Standard errors for the Laspeyres index number with autocorrelated error models

ABSTRACT

This paper deals with the stochastic approach to Laspeyres price index number with the assumption of serial correlation of orders 1 and 2. The first round of estimation provides the estimates of Laspeyres index numbers in the presence of serial correlation assuming that variance is independent of time. In the second round of estimation, we use the weighted least square approach to derive the standard errors of Laspeyres index number assuming variance is dependent on time. These standard errors are linked to the variability of relative prices and are simple to evaluate. It shows that the larger index numbers are expected to estimate with less degree of precision. The results are illustrated with price data of Pakistan.

KEYWORDS:

• Laspeyres price index number
• Serial correlation
• Standard Errors
• Weighted least square.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M10
• 62J12

Acknowledgment

The authors are thankful to the Department of Statistics, University of Karachi, for providing computing and research facilities. The authors thank the anonymous referees of the journal Communication in Statistics—Theory and Methods for their helpful suggestions and comments. They also thank Dr. Tahseen Ahmed Jilani for his research assistance.