet transform with the adaptive Stein risk estimation threshold is utilized to enhance the quality of meteorological data. Using detrended cross-correlation analysis (DCCA), the mutual association between pollution elements and meteorological elements is then quantified. On short, medium, and long scales, the prediction model's accuracy increases by 1%, 1.6%, 2%, and 5% for window sizes (h) of 24, 48, 168, and 5000, and the efficiency increases by 5.72%, 8.64%, 8.29%, and 3.42%, respectively. The model developed in this paper has a substantial improvement effect, and its application to the forecast of air quality is of immense practical significance. A 2023 13 2796 2023 13 2796 2023 13 2796 2  
neural networks. Among the correlation coefficient methods are the linear correlation coefficient, the rank correlation coefficient, and the tail correlation coefficient. [PERSON] et al. used geographically weighted Pearson correlation coefficients to investigate the spatial interactions between Pb and Al in soils, studying independently their positive and negative correlations based on the results at various scales [6]. [PERSON] et al. studied the number of multiscale inter-relationships between PM2.5 and O3 in three Chinese metropolises (Beijing, Shanghai, and Guangzhou) to address the complexity characteristics of PM2.5 and O3 at various spatial and temporal scales [7]. [PERSON] et al. explored the nonlinear interplay between economic growth and environmental degradation in five industrialized European nations using wavelet-based analysis approaches [8]. [PERSON] et al. modeled the nonlinear fluctuation of corrosion in two SiO2 nanostructured copper vessels in the marine atmosphere using statistical analysis and artificial neural networks [9]. Air pollution data and meteorological data are typical time series data with nonstationary, periodic fluctuations and a multiscale structure, and conventional correlation analysis techniques may produce erroneous outcomes [10]. Compared to conventional correlation analysis, the detrended cross-correlation analysis (DCCA) examination of power-law inter-relationships among nonstationary time series can disclose more information regarding the correlation between AQI and meteorological parameters and is a relatively reliable method for detecting the correlation between AQI and meteorological data [11]. [PERSON] et al. examined the influence of detrended inter-relation numbers in fragments with long-range-memory time series and demonstrated that detrended inter-relation numbers are robust for the analysis of fragmented time series [12]. [PERSON] et al. expanded detrended correlation analysis to signals with extremely inhomogeneous structures, demonstrating the benefits of DCCA for analyzing medical data and two-scale kinetic changes: the indicators of detrended covariance and nonstationary effects due to local fluctuations [13]. [PERSON] et al. utilized the conditional distribution of time series in conjunction with detrended correlation analysis to examine the link between the spot price of WTI crude oil and the S&P 500 from January 1986 to August 2021 under various oil and stock market situations [14]. LSTM (long short-term memory) is a deep learning prediction model that adds an oblivion layer to recurrent neural networks (RNN).