Air pollution remains a critical public health and environmental issue in megacities, with fine particulate matter (PM2.5) posing significant risks in Tehran, Iran. Traditional modeling methods often fail to capture the non-stationary and multiscale characteristics of urban air pollution dynamics. This study introduces a wavelet-based analytical framework to uncover both long-term seasonal trends and short-lived pollution events using a seven-year dataset (March 2017–March 2024) from nine monitoring stations across Tehran. We applied the Continuous Wavelet Transform (CWT) with Morlet and Daubechies 6 (db6) wavelets to decompose the PM2.5 time series into multiple temporal scales. The Morlet wavelet identified persistent winter peaks associated with temperature inversions and atmospheric stagnation, while db6 revealed abrupt, high-frequency pollution spikes linked to localized traffic emissions and industrial activity. Wavelet coherence analysis further illustrated the relationship between meteorological variables such as temperature, east-west winds, and north-south winds and PM2.5 concentrations, highlighting how these factors modulate air quality across different spatial and temporal scales. While ARIMA demonstrated stronger point-forecasting accuracy, the wavelet-based framework provided superior interpretability by preserving both gradual seasonal cycles and transient anomalies simultaneously structures that conventional models tend to smooth out. This comparison was conducted not to establish forecasting superiority, but to highlight the distinct and complementary role of wavelet analysis as a diagnostic tool for pollution hotspot identification and early-warning systems rather than pure numerical prediction. These findings underscore the value of wavelet analysis as not only an advanced analytical tool but also a decision-support system for real-time air quality monitoring and spatially targeted policy planning. By capturing the full spectrum of PM2.5 dynamics from chronic seasonal exposure to acute pollution spikes, this approach offers a more comprehensive framework for adaptive urban air quality management in complex environments like Tehran.

This paper investigates the dynamics of the NASDAQ topology before, during, and after 2008 financial crisis. First, multiresolution analysis by virtue of wavelet transform is employed to denoise each NASDAQ sector return series. Second, the correlation matrix of sectors is built and analyzed in each time period to view comovements of sectors. Third, hierarchical clustering trees are constructed in each time period to find out how the structure of the NASDAQ market evolves through time. Our results suggest that interrelationships between sectors become stronger in times of crisis and especially in post-crisis period. In addition, some markets tend to form the same cluster in all time periods; for instance the Industrial and Bank sectors and the Telecommunication and Computer sectors. However, the general topology of the NASDAQ market has been considerably changed over periods. In sum, the complex structure of the NASDAQ market is dynamic and is more integrated after 2008 financial crisis. This result indicates that there are less diversification opportunities in the post-crisis period in comparison with pre-crisis period. These empirical findings are important for the development of subsequent portfolio strategies.