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

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.

Share and Cite:

Burney, S. and Maqsood, A. (2014) Influential Observations in Stochastic Model of Divisia Index Numbers with AR(1) Errors. Applied Mathematics, 5, 975-982. doi: 10.4236/am.2014.56093.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Prais, G.J. and Winsten, C.B. (1954) Trend Estimates and Serial Correlation. Cowles Commission Discussion Paper, Stat. No. 383, University of Chicago.
[2] Kadiyala, K.R. (1968) A Transformation Used to Circumvent the Problem of Autocorrelation. Econometrica, 36, 93-96.
http://dx.doi.org/10.2307/1909605
[3] Griliches, Z. and Rao, P. (1969) Small-Sample Properties of Several Two-Stage Regression Methods in the Context of Autocorrelated Disturbances. Journal of American Statistical Association, 64, 253-272.
http://dx.doi.org/10.1080/01621459.1969.10500968
[4] Maeshiro, A. (1979) On the Retention of the First Observation in Serial Correlation Adjustment of Regression Models. International Economic Review, 20, 259-265.
http://dx.doi.org/10.2307/2526430
[5] Park, R.E. and Mitchell, B.M. (1980) Estimating the Autocorrelated Error Model with Trended Data. Journal of Econometrics, 13, 185-201.
http://dx.doi.org/10.1016/0304-4076(80)90014-7
[6] Belsley, P.A., Kuh, E. and Welsch, R.E. (1980) Regression Diagnostics. John Wiley, New York.
http://dx.doi.org/10.1002/0471725153
[7] Cook, R.D. (1977) Detection of Influential Observations in Linear Regression. Technometrics, 19, 15-18.
http://dx.doi.org/10.2307/1268249
[8] Cook, R.D. (1979) Influential Observations in Linear Regression. Journal of American Statistical Association, 74, 169174.
http://dx.doi.org/10.1080/01621459.1979.10481634
[9] Cook, R.D. and Weisberg, S. (1982) Residuals and Influence in Regression. Chapman and Hall, New York.
[10] Draper, N.R. and John, J.A. (1981) Influential Observations and Outliers in Regression. Technometrics, 23, 21-26.
http://dx.doi.org/10.1080/00401706.1981.10486232
[11] Draper, N.R. and Smith, H. (1998) Applied Regression Analysis. 3rd Edition, John Wiley, New York.
[12] Puterman, M.L. (1988) Leverage and Influence in Autocorrelated Regression Model. Journal of the Royal Statistical Society, 37, 76-86.
[13] Cochrane, D. and Orcutt, G.H. (1949) Application of Least Squares Regression to Relationships Containing Autocorrelated Error Terms. Journal of American Statistical Association, 44, 32-61.
[14] Stemann, D. and Trenkler, G. (1993) Leverages and Cochrane-Orcutt Estimation in Linear Regression. Communication in Statistics-Theory and Methods, 22, 1315-1333.
http://dx.doi.org/10.1080/03610929308831088
[15] Barry, A.M., Burney, S.M.A. and Bhatti, M.I. (1997) Optimum Influence of Initial Observatins in regression Models with AR (2) Errors. Applied Mathematics and Computations, 82, 57-65.
http://dx.doi.org/10.1016/S0096-3003(96)00024-0
[16] Judge, G.G., Griffiths, W.E., Hill, R.C., Lutkepohl, H. and Lee, T.C. (1985) The Theory and Practice of Econometrics. 2nd Edition, John Wiley, New York.
[17] Gujarati, D.N. (2003) Basic Econometrics. 4th Edition, McGraw-Hill, New York.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.