I'm a backpacker sharing my journey into quantitative financial risks in the hopes that you don't have to suffer on your journey too.

Henrique Costa

<strong>
 Rambling (proxy for an introduction)
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We are experiencing the chaos of the information age, and its technological advents with voracious evolution and expansion. And in the midst of all this we have the advent of Big Data that has reached the delights of many with Data Science, Machine Learning and Artificial Intelligence. As a result, the idea of mathematical and statistical “models” became the rage, gaining visibility.

Trivia Series: Regression

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<strong>
 Modeling Principles
</strong>
Almost all, if not all, applied science is based on the idea of a model. There are problems in the real world, and we would like to create a theory to solve such problems. One of the pillars or the main foundation of quantitative modeling is its effectiveness. But how can a model be effective? By demonstrating that it is simple, reproducible, and applicable in other areas of knowledge.

Trivia Series: Modelling foundations

I started this website some time ago with the aim of writing down the expansion of my knowledge and experience in the area of financial risk management. And also other things like programming with R, econometric modeling and a little about
<em>
 data science
</em>
and
<em>
 machine learning
</em>
. So I’m going to use this publication as a starting point, and start discussing texts and examples applied to financial risks.

A few words about risk management

Having decided to improve my skills in the short space of time left between my professional life and personal life, I started researching the available data science options.

For me, the choice was R or Python

Na publicação de hoje, quero trazer uma brincadeira que fiz comigo mesmo, um pequeno incentivo para voltar a publicar conteúdos sobre R (eu já estava enferrujado) entre outros assunto sobre economia. Passeando pelo instagram, encontrei um perfil que pública muita informação sobre economia em formato de visualização, o Economista Visual.

Reproduzindo gráfico do Economista Visual - Valor da cesta básica (PT-BR)

In today’s post, I want to start a discussion about the use of mathematics and statistics in economics, and with this shocking sentence:  When a person studies economics for the first time, it is likely that they will not encounter “crazy” equations that go beyond basic mathematics.

The mathematization of Economics

When it comes to job titles, data scientist is one of the biggest buzzwords in recent years. It is also one of the fastest growing fields of professional activity. Can an economist really be a data scientist? What skills are needed?

Can Economists Become Data Scientists?

I will present here some personal reflections on a concept that is considered very simple and perhaps common in economics, but which is labeled as the height of ignorance for making an assumption that cannot be observed in reality, but which in my view is a mistake. mistake.

The Ceteris Paribus Condition

Risk Taker!

[![](https://hcostax.com/blog/modelling_foundations/feature.jpg){.img-fluid}](feature.jpg){.lightbox
gallery="quarto-lightbox-gallery-1"}

:::::::: {#modeling-principles .section .level1}
# Modeling Principles

Almost all, if not all, applied science is based on the idea of a model.
There are problems in the real world, and we would like to create a
theory to solve such problems.

One of the pillars or the main foundation of quantitative modeling is
its effectiveness. But how can a model be effective? By demonstrating
that it is simple, reproducible, and applicable in other areas of
knowledge.

A second pillar of modeling is the ability to make decisions and
choices. And such choices are, and should be, made at any and all times
in the process of specifying a model.

Another pillar is testing. A model cannot exist without its due testing
process. These tests are experiments, where choices must be made and
tested to ensure the effectiveness of the model.

A model has a simple objective: to be a simplistic representation of the
real world. Based on the central limit theorem, sampling, and
randomness, a model is nothing more than a specific/local/unitary idea
that represents the general/total.

The sample will never be equal to the population, and a unit will never
be the total, but a model finds a pattern that it will assume as central
and how far the units are from this pattern, which we formally call
"effect" and "residue".

The "effect" is what we seek, in a simplified way, to solve the real
problem, and the "residue" is what corroborates our effect, the residue
is the acid test of the model and will demonstrate how too simple the
model is, or how too complex the model is.

It is necessary to move between the simple and the complex to centralize
the effect. If the effect is central, and the residue is coherent and
parsimonious, then the model has fulfilled its main objective: in a
simple way, to represent the complex reality.

And here is how this process works:

[![](https://hcostax.com/blog/modelling_foundations/img/flux_one.png){.img-fluid}](./img/flux_one.png){.lightbox
gallery="quarto-lightbox-gallery-2"}

  

The problems observed in the real world are very complex, and to solve
them we need to look for the exact solution.

But if the problem is complex, the solution must be just as complex, and
that is why it is necessary to simplify. We can solve some problems with
approximate solutions, and this is feasible. However, an approximate
solution requires an approximate problem.

In this sense, we observe the real problem and conditionally create a
simplified version that we call an approximate problem, since it is in
fact close to the real one, only some simplifications have occurred to
allow us to study, estimate, test and theorize.

From the approximated (simplified) problem it is possible to obtain an
exact solution. Therefore, it is feasible that the exact solution of the
approximated problem is the approximate solution of the real problem.

And so the fundamental process of modeling occurs:

[![](https://hcostax.com/blog/modelling_foundations/img/flux_two.png){.img-fluid}](./img/flux_two.png){.lightbox
gallery="quarto-lightbox-gallery-3"}

This very simplistic process allows us to see that the model is nothing
more than a simplification of the real problem, as I mentioned before.
Using the model, it is possible to analyze the results found without
needing to have the solution. The analysis of the model serves to
understand the nuances of the results in order to draw conclusions about
the simplification that was created. Sometimes we will not have the
solution we are looking for, but we can have conclusions, even if
simplified, about the real problem.

The analysis and conclusions of the model allow us to generate
inference, which is the deduction made based on the reasoning generated
by the analysis, and from the inference we can explain, even if in a
simplified way, the real problem and make estimates and predictions.

The final step is the decision or choice that we make based on the
understanding and estimates. With this, we monitor and verify whether
our model is sufficient to reach an approximate solution to the real
problem. Therefore, we verify whether our choices for applying the model
results are meeting the expectations based on the estimates of our
model.

If our model is not sufficient, that is, if the estimates are not
observed in the real world, we need to recalibrate this model or even
specify a new one. This means that we failed in one of the steps
outlined in the flows above.

We usually make a lot of mistakes when simplifying the problem, in the
initial specification of the model. It seems trivial, and it is, but
this step requires a lot of creativity, because modeling is an art. If
we simplify the model too much, it loses its sensitivity to reality, and
if we simplify it too little, the model can be so complex that it cannot
be distinguished from the real problem, and this causes failure, due to
the difficulty in obtaining an exact solution.

The second point where we fail the most is in decision-making and
verification, because this process can be expensive. Monitoring is a
cost that may never be proposed or included in a project (specifying a
model). The choice of how to apply it can also be made without due
proportions. In general, the decision-making process can be poorly done,
generating the inconsistency that leads the model to failure.

Generally, the person who makes the decisions is not always the same
person who collected the information, nor may it be the person who
specified and executed the model, much less the person who performed the
prior analysis and reached the conclusions and inferences.

The modeling process is a process that has an indefinite temporality,
but it has steps that need to be respected, as if it were a natural
rule. So far, these rules are valid and work very well. For example, we
have many powerful models that are sometimes defined theoretically and,
when applied, perform their role accurately.

There is no defined time, but it can have a cost. The longer it takes,
the higher the cost. This is only valid if, and only if, time has a
monetary value (such as working hours, the researcher's salary or the
project budget).

So, even if it is trivial, do not ignore this knowledge. A model is not
specified in minutes, and executing a famous or currently fashionable
algorithm is not enough. It is necessary to abstract in order to think
about the complexity of the real problem, as well as to think about the
conditioning paths of simplification.

A very interesting topic in simplifying a real problem and finding an
approximate solution is the idea of [ceteris
paribus](https://hcostax.com/blog/ceteris_paribus/) used in economics,
where the general idea is to apply, in a subjective and abstract way, an
implicit equilibrium condition in which the relationship between
phenomena is balanced and therefore any change in the other phenomena
not used in the model has no effect, isolating only the phenomenon
chosen to estimate the effect of one phenomenon on the other in order to
draw conclusions, make inferences and make decisions.

From now on, you already know how to start your modeling process, which
is not just visiting your data lake, selecting a multitude of variables
and running a convolutional neural network calculation and hoping that
your model is as accurate as your accuracy test tells you it is.
Sometimes, a linear regression with 3 variables is enough, and this
would be following the first step of simplification.

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## Reuse {#reuse .anchored .quarto-appendix-heading}

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[CC BY 4.0](https://creativecommons.org/licenses/by/4.0/){rel="license"}

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## Citation {#citation .anchored .quarto-appendix-heading}

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For attribution, please cite this work as:
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::: {#ref-costa2024 .csl-entry .quarto-appendix-citeas}
Costa, Henrique. 2024. "Trivia Series: Modelling Foundations." August
25, 2024. <https://doi.org/10.59350/rzbj1-p3865>.
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