# Application of empirical likelihood ratio test in AR(1) time series model for PM2.5 forecasting in Guwahati city of Assam

## TL;DR

This paper introduces a new statistical test for improving AR(1) model accuracy in forecasting PM2.5 levels in Guwahati, Assam.

## Contribution

The study proposes an Empirical Likelihood Ratio Test (ELRT) for AR(1) model identification, showing better performance than traditional methods.

## Key findings

- The ELRT outperforms the Ljung-Box test in empirical size and power according to Monte Carlo simulations.
- Application of ELRT on PM2.5 data shows forecasts mostly in 'Poor' to 'Very Poor' air quality range.
- The proposed ELRT method provides a robust alternative for AR(1) model identification in air quality forecasting.

## Abstract

The Autoregressive model plays a vital role in time series analysis, as it efficiently captures short-term dependencies while maintaining simplicity. Accurate identification of the order of autoregressive models is essential for enhanced model performance and reliable forecasting. Traditional method of identifying AR (1) models relying on autocorrelation and partial autocorrelation plots, along with the Ljung-Box (LB) test, often suffer from subjectivity and potential overfitting. To overcome this limitation, this study proposes an Empirical Likelihood Ratio Test (ELRT) for assessing the suitability of AR (1) model in time series analysis. Through Monte Carlo simulation, performance of the ELRT is compared with the LB test in terms of empirical size and power. Simulation results indicate that the ELRT maintains empirical size more accurately while exhibiting superior power compared to LB test. The proposed test is further validated using major air pollutant, PM2.5 data from Guwahati, Assam. The empirical results show that the forecasted PM2.5 levels remain mostly in the “Poor” to “Very Poor” range during the initial months, indicating unhealthy air quality. A slight improvement to ‘Moderately Polluted’ is observed in the fourth month. The proposed approach offers a robust alternative for AR (1) model identification and improves the reliability of forecasts in air quality studies.