In data-driven environmental health, incomplete monitoring records bias inference, reduce model accuracy, and impede policy decisions; addressing missing data through imputation and machine learning (ML) is essential for reliable PM2.5 particulate matter assessment and intervention planning (Jäger et al., 2021). Combining machine-learning forecasts and statistical imputation utilizes multi-source inputs (meteorology, traffic, remote sensing) to reconstruct high-resolution PM2.5 time series, improving predictive performance while remaining computationally efficient for local and regional applications (Fan et al., 2023; Saheer et al., 2022). Benchmarking imputation approaches and adapting methods to the temporal and spatial structure of urban PM2.5 maximizes reconstruction fidelity and supports robust exposure–health analyses in Pakistani cities, thereby strengthening evidence for air quality and public health policy (Darji et al., 2024; Mendes et al., 2022).

Ambient air pollution represents one of the most significant environmental and public health challenges of the 21st century. Among the various pollutants, particulate matter with an aerodynamic diameter of size than 2.5 μm (PM2.5) (Liang et al., 2016) which poses significant health risks and environmental challenges globally. Accurate PM2.5 data is essential for effective monitoring, policy-making, and public health interventions. In developing countries like Pakistan, rapid industrialization, urbanization, and increased vehicular emissions have led to a significant deterioration of air quality, especially in major urban centers like Lahore, Karachi, Peshawar and Islamabad. A major and predominant source of fine particles in the studied region is the vehicular activity, biomass fires and industry (Ngangmo et al., 2023; Mezoue et al., 2023). The country frequently ranks among those with the highest levels of PM2 pollution globally, posing a severe threat to the economy and to the health of millions of its citizens leading to estimate an annual cost of 6.5% of GDP per year due to health cost, reduce productivity and agricultural degradation (Suleman, 2022). Recognizing this crisis, government has installed air quality monitoring stations across the country to generate time-series data that is fundamental for various research and regulatory purposes.

However, the data collected from these monitoring stations are notoriously prone to incompleteness. Missing values in time-series data presents an inherent challenge, often arising from a confluence of factors: instrument malfunctions (e.g., sensor drift, calibration periods), harsh environmental conditions, sensor failures, power outages, communication failures, and routine maintenance schedules (Hua et al., 2024; Sun et al., 2023; Arnaut et al., 2024). The presence of missing data creates a significant impediment for data scientists and environmental researchers, as most statistical models and machine learning algorithms require complete datasets for training and inference. The critical question, therefore, shifts from whether data is missing to how to handle its absence effectively.

(Wijesekara and Liyanage, 2023) describe three different approaches to dealing with missing data: data deletion, imputation, and predictive estimation. In univariate time-series data, where a single variable is studied across time, the handling of missing data is especially problematic for the purpose of maintaining temporal dependency structures within imputation. Missing values in time series, if not handled properly, may often lead to biased results, subdue statistical power, and distort findings (Wijesekara and Liyanage, 2021). Avoiding these gaps or using assumptions such as mean imputation generates datasets that do not adequately model reality, resulting in erroneous insights. Consequently, many researchers have developed sophisticated imputation techniques, each with their unique advantages and disadvantages.

The missing data in PM10 time series has been shown to lead to underestimating pollution level exceedances, making the assessment and management of air quality more problematic (Albano et al., 2018). This poses major difficulties in fulfilling public health protection obligations outlined in European law. Failing to acknowledge missing data can result in inadequate sampling, faulty measurements and data collection problems (Junninen et al., 2004). Some of the literature reviews the principal techniques developed to accommodate missing values within the context of univariate time series data, assessing their effectiveness, theory, and application. Two common approaches to cope with missing data include a single imputation (SI) approach and a multiple imputation (MI) approach (Noor et al., 2015). It has been shown that the choice of imputation technique is determined by the attributes of the time series, the proportion of missing data, and the acceptable margin of error (Ribeiro and Castro, 2022). Single imputation methods are more straightforward and quicker to execute, yet multiple imputation and model-driven methods are advanced, trustworthy and precise. As noted by Chhabra (2023), the approach to deal with the missing values in a univariate time series is either simple imputation-based or model-based strategies. Imputation-based techniques involve direct estimation of missing values with mean, median or mode while methods that solve equations, based on likelihoods are model-based methods (Armina et al., 2017; Aljuaid and Sasi, 2016; Pereira et al., 2024).

To understand missing data in detail, it is necessary to acknowledge the various missing data mechanisms. These include missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR), all of which need custom approaches to formulate effective imputation strategies (Kleinke et al., 2020).

The primary objective of this study is to develop and evaluate a robust imputation framework for addressing missing values in PM2.5 air quality datasets using advanced statistical and machine learning methods. Thus, this paper provides the first systematic evaluation of missing data methods such as (BR), (KNN), missForest, (PMM), and (RF), with a focus on the multi-year PM2.5 data from four major Pakistani cities. By simulating realistic missing data mechanisms and measuring the accuracy of imputations through metrics like RMSE and MAE, the researcher provides a solid framework to combat the gaps in the gaps in sparse air quality monitoring networks. These findings will be useful to policymakers and researchers that rely on proper estimates of PM2.5 in health risk assessment and environmental planning.

Here we discuss how scholars try to mitigate the still overwhelming issue of high rates of missing data. Several methodological frameworks are discussed, highlighting both the advances and ongoing challenges of the problem. Some basic imputation methods, such as simple mean imputation and spline interpolation, often perform poorly in univariate settings due to their reliance on inter-attribute dependencies (Moritz et al., 2015). Likewise, Lien et al. (2023), mean imputation, in which missing data points were replaced with the mean of the available data, has been shown to yield inadequate results in datasets with more than 10% missing data because of temporal variability in PM2.5 data. Niako et al. (2024) applied and compared multiple imputation methods, including Kalman filtering, linear interpolation, and moving averages, quantifying their effects on forecasting accuracy of the ARIMA and LSTM models. Advanced methods such as ARIMA state-space models with Kalman smoothing have been proven to be robust against shifts of means and heavy-tailed distributions (Zainuddin et al., 2022; Haile et al., 2024; Sharma et al., 2025) used ARIMA model to predict PM2.5 concentration in Indian satellite cities and the model exhibited a high level of accuracy (Kumar et al., 2024). Implemented the machine learning models by building intricate relationships with various metrological variables and considered the linear regression model as the most favorable methods to PM2.5 concentration. Some studies employed various predictive modelling techniques to predict PM2.5, PM10 and other leading pollutants. For instance, Researchers used machine learning and data mining algorithms including Independent component regression (ICR), ElasticNet (ENET), boosted tree (BT), Random Forest (RF), Support Vector Machine (SVM), Bagged Multivariate Adaptive Regression Splines (MARS), and Bayesian Regularized Neural Networks (BRNN) to predict the distribution of pollutants like P M 2.5 , P M 10 , N O 2 , a n d   S O 2 (Kumar P. et al., 2025; Choudhary et al., 2023).

Further to this Wijesekara and Liyanage (2020) found that Kalman smoothing on Structural Time Series showed strong performance compared to six other methods of imputation on air quality data. A study by Arnaut et al. (2024) investigated the application of the Random Forest (RF) algorithm for bi-directional imputation of missing values for air quality data, with emphasis on PM2.5 concentrations, and analyzed its performance compared to the rather simple approaches of imputation such as mean and median imputation.

A study by Tyagi et al. (2021) analyzed air quality data and investigated five imputation techniques: K-Nearest Neighbors (KNN), Linear Interpolation (LI), Expectation-Maximization (EM), Multiple Imputation by Chained Equations (MICE), and Random Forest (RF). The outcomes suggest that Random Forest imputation is the optimal method for filling in absent data (Alsaber, Pan, and Al-Hurban, 2021). Used imputation methods for missing values in environmental data sets collected in Kuwait and evaluates the performance of missForest, K-Nearest Neighbors (KNN), and Bayesian principal component analysis (Bayesian PCA) in a systematic way. Results showed that missForest has the lowest imputation error for varying degrees of missing data. The R statistical software has several packages designed for missing data, including imputation. A prominent R package, mice (Multivariate Imputation by Chained Equations), while primarily designed for multivariate data, can also be applied to univariate time series by treating lagged values of the series as predictors (Buuren and Groothuis-Oudshoorn, 2011). Bayesian regression also offers a robust statistical approach for dealing with the missing data. According to Aßmann et al. (2023), a Bayesian regression statistical approach, which incorporates prior knowledge and manages uncertainty during the imputation process is very useful for dealing with missing data in air quality datasets.

Several studies highlight the role of evaluation metrics in comparing imputation methods. Rantou et al. (2017) advocate for using Mean Root Squared Error (MRSE) and Mean Absolute Percentage Error (MAPE) to assess imputation accuracy, particularly in predictive modelling contexts. The approach with the lowest expected mean square error (EMSE) for each type of missing data for six imputation techniques across various scenarios, intended to improve logistic regression models. Junninen et al. (2004) assesses different techniques for imputing missing values in air quality data sets, classifying them into univariate, multivariate, and hybrid methods, as well as multiple imputation approaches. The main objective was to evaluate their efficacy in addressing data shortages. The effectiveness of each imputation method was assessed using the Root Mean Square Error (RMSE) and the Normalized Root Mean Square Error (NRMSE), which compare predicted values to actual observed values (Tyagi et al., 2021). Lien et al. (2023) applied classical imputation methods and advanced approaches on a crowd-sourced Fitbit data set, revealing that KNN performs best under low to moderate missingness (<30%).

This paper evaluates multiple imputation methodologies for PM2.5 air quality data, emphasizing their effectiveness in addressing different missing data scenarios. The analysis systematically compares established and emerging techniques. These include multiple imputation methods, as well as spectral and machine learning-based approaches. The study considers each method under a range of missing data mechanisms to inform the selection of optimal imputation strategies (Libasin et al., 2020; Zhang and Thorburn, 2022). The data set, from four monitoring stations or US consulates in Pakistan, has missing data, for various possible reasons. One reason is that there were many changes to the routine maintenance at the monitoring sites. Human error is a second reason. Thirdly, the PM2.5 data-sharing network needed to publish the information has been put on hold because of a lack of funds, resulting in missing data in the studied data set.

To investigate the trend and percentage of missing in PM2.5 data in urban cities of Pakistan.

This section consists of data collection, analysis of missing data and implementation of various imputation methods.

Although this study provides valuable insights into the performance of various imputation techniques for PM2.5 data, certain limitations should be acknowledged. The analysis focused primarily on daily averages from four urban monitoring stations, which may not capture short-term variability or spatial heterogeneity in air quality. Additionally, only five imputation methods were evaluated, excluding emerging deep learning–based approaches that may further enhance accuracy. Future research should extend this framework to incorporate high-frequency and multi-pollutant datasets, explore hybrid or ensemble deep learning models, and examine the influence of meteorological and socioeconomic factors to develop more adaptive and scalable imputation strategies for environmental monitoring systems.

The results of this study provide critical insights into the comparative performance of statistical and machine learning-based imputation techniques applied to PM2.5 air quality datasets across major Pakistani cities. By systematically evaluating five methods—Bayesian Regression (BR), K-Nearest Neighbors (KNN), missForest, Predictive Mean Matching (PMM), and Random Forest (RF) under varying missingness mechanisms (MCAR, MAR, MNAR) and rates (5%–25%), the analysis reveals distinct patterns of imputation accuracy and reliability. The findings underscore the sensitivity of model performance to both the volume and mechanism of missing data, demonstrating that improper handling of missingness can lead to substantial estimation errors and distort temporal pollution trends. The study used data from four major cities of Pakistan from May 2019 to December 2024, which allowed for an in-depth analysis of the various missing data mechanisms (MCAR, MAR, MNAR) and missing data rates (5%–25%) considered. The results indicate that as the amount of missing data increases, the quality of the data also diminishes. Moreover, data that is classified as Missing at Random (MAR) was found to have relatively less imputation error than MCAR (Missing Completely at Random) and MNAR (Missing Not at Random) because of the inherent temporal or spatial correlations within the datasets. Among all the methods, missForest had the lowest error overall, in terms of RMSE and MAE measures, and KNN also had relatively good results. These two techniques maintained the trends, cycles, and extremes of the time series data that are necessary for the robust analysis of environmental data. On the other hand, the Bayesian Regression, PMM technique and Random Forest technique, although more stable, lacked adequate reliability especially at higher levels of missingness. These examples confirmed the importance of customizing imputation strategies for the missingness mechanism and the attributes of the data set. In particular, imputation methods have not, to our knowledge, been studied for PM2.5 data from Pakistan and the use of missForest is recommended for imputation of missing PM2.5 data in that context.

In short, this study demonstrates that ensemble missForest and neighbor-based methods, the missForest, is the most effective machine learning approach for partial PM2.5 data set imputation relatively to KNN. Accurate imputations are necessary for improving the statistical credibility of environmental assessments and to ensure effective policy formulation for air quality management.