Estimating the Consumer Price Index using the lognormal diffusion process with exogenous factors: The Colombian case

Antonio Barrera; Arnold de la Peña Cuao; Juan José Serrano-Pérez; Francisco Torres-Ruiz; Antonio Barrera; Arnold de la Peña Cuao; Juan José Serrano-Pérez; Francisco Torres-Ruiz

doi:10.3934/math.2025155

AIMS Mathematics

2025, Volume 10, Issue 2: 3334-3380. doi: 10.3934/math.2025155

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Estimating the Consumer Price Index using the lognormal diffusion process with exogenous factors: The Colombian case

1.
Department of Mathematical Analysis, Statistics and Operations Research and Applied Mathematics, University of Málaga, Bulevar Louis Pasteur 31, 29010, Málaga, Spain
2.
Institute of Mathematics of the University of Granada (IMAG), Calle Ventanilla 11, 18001, Granada, Spain
3.
Department of Statistics and Operations Research, University of Granada, Avenida de Fuente Nueva s/n, 18071, Granada, Spain

Received: 10 November 2024 Revised: 02 February 2025 Accepted: 14 February 2025 Published: 21 February 2025
MSC : 60J60, 62M20

In this paper, a model based on the lognormal diffusion process with exogenous factors was considered, aiming to describe the dynamics of the basic Consumer Price Index (CPI) in Colombia. To this end, a Bayesian procedure was employed for the selection of factors using real data from different economic sources such as the Central Bank (Banco de la República de Colombia), among others. A model with five exogenous factors (economic variables) was obtained, carrying out maximum likelihood estimation for its parameters. Fitting and forecasting procedures under different conditions showed that the proposed model outperformed the predictions made by the Central Bank. In addition, potential future economic scenarios were analyzed for testing purposes. This model provided valuable insight into the main determinants of inflation in Colombia, reflecting the importance of the factors under the control of economic authorities, labor market dynamics, and external economic conditions. This new approach also gave rise to asking questions concerning impact analysis of economic shocks, and the search of possible scenarios for given CPI dynamics.
- lognormal diffusion process,
- exogenous factors,
- inference in diffusion processes,
- Bayesian model selection,
- economic forecasts
Citation: Antonio Barrera, Arnold de la Peña Cuao, Juan José Serrano-Pérez, Francisco Torres-Ruiz. Estimating the Consumer Price Index using the lognormal diffusion process with exogenous factors: The Colombian case[J]. AIMS Mathematics, 2025, 10(2): 3334-3380. doi: 10.3934/math.2025155

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Abstract

In this paper, a model based on the lognormal diffusion process with exogenous factors was considered, aiming to describe the dynamics of the basic Consumer Price Index (CPI) in Colombia. To this end, a Bayesian procedure was employed for the selection of factors using real data from different economic sources such as the Central Bank (Banco de la República de Colombia), among others. A model with five exogenous factors (economic variables) was obtained, carrying out maximum likelihood estimation for its parameters. Fitting and forecasting procedures under different conditions showed that the proposed model outperformed the predictions made by the Central Bank. In addition, potential future economic scenarios were analyzed for testing purposes. This model provided valuable insight into the main determinants of inflation in Colombia, reflecting the importance of the factors under the control of economic authorities, labor market dynamics, and external economic conditions. This new approach also gave rise to asking questions concerning impact analysis of economic shocks, and the search of possible scenarios for given CPI dynamics.

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