Metamodel-Based Decision Support for Forecasting Model Selection in Royalty Valuation

June 2026/ PFE N° : 102
ROYAUME DU MAROC
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HAUT COMMISSARIAT AU PLAN
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INSTITUT NATIONAL
DE STATISTIQUE ET D’ECONOMIE APPLIQUEE
Final Year Project
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Prepared by : Ms. MERYEM FAKIR
Under the supervision of : Mr. ILYAS HIMMICH (INSEA)
Mr. JUSTUS BARON (BRELA)
Mr. SANTIAGO BERGALLO (BRELA)
Publicly defended as a partial requirement for the degree of
State Engineer Degree
Field of Study: OPERATIONS RESEARCH AND DECISION SUPPORT
Examination Committee :
 Mr. ILYAS HIMMICH ( INSEA)
 Mr. FAYCAL MIMOUNI ( INSEA)
 M. JUSTUS BARON (BRELA)
Metamodel-Based decision support for forecasting
model selection in royalty valuation
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Dedication
To my parents: I wish to express my deepest respect and regard for your unwavering
support, your encouragement, and your boundless love. I dedicate this work to you in
recognition of the love you give me every day. This modest work is the fruit of all the
sacrifices you have made for my education. May Allah the Almighty keep you in good
health and fill your lives with happiness.
To my sisters, and especially Amina and FatimaEzzahra: All the moments I have
shared with you since my childhood are a testament to my deep gratitude for the help
and love you have always provided me. You have never ceased to support, comfort,
and encourage me through every step of this journey. I am grateful to you from the
bottom of my heart for everything you have done for me.
To my dear friends Meryem and Kawtar: Thank you for your unwavering support,
your belief in me, your trust, and your encouragement. The time you dedicated to me
and the kind words you offered whenever I needed them meant more than you will ever
know. I am sincerely grateful to have you by my side.
To my professors: Please find here the expression of my deepest respect and ap-
preciation for the guidance and efforts you have never ceased to provide. I will remain
eternally thankful.
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Acknowledgments
This report is the result of sustained work, which would not have been possible
without the support and guidance of a number of individuals. I take this opportunity
to express my sincere gratitude to all those who contributed to its completion.
I begin by thanking Allah for granting me the strength and opportunity to carry
out this experience.
I would like to express my sincere gratitude to my family for their moral support
and constant encouragement throughout this period. Your love and belief in me have
been my greatest source of strength.
I extend my appreciation to Dr. Justus BARON, Founder and Chief Executive Of-
ficer of BRELA, for welcoming me into his institution and for his guidance, availability,
and support throughout this internship, as well as for providing access to all necessary
resources and information.
I would also like to thank Mr. Santiago BERGALLO and Mr. Yanis Luca GAMARRA
for their advice, explanations, and support throughout the course of this work. I equally
thank Ms. Kenza ELKABIR and the entire BRELA team for their collegiality and the
pleasant working environment they maintained throughout my time there.
I would like to express my deep gratitude to my supervisor, Professor Ilyas HIM-
MICH, for his continuous guidance, valuable advice, and close follow-up throughout
this work. His rigor and availability made a decisive difference in the quality of this
project.
I would also like to extend my heartfelt gratitude to the Operations Research de-
partment at INSEA, whose teaching and support over these three years have been
fundamental to my development as an engineer. I am particularly grateful to Mr.
M. Ouzineb, Mr. R. Benmansour, and Mr. A. Kadrani, whose dedication, passion
for the field, and generosity with their time have left a lasting mark on my academic
journey. I would like to thank my friends for their support, encouragement, and pres-
ence throughout this period. The moments we shared made this journey all the more
meaningful.
Finally, I would like to thank all my professors at INSEA for the quality of their
teaching and supervision, which provided me with the necessary foundations to under-
take this internship and bring this work to completion.
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Abstract
This work addresses the problem of forecasting phone shipment volumes for use in
Standard-Essential Patent (SEP) royalty valuation. In patent litigation, when compa-
rable licenses take the form of lump-sum payments, reconstructing a per-unit royalty
rate requires estimating the sales expectations that parties held at the time of the
agreement. Existing approaches rely either on subjective expert testimony or on ac-
tual sales figures, both of which carry significant limitations in a litigation context. To
overcome these limitations, we develop a data-driven decision framework that produces
objectively reasonable forecasts grounded solely in publicly available information.
The framework consists of three contributions. First, we propose a Best-Worst
Method (BWM)-based metamodel that automatically selects the most suitable fore-
casting model among five candidates, namely SARIMA, ETS, BSTS, Random Forest,
and Gradient Boosting, based on four time-series features extracted from each com-
pany’s shipment series: trend, seasonality, curvature, and spikiness. The fixed score
matrix governing model assignment is estimated via Simulated Annealing on an aug-
mented dataset of artificially generated series. Second, we develop a constrained linear
programme to handle the high rate of missing observations in the panel, while enforcing
global consistency with the known total market shipments at each period. Each im-
puted value is assigned a confidence interval reflecting the reliability of the estimation.
Third, we assess the impact of this imputation procedure on both model selection and
forecast accuracy through a comparative analysis conducted on three companies.
The framework is validated against professional analyst forecasts for major manu-
facturers, demonstrating that the proposed approach constitutes a transparent, repli-
cable, and objective basis for reconstructing historical sales expectations in the context
of SEP damages valuation.
Keywords: Standard-Essential Patents, FRAND royalty valuation, forecasting model
selection, Best-Worst Method, missing value imputation, time series features, Simu-
lated Annealing.
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