Detecting change-points and trends in the petrol consumption and petrol prices
Research Group: Camilo Santa Cruz, Benedikt Schmidt and Tanzer Siddique
E-mail: camilo.santacruz@tu-dortmund.de
Msc. Econometrics
Case Studies
July 22 - Sommer Semester 2025
Introduction
The present research project investigates the presence of change-points in petrol consumption and prices, using two datasets of refueling records: Karriert (Database 1, 1986-2015) and Grau (Database 2, 1996-2014). To this end, a range of different statistical techniques are employed, including Linear Auto- regressive models and structural break tests such as: the Chow test, CUSUM, CUSUMSQ, the Likelihood Ratio-At Most One Change (LR-AMOC), and the Pruned Exact Linear Time (PELT) algorithm.
The study is organized as follows: Chapter 2 describes the data generation process, provides an overview of the variables used, and evaluates the quality and nature of the measurements. Chapter 3 outlines the methodological strategy for addressing data quality issues, details the assumptions underlying the construction of the consumption function, presents the theoretical properties of the change-point detection tests, as well as the accuracy measure for detecting change-points. Chapter 4 presents the empirical results, focusing on the identification of change-points in both price and petrol consumption, the relationship between consumption shifts and vehicle changes, and the impact of the introduction of the Euro on price behavior.
At an overall level, the results for petrol consumption reveal that: In Database 1, initial analyses with PELT yielded multiple non-interpretable change-points. However, when liters were analyzed directly with the search constrained to a single break, the LR-AMOC method successfully identified the vehicle change, achieving an Absolute Index Location Error (AIE) of 3. For Database 2, PELT detected a single change-point (AIE = 1), corresponding to the documented vehicle substitution. The recursive Chow test applied with a Linear Trend Model (LTM) identified the breakpoints in years of car change in line with PELT and LR-AMOC estimates.
For petrol prices: In Database 1, recursive Chow tests applied to AR(1) models with a deterministic trend and to first-difference specifications revealed significant structural breaks in 1999 and 2002. These breakpoints align with the two phases of the Euro’s introduction (accountability in 1999 and physical circulation in 2002). The CUSUM test did not detect significant coefficient shifts, while CUSUMSQ indicated parameter instability during these periods. This result is consistent with theoretical expectations, as CUSUM is more sensitive to mean shifts, whereas CUSUMSQ is better suited for detecting variance changes.
In Database 2, structural breaks in mean and variance were observed only under a Linear Trend Model (LTM). When auto-regressive terms were included (with deterministic trend or in FD), no significant breaks were detected.
Across all models, coefficients generally exhibited the desired theoretical properties of stability and no evidence of unit roots. However, residual diagnostics and Shapiro-Wilk tests consistently rejected normality for all specifications of both consumption and price.
Future research directions include refining the price variable by incorporating higher-frequency exchange rate data, as well as extending the application of PELT and LR-AMOC methods to price series and exploring the joint effects of the Euro’s introduction on price and consumption within a multivariate linear framework.