Um Tutorial sobre Modelos Garch no R



Artigo principal Conteúdo

Marcelo Scherer Perlin
Mauro Mastella
Daniel Francisco Vancin
Henrique Pinto Ramos

Resumo

Contexto: a modelagem de volatilidade é uma técnica avançada em econometria financeira, com diversas aplicações em pesquisa acadêmica. Objetivo: neste artigo tutorial abordaremos o tópico da modelagem de volatilidade na plataforma R. Discutiremos a lógica subjacente dos modelos GARCH, seus processos de representação e estimação, juntamente com um exemplo descritivo de uma aplicação no mundo real. Métodos: usamos um modelo GARCH para investigar quanto tempo levará, após a última crise, para que o índice Ibovespa volte a atingir seu pico histórico mais uma vez. Os dados empíricos cobrem o período entre os anos 2000 e 2020, incluindo a crise financeira de 2009 e o episódio atual de 2020 da pandemia do COVID-19. Conclusão: de acordo com nosso modelo GARCH, as chances de o Ibovespa atingir o seu pico passam de 50% um ano e seis meses após junho de 2020. Todos os dados e códigos R usados para produzir este tutorial estão disponíveis gratuitamente na internet e todos os resultados podem ser facilmente replicados.



Histórico de Downloads

Não há dados estatísticos.


Detalhes do artigo

Como Citar
Perlin, M. S., Mastella, M., Vancin, D. F., & Ramos, H. P. (2020). Um Tutorial sobre Modelos Garch no R. Revista De Administração Contemporânea, 25(1), e200088. https://doi.org/10.1590/1982-7849rac2021200088
Seção
Artigos

Referências

Aas, K. (2004). To log or not to log: The distribution of asset returns (Technical Report SAMBA nº 03/04), Oslo, Norway, Norwegian Computing Center, Applied Research and Development. Retrieved from https://www.nr.no/files/samba/bff/SAMBA0304.pdf
Aït-Sahalia, Y., Mykland, P. A., & Zhang, L. (2011). Ultra high frequency volatility estimation with dependent microstructure noise. Journal of Econometrics, 160(1), 160-175. https://doi.org/10.1016/j.jeconom.2010.03.028
Ardia, D., Bluteau, K., Boudt, K., Catania, L., & Trottier, D.-A. (2019). Markov-switching GARCH models in R: The MSGARCH package. Journal of Statistical Software, 91(4), 1-38. http://dx.doi.org/10.18637/jss.v091.i04
Bauwens, L., Laurent, S., & Rombouts, J. V. K. (2006). Multivariate GARCH models: A survey. Journal of Applied Econometrics, 21(1), 79-109. https://doi.org/10.1002/jae.842
Bernardino, W., Brito, L., Ospina, R., & Melo, S. (2018). A GARCH-VaR investigation on the Brazilian sectoral stock indices. Brazilian Review of Finance, 16(4), 573-610. http://dx.doi.org/10.12660/rbfin.v16n4.2018.74676
Black, F. (1976, August). Studies of stock market volatility changes. Proceedings of the 1976 Meeting of the Business and Economic Statistics Section, American Statistical Association, Washington, DC, USA.
Bollerslev, T., Engle, R. F., & Nelson, D. B. (1994). Arch models. Handbook of Econometrics, 4, 2959–3038.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
Box, G. E. P., & Jenkins, G. M. (1976). Time series analysis: Forecasting and control San Francisco. San Francisco, CA: Holden Day.
Brockwell, P. J., & Davis, R. A. (2016). Introduction to time series and forecasting. New York, NY: Springer International Publishing
Bueno, R. D. S. (2011). Econometria de séries temporais. São Paulo, SP: Cengage Learning
Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods & Research, 33(2), 261-304. https://doi.org/10.1177%2F0049124104268644
Byström, H. N. E. (2004). Orthogonal GARCH and covariance matrix forecasting: The Nordic stock markets during the Asian financial crisis 1997–1998. The European Journal of Finance, 10(1), 44-67. https://doi.org/10.1080/1351847032000061379
Caldeira, J. F., Moura, G. V., Perlin, M. S., & Santos, A. A. P. (2017). Portfolio management using realized covariances: Evidence from Brazil. EconomiA, 18(3), 328-343. https://doi.org/10.1016/j.econ.2017.04.002
Carson, J. M., Elyasiani, E., & Mansur, I. (2008). Market risk, interest rate risk, and interdependencies in insurer stock returns: A system‐GARCH model. Journal of Risk and Insurance, 75(4), 873-891. https://doi.org/10.1111/j.1539-6975.2008.00289.x
Cont, R. (2001). Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1(2), 223–236. https://doi.org/10.1080/713665670
Costa, C. H., Porto Junior, S. S., & Menezes, G. R. (2018). Um estudo empírico da dinâmica da correlação do retorno das ações do Brasil. Brazilian Review of Finance, 16(4), 635-667. http://dx.doi.org/10.12660/rbfin.v16n4.2018.72142
De Goeij, P., & Marquering, W. (2004). Modeling the conditional covariance between stock and bond returns: A multivariate GARCH approach. Journal of Financial Econometrics, 2(4), 531-564. https://doi.org/10.1093/jjfinec/nbh021
Deng, L., Ma, C., & Yang, W. (2011). Portfolio optimization via pair copula-GARCH-EVT-CVaR model. Systems Engineering Procedia, 2, 171-181. https://doi.org/10.1016/j.sepro.2011.10.020
Engle, R. F., Focardi, S. M., & Fabozzi, F. J. (2012). ARCH/GARCH models in applied financial econometrics. In F. J. Fabozzi (Ed.), Encyclopedia of financial models. Hoboken, NJ: John Wiley & Sons
Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987-1007. https://doi.org/10.2307/1912773
Engle, R. (2001). GARCH 101: The use of ARCH/GARCH models in applied econometrics. Journal of Economic Perspectives, 15(4), 157-168. https://doi.org/10.1257/jep.15.4.157
Ferreira, P. G. C. (2018). Análise de séries temporais em R: Curso introdutório. São Paulo, SP: GEN Atlas
Fioruci, J. A., Ehlers, R. S., & Andrade Filho, M. G. (2014). Bayesian multivariate GARCH models with dynamic correlations and asymmetric error distributions. Journal of Applied Statistics, 41(2), 320-331. https://doi.org/10.1080/02664763.2013.839635
Fisher, I. (1896). Appreciation and interest: A study of the influence of monetary appreciation and depreciation on the rate of interest with applications to the bimetallic controversy and the theory of interest. New York: Macmillan Company.
Francq, C., & Zakoian, J. M. (2019). GARCH models: Structure, statistical inference and financial applications. Hoboken, NJ: John Wiley & Sons.
Ghalanos, A. (2020). Introduction to the rugarch package (version 1.3-8). Retrieved from http://cran.r-project.org/web/packages/rugarch
Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779-1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
Hamilton, J. D. (1994). Time series analysis. Princeton, NJ: Princeton University Press.
Hansen, P. R., & Lunde, A. (2005). A forecast comparison of volatility models: Does anything beat a GARCH (1, 1)?. Journal of Applied Econometrics, 20(7), 873-889. https://doi.org/10.1002/jae.800
Härdle, W. K., Chen, C. Y. H., & Overbeck, L. (2017). Applied quantitative finance. Heidelberg, Germany: Springer-Verlag
Katsiampa, P. (2017). Volatility estimation for bitcoin: A comparison of GARCH models. Economics Letters, 158(C), 3-6. https://doi.org/10.1016/j.econlet.2017.06.023
Kuha, J. (2004). AIC and BIC: Comparisons of assumptions and performance. Sociological Methods & Research, 33(2), 188-229. https://doi.org/10.1177%2F0049124103262065
Lobão, J., & Fernandes, J. (2018). Psychological barriers in single stock prices: Evidence from three emerging markets. Revista Brasileira de Gestão de Negócios, 20(2), 248-272. https://doi.org/10.7819/rbgn.v20i2.3049
Mastella, M., & Coster, R. (2014). O impacto da crise de 2008 na estrutura temporal de correlação condicional da BM&FBovespa. Revista Brasileira de Gestão de Negócios, 16(50), 110-123. https://doi.org/10.7819/rbgn.v16i50.1534
Meng, X. L., & Rubin, D. B. (1992). Performing likelihood ratio tests with multiply-imputed data sets. Biometrika, 79(1), 103-111. https://doi.org/10.2307/2337151
Morettin, P. A., & Toloi, C. (2006). Análise de séries temporais. São Paulo, SP: Blucher
Morettin, P. A. (2017). Econometria financeira: Um curso de séries temporais financeiras. São Paulo, SP: Blucher
Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59(2), 347-370. https://doi.org/10.2307/2938260
Omran, M. F., & McKenzie, E. (2000). Heteroscedasticity in stock returns data revisited: Volume versus GARCH effects. Applied Financial Economics, 10(5), 553-560. https://doi.org/10.1080/096031000416433
Perlin, M., Mastella, M., Vancin, D., & Ramos, H. (2020). Replication data for: A garch tutorial with R. Harvard Dataverse, v1. https://doi.org/10.7910/DVN/C4WHUJ
Perlin, M. S. (2018) Processamento e análise de dados financeiros e econômicos com o R (2nd ed.). Porto Alegre, RS: Author
Quigley, L., & Ramsey, D. (2008). Statistical analysis of the log returns of financial assets (Bachelor dissertation). University of Limerick, Ireland. Retrieved from https://www.uni-muenster.de/Stochastik/paulsen/Abschlussarbeiten/Diplomarbeiten/Quigley.pdf
R Core Team (2017). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from https://www.r-project.org/
Ruppert, D., & Matteson, D. S. (2015). GARCH models. In D. Ruppert, D. S. Matteson (Eds.), Statistics and data analysis for financial engineering (pp. 405-452). New York, NY: Springer.
Tsay, R. S. (2005). Analysis of financial time series (3rd ed.). Hoboken, NJ: John Wiley & Sons.
Varga-Haszonits, I., & Kondor, I. (2007). Noise sensitivity of portfolio selection in constant conditional correlation GARCH models. Physica A: Statistical Mechanics and its Applications, 385(1), 307-318. https://doi.org/10.1016/j.physa.2007.06.017
Wuertz, D., Setz, T., Chalabi, Y., Boudt, C., Chausse, P., & Miklovac, M. (2020). fGarch: Rmetrics - Autoregressive conditional heteroskedastic modelling [R package version 3042.83.2]. Retrieved from https://CRAN.R-project.org/package=fGarch