On the evolution of the United Kingdom price distributions

Abstract

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 that exploits the time dependence of distributions. Our out-of-sample forecast compares favorably with the random walk forecast.

Big data forecasting of South African inflation

“…Hence, these datasets also incorporate a period of 12 months, over which various lockdown measures were imposed. When measured at higher levels of disaggregation, it has been suggested that such a dataset contains information that relates to the idiosyncratic behaviour of consumer prices, where the frequency and dispersion of price adjustments can vary across items and over time (Chu et al 2018;Petrella et al 2019;Stock and Watson 2020;Chetty et al 2020;Carvalho et al 2020;Cavallo 2020). Given these characteristics of the data, we could conceive that when the price indices are subjected to various forms of aggregation, their predictive power may decline.…”

WITHDRAWN: Forecasting UK inflation bottom up

“…But the dynamics and inter-dependencies of disaggregated price items are complex and the distributional moments of item indices do not necessarily translate linearly to the aggregate level. As such, prices of different items or sectors can behave asynchronously, the frequency and dispersion of price adjustments can vary across items and over time, and the characteristics of certain groups of items can be over-represented in the aggregate (Chu et al, 2018;Petrella et al, 2019;Stock and Watson, 2019). This suggests that by incorporating item indices directly into a flexible model the forecaster is able to exploit a rich set of information (Hendry and Hubrich, 2011).…”

Nonparametric Estimation of Repeated Densities with Heterogeneous Sample Sizes

“…Most of the existing work consider random densities that are completely observed or are reconstructed from densely observed data points. This type of density objects was first analyzed by Kneip and Utikal (2001) by directly applying functional principal component analysis (FPCA), a technique that has also been applied to analyze the trend of time-varying densities (Huynh et al 2011;Tsay 2016;Chu et al 2018). Recognizing the density constraints, Delicado (2011) and Petersen and Müller (2016) proposed to analyze densities by utilizing one-to-one transformations to map them into an unconstrained space, where the transformed densities are then represented using FPCA and subsequently back transformed into densities.…”