On the Asymptotic Behavior of the Estimates of Quantile Regression for Inflation Rates and Consumer Price Index

Abstract

This paper investigates the asymptotic behavior of quantile regression which is a nonparametric procedure used for prediction. This method is more robust compared to the Ordinary Least Squares (OLS) for asymmetric data. This was the procedure used in the analysis of the annual data of Inflation Rates (IR) and Consumer Price Index (CPI) of
the Philippines from 1958 to 2007. The package Quantreg of the free Statistical Software R was used in the computation of the estimates at different quantiles. The findings revealed that the data are asymmetric thereby resulting to non significant simple linear regression for both the Median and Least Squares Regression Procedures. However, at some quantiles at the left and right of the distribution, the regression models yield positive and negative significant linear regressions respectively. Simulation results reveal that in general, the inflation rates cannot predict the consumer price index by using quantile linear regressions or the least squares method. It is recommended to explore the nonlinear quantile regression procedures in modelling the inflation rates. Moreover, a study on the similarity and differences of Quantile Regression Procedu.res and L~ast Trimmed Squares (LTS) be investigated for Nonhnear Regression.