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Investigating stochastic volatility and jumps in inflation dynamics: an empirical evidence with oil price effect

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Abstract

This paper deals with an analysis of the inflation dynamics using Stochastic Differential Equations framework. We design a novel model which aims to reveal the outstanding features of the inflation rate including stochastic volatility and spikes. The considered modeling approach enhances the pre-existing models by introducing stochastic volatility, mean-reversion and jumps in the concerned state process. The mathematical framework combines an economic model derived from inflation theories and a diffusion model based on probability analysis, which are successfully tested using empirical estimation and simulation tools. The Joint Maximum Likelihood equation is then calculated to estimate the model parameters for the U.S. inflation rate. We find that integrating stochastic volatility and jumps in the inflation rate process is absolutely essential to effectively simulate the actual dynamics. We derive inflation rate responses to oil price shocks and confirm the validity of the resulting models by their potential to incorporate observed inflation dynamics. The study provides a realistic and reproducible modeling approach to address the inflation rate challenges.

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Data Availability Statement

This manuscript has associated data in a data repository. [Author comments: The data that support the findings of this study are freely available from Federal Reserve Economic Data (FRED) and Energy Information Administration (EIA).]

Notes

  1. A representation of volatility instead of variance process in SV models is given by Stein and Stein [52].

  2. For a similar representation, see for instance Larsson and Nossman [40] model.

  3. As the reader will notice, the persistence value is given by \((1-\beta )\) for inflation rate and \((1-\kappa )\) for volatility.

  4. It is calculated as the khi-squared law of the log-likelihood using the number of parameters as the degree of freedom.

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Acknowledgements

The authors of this paper would like to extend heartfelt gratitude to the High Commission for Planning (HCP)—Morocco for their commitment to fostering a collaborative environment between the HCP research team and the Academia. This collaboration has been instrumental in advancing our work. Special thanks are due to the High Commissioner for Planning, Ahmed LAHLIMI ALAMI, for his insights and dedication to promoting scientific inquiry, which have inspired a deeper understanding and appreciation of the economic field in Morocco. This collaboration has been a cornerstone of our achievements, and we are profoundly thankful for the opportunity to work in such a stimulating and supportive research environment.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Technology, Cadi Ayyad University, 549, 40.000, Marrakesh, Morocco

    Mariem Bikourne, Khadija Akdim & Adil Ez-Zetouni

  2. High Commission for Planning, 31-3, 178, Rabat, Morocco

    Ayache Khellaf & Adil Ez-Zetouni

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  1. Mariem Bikourne
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  2. Khadija Akdim
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  4. Adil Ez-Zetouni
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Correspondence to Khadija Akdim.

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Appendix: Pseudocodes

Appendix: Pseudocodes

Algorithm 1
figure a

Algorithm to obtain the parameter estimation

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Algorithm 2
figure b

Algorithm to obtain the simulation paths of inflation rate

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Algorithm 3
figure c

Algorithm to obtain the Impulse Response Function

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Bikourne, M., Akdim, K., Khellaf, A. et al. Investigating stochastic volatility and jumps in inflation dynamics: an empirical evidence with oil price effect. Eur. Phys. J. Plus 138, 1142 (2023). https://doi.org/10.1140/epjp/s13360-023-04778-5

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