INTEGRATION OF QUADRATIC REGRESSION-ARIMA MODEL ESTIMATING AIR QUALITY INDEX ON PM2.5 CONCENTRATION
Abstract
In Air Quality Index (AQI) computation, the relationship between AQI and PM2.5 is defined through an interpolation approach, which forms a nonlinear relationship between PM2.5 and AQI, thereby rendering linear regression less capable of representing this relationship. This research selects quadratic regression because it explicitly represents the nonlinear relationship between PM2.5 and AQI while remaining easy to interpret and minimizing the risk of overfitting compared with more complex nonlinear models. However, in time series data, this model still generates residuals that violate classical assumptions due to time dependence. Hence, a hybrid modeling approach integrates quadratic regression and Autoregressive Integrated Moving Average (ARIMA) to represent nonlinear relationships while correcting the time dependence on the quadratic regression residuals. This research aims to estimate AQI based on PM2.5 in Pontianak in 2024 using the Quadratic Regression-ARIMA model, also comparing the performance of quadratic regression models and quadratic regression-ARIMA models. This research focuses on estimation and interpolation within the sample, not forecasting. The dataset consists of 366 daily observations of AQI and PM2.5 throughout 2024, obtained from the official air quality monitoring website, AQI. The analysis was carried out by estimating the AQI from PM2.5 using a Quadratic Regression model, and the regression residuals were rendered stationary before ARIMA modeling. The results showed that the Quadratic Regression-ARIMA model yields estimate with a better residual structure than the quadratic regression model. The in-sample evaluation of the Quadratic Regression-ARIMA model showed better performance, with a higher coefficient of determination of 0.95, compared with 0.91 for quadratic regression and 0.80 for linear regression.
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