Comparison of Imputation Methods for Missing Values in Air Pollution Data: Case Study on Sydney Air Quality Index

Abstract

Missing values in air quality data may lead to a substantial amount of bias and inefficiency in modeling. In this paper, we discuss six methods for dealing with missing values in univariate time series and compare their performances. The methods we discuss here are Mean Imputation, Spline Interpolation, Simple Moving Average, Exponentially Weighted Moving Average, Kalman Smoothing on Structural Time Series Models and Kalman Smoothing on Autoregressive Integrated Moving Average (ARIMA) models. The performances of these methods were compared using three different performance measures; Mean Squared Error, Coefficient of Determination and the Index of Agreement. Kalman Smoothing on Structural Time Series method is the best method among the methods considered, for imputing missing values in the context of air quality data under Missing Completely at Random (MCAR) mechanism. Kalman Smoothing on ARIMA, and Exponentially Weighted Moving Average methods also perform considerably well. Performance of Spline Interpolation decreases drastically with increased percentage of missing values. Mean Imputation performs reasonably well for smaller percentage of missing values; however, all the other methods outperform Mean Imputation regardless the number of missing values.