Extracting the Influential Commodities in Stochastic Model of Simple Laspeyre Price Index Numbers with AR(2) Errors

Abstract

This paper, on the first hand, deals with the problem of estimation of Laspeyre price index number when the errors are assumed to be generated from AR(2) process. The general expression of hat matrix and DFBETA measure to find the influential consumer commodities in stochastic Laspeyre price model with AR(2) errors are developed on the other. The hat values show the noteworthy findings that the corresponding weights of consumer items have large influence on the parameter estimates for simple Laspeyre price index number and are not affected by the parameter of autoregressive process of order two. While, DFBETA measures are the functions of both weights and autocorrelation parameters. Lastly, an example is presented with reference to price data of Pakistan, and shows its practical importance in financial time series.

An Algorithm to Find Significant Commodities in Stochastic Laspeyres Regression Model.

“…The transformation matrix Q is obtained by Burney and Maqsood (2014) when the errors are generated from autoregressive process of order p with p=1, and by Maqsood and Burney (2014) for p=2. With these assumptions Maqsood and Burney (2014) obtained the estimator of  , the familiar Laspeyres index number, written as…”

“…Similarly, the last cell confirms about the significant influence of respective commodity falling in rejection region. The analysis done by Maqsood and Burney (2014) is actually an example of determining influential commodities in Laspeyres index model using this algorithm. The first phase of computation requires the estimation of parameter vector based on observed price data.…”

“…The first phase of computation requires the estimation of parameter vector based on observed price data. While in the second phase the hat values and DFBETA values are computed using the formulae given in equations (7) and (9). The results on Laspeyres index estimates and estimates of influential measures are presented in Maqsood and Burney (2014).…”

“…Özkale and Açar (2015) used these influence measures to find unusual observations in linear regression model with more than one regressors. Maqsood and Burney (2014) and Burney and Maqsood (2014) used the technique of hat matrix and DFBETA measure to find the influential commodities in Laspeyres index number model with autocorrelated errors.…”