Influential Observations in Stochastic Model of Divisia Index Numbers with AR(1) Errors

Syed Muhammed Aqil Burney,Arfa Maqsood

doi:10.4236/am.2014.56093

Abstract

We use the general form of hat matrix and DFBETA measures to detect the influential observations in order to estimate the Divisia price index number when the error structure is first order serial correlation. An example is presented with reference to price data of Pakistan. Hat values show the noteworthy findings that the corresponding weights of consumer items have large influence on the parameter estimates and are not affected by the parameter of autoregressive process AR(1). Whereas DFBETAs for Divisia index numbers depend on both the weights and autoregressive parameter.

Highlights

A number of studies are available on the detection of leverages and influential observations in a regression model when the errors are assumed to be serially correlated with AR(1) and AR(2) processes
Barry et al [15] extended the study of influential observations to the regression model with AR(2) errors and developed the diagnostic techniques using a hat matrix
The objective of this paper is to use the analytical tools of hat matrix and DFBETA measures to identify the influential observations in estimating the Divisia price index number

Summary

Introduction

A number of studies are available on the detection of leverages and influential observations in a regression model when the errors are assumed to be serially correlated with AR(1) and AR(2) processes. Influence diagnostics are developed and studied by many authors, including Belsley et al [6], Cook ([7] [8]), Cook and Weisberg [9], Draper and John [10], and Draper and Smith [11] They examined the effect of individual observation or a set of observations on the estimation of model parameters. Barry et al [15] extended the study of influential observations to the regression model with AR(2) errors and developed the diagnostic techniques using a hat matrix. The objective of this paper is to use the analytical tools of hat matrix and DFBETA measures to identify the influential observations in estimating the Divisia price index number. An application with reference to Pakistan price data is illustrated in Section 4 and lastly, Section 5 recapitulates the results

Regression Model

D P and the design matrix

Influence and Hat Matrix

An Application

Conclusion