Um Tutorial sobre Modelos Garch no R

Perlin, Marcelo Scherer; Mastella, Mauro; Vancin, Daniel Francisco; Ramos, Henrique Pinto

Marcelo Scherer Perlin

Universidade Federal do Rio Grande do Sul, Escola de Administração, Porto Alegre, RS, Brazil.

Marcelo Scherer Perlin*, Universidade Federal do Rio Grande do Sul, Escola de Administração. Rua Washington Luiz, nº 855, Centro, 90040-060, Porto Alegre, RS, Brazil. E-mail address: marceloperlin@gmail.com. https://orcid.org/0000-0002-9839-4268

http://orcid.org/0000-0002-9839-4268

Mauro Mastella

Universidade Federal de Ciências da Saúde de Porto Alegre, Porto Alegre, RS, Brazil.

Mauro Mastella, Universidade Federal de Ciências da Saúde de Porto Alegre. Rua Sarmento Leite, nº 245, Centro Histórico, 90050-170, Porto Alegre, RS, Brazil. E-mail address: mmastella@gmail.com. https://orcid.org/0000-0002-7163-9448

http://orcid.org/0000-0002-7163-9448

Daniel Francisco Vancin

Universidade do Vale do Rio dos Sinos, Programa de Pós Graduação em Ciências Contábeis, Porto Alegre, RS, Brazil.

Daniel Francisco Vancin, Universidade do Vale do Rio dos Sinos, Programa de Pós-graduação em Ciências Contábeis. Av. Dr. Nilo Peçanha, nº 1600, Boa Vista, 91331-002, Porto Alegre, RS, Brazil. E-mail address: daniel_vancin@hotmail.com. https://orcid.org/0000-0001-6303-0555

http://orcid.org/0000-0001-6303-0555

Henrique Pinto Ramos

Universidade Federal do Rio Grande do Sul, Escola de Administração, Porto Alegre, RS, Brazil.

Henrique Pinto Ramos, Universidade Federal do Rio Grande do Sul, Escola de Administração. Rua Washington Luiz, nº 855, Centro, 90040-060, Porto Alegre, RS, Brazil. E-mail address: hpramos4@gmail.com. https://orcid.org/0000-0002-7998-7033

http://orcid.org/0000-0002-7998-7033

*Corresponding Author

Editor-in-chief: Wesley Mendes-Da-Silva (Fundação Getulio Vargas, EAESP, Brazil) https://orcid.org/0000-0002-5500-4872

Associate Editor: Henrique Castro Martins (PUC Rio, IAG, Brazil) https://orcid.org/0000-0002-3186-4245

Reviewers: Pedro Raffy Vartanian (Universidade Presbiteriana Mackenzie, Brazil) https://orcid.org/0000-0002-1492-7128

Júlio César Araújo da Silva Junior (Universidade Federal de Viçosa, Departamento de Economia, Brazil) https://orcid.org/0000-0002-6037-6363

One of the reviewers chose not to disclose his/her identity.

Marcelo Scherer Perlin*, Universidade Federal do Rio Grande do Sul, Escola de Administração. Rua Washington Luiz, nº 855, Centro, 90040-060, Porto Alegre, RS, Brazil. E-mail address: marceloperlin@gmail.com. https://orcid.org/0000-0002-9839-4268

Mauro Mastella, Universidade Federal de Ciências da Saúde de Porto Alegre. Rua Sarmento Leite, nº 245, Centro Histórico, 90050-170, Porto Alegre, RS, Brazil. E-mail address: mmastella@gmail.com. https://orcid.org/0000-0002-7163-9448

Daniel Francisco Vancin, Universidade do Vale do Rio dos Sinos, Programa de Pós-graduação em Ciências Contábeis. Av. Dr. Nilo Peçanha, nº 1600, Boa Vista, 91331-002, Porto Alegre, RS, Brazil. E-mail address: daniel_vancin@hotmail.com. https://orcid.org/0000-0001-6303-0555

Henrique Pinto Ramos, Universidade Federal do Rio Grande do Sul, Escola de Administração. Rua Washington Luiz, nº 855, Centro, 90040-060, Porto Alegre, RS, Brazil. E-mail address: hpramos4@gmail.com. https://orcid.org/0000-0002-7998-7033

Authors' Contributions

1^st author: project administration (lead); writing - original draft (lead); writing - review & editing (lead); software (lead); data curation (lead); formal analysis (lead); investigation (equal); visualization (equal); validation (equal); conceptualization (equal); methodology (equal); resources (equal).

2^nd author: visualization (equal); validation (equal); methodology (equal); investigation (equal), resources (equal), writing - original draft (supporting); writing - review & editing (supporting); data curation (supporting); formal analysis (supporting).

3^rd author: visualization (equal); validation (equal); methodology (equal); investigation (equal), resources (equal), writing - original draft (supporting); writing - review & editing (supporting); data curation (supporting); formal analysis (supporting).

4^th author: visualization (equal); validation (equal); methodology (equal); investigation (equal), resources (equal), writing - original draft (supporting); writing - review & editing (supporting); data curation (supporting); formal analysis (supporting).

Conflict of Interests

The authors have stated that there is no conflict of interest.

Model	Variance equation
ARCH (q)	$R_{t} = σ_{t} ɛ_{t}, σ_{t}^{2} = α_{0} + α_{1} R_{t - 1}^{2} + ... + α_{q} R_{t - q}^{2}$
GARCH (p,q)	$R = σ_{t} ɛ_{t}, σ_{t}^{2} = α_{0} + Σ_{i = 1}^{q} α_{i} R_{t - i}^{2} + Σ_{j = 1}^{p} β_{j} σ_{t - q}^{2}$
EGARCH (p,q)	$R_{t} = σ_{t} ɛ_{t}, \ln (σ t^{2}) = α_{0} + Σ_{i = 1}^{q} \frac{\|R_{t - i}\| + δ_{i} R_{t - i}}{σ_{t - i}} + Σ_{j = 1}^{p} β_{j} \ln (σ_{t - j}^{2})$
GJR-GARCH (p,q)	$R_{t} = σ_{t} ɛ_{t}, σ_{t}^{2} = α_{0} + Σ_{i = 1}^{q} (α_{i} + γ_{i} N_{t - i}) R_{t - i}^{2} + Σ_{j = 1}^{p} β_{j} σ_{t - j}^{2}$

Filename	Description
00-Prepare_Computer.R	Mandatory step. Setup the computer by installing all required R packages. Also provides further steps for alternative operating systems such as Linux.
01-Get_Index_Data.R	Using the internet and R package BatchGetSymbols, imports a dataset of prices of the Ibovespa index.
02-Do_Descriptive_Figures.R	Creates and saves the descriptive figure presented in the paper, Figure 2 and Figure 3.
03-Do_ARCH_Test.R	Performs the ARCH test in the data and exports Table 3.
04-Estimate_Garch_Model.R	Estimate an introductory GARCH model in three different volatility formulas and exports the estimation results into a html file (Table 4).
05-Find_Best_Garch_Model.R	Finds the best ARMA(ar,ma)-GARCH(p,q) model for the dataset, including changes in variance equation and distribution parameter. Also produces Figure 4.
06-Simulate_Garch_Model.R	Simulates the previous GARCH model and plot simulated paths and probabilities. Produces Figures 5 and 6.

Lag	LMStatistic	pvalue
1	597,2498568	6,6371E-132
2	1234,384594	9,053E-269
3	1280,125377	3,0214E-277
4	1293,000984	1,0956E-278
5	1326,368275	1,2376E-284

	Model 1	Model 2	Model 3
mu	0.001^ p < 0.01; *p < 0.05.	0.000	0.000
	(0.000)	(0.000)	(0.000)
omega	0.000^* ***** p < 0.001;	-0.234^* ***** p < 0.001;	0.000^* ***** p < 0.001;
	(0.000)	(0.009)	(0.000)
alpha1	0.081^* ***** p < 0.001;	-0.081^* ***** p < 0.001;	0.021^* ***** p < 0.001;
	(0.004)	(0.008)	(0.003)
beta1	0.894^* ***** p < 0.001;	0.971^* ***** p < 0.001;	0.899^* ***** p < 0.001;
	(0.006)	(0.001)	(0.005)
gamma1		0.145^* ***** p < 0.001;	0.102^* ***** p < 0.001;
		(0.012)	(0.011)
Variance Model	sGARCH	eGARCH	gjrGARCH
Distribution	norm	norm	norm
Log likelihood	13494.206	13528.679	13532.310
AIC	-5.412	-5.426	-5.427
BIC	-5.407	-5.419	-5.421

[1] *Corresponding Author

Brasil

Brasil

Um Tutorial sobre Modelos Garch no R

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