Annals of Applied Statistics

On the evolution of the United Kingdom price distributions

Ba Chu, Kim Huynh, David Jacho-Chávez, and Oleksiy Kryvtsov

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We propose a functional principal components method that accounts for stratified random sample weighting and time dependence in the observations to understand the evolution of distributions of monthly micro-level consumer prices for the United Kingdom (UK). We apply the method to publicly available monthly data on individual-good prices collected in retail stores by the UK Office for National Statistics for the construction of the UK Consumer Price Index from March 1996 to September 2015. In addition, we conduct Monte Carlo simulations to demonstrate the effectiveness of our methodology. Our method allows us to visualize the dynamics of the price distribution and uncovers interesting patterns during the sample period. Further, we demonstrate the efficacy of our methodology with an out-of-sample forecasting algorithm which exploits the time dependence of distributions. Our out-of-sample forecasts compares favorably with the random walk forecast.

Article information

Ann. Appl. Stat., Volume 12, Number 4 (2018), 2618-2646.

Received: July 2017
Revised: April 2018
First available in Project Euclid: 13 November 2018

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Zentralblatt MATH identifier

Consumer price distributions nonparametric methods Functional Principal Component Analysis (FPCA) stratified random sampling strong mixing


Chu, Ba; Huynh, Kim; Jacho-Chávez, David; Kryvtsov, Oleksiy. On the evolution of the United Kingdom price distributions. Ann. Appl. Stat. 12 (2018), no. 4, 2618--2646. doi:10.1214/18-AOAS1172.

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Supplemental materials

  • Supplement to “On the evolution of the United Kingdom price distributions.”. In supplementary material we provide mathematical proofs of all the main results in the manuscript.