Resumen
El modelo GARCH (modelo autorregresivo condicional heterocedástico generalizado) es un modelo estadístico para series de tiempo usado para describir la varianza del error como una función de los errores al cuadrado pasados y de las varianzas. Estos modelos GARCH son usados para modelar la volatilidad variando en el tiempo y los clusters de volatilidad. Si además el efecto de la varianza es incluido en las observaciones para predecir la media, se tiene un GARCH-M (GARCH en media). En este artículo, se analizan estos modelos en un contexto bayesiano para series de tiempo bivariadas, donde las observaciones son asumidas de comportarse como un modelo VAR-GARCH-M. Una aplicación del modelo bivariado es ajustado para medir el efecto de la variabilidad de la inflación y crecimiento del producto en la media de la inflación y crecimiento del producto.
Citas
I. A. Alonzo Matamoros y C. A. Cruz Torres, varstan: An R package for bayesian analysis of struc- tured time series models with Stan. Arxiv. 2020. doi: 10.48550/arXiv.2005.10361
D. Ardia y L. Hoogerheide, Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations. The R Journal 2(2010), no. 2, 41-47. doi: 10.32614/RJ-2010-014
T. Bali, An Extreme Value Approach to Estimating Volatility and Value at Risk. The Journal of Business 76(2003), no. 1, 83-108. doi: 10.1086/344669
M. Betancourt, A Conceptual Introduction to Hamiltonian Monte Carlo. 2018. arXiv: 1701.02434 [stat.ME].
T. Bollerslev, A conditionally heteroskedastic time series model for speculative prices and rates of return. The Review of Economics and Statistic 69(1987), no. 3, 542-547. doi: 10.2307/1925546
S. Chib y S. Ramamurthy, DSGE models with Student-t errors. Econometrics Reviews 33(2014), no. 1-4, 152-171. doi: 10.1080/07474938.2013.807152
C. Chua, S. Suardi y S. Tsiaplias, An impulse-response function for a VAR with multivariate GARCH-in-Mean that incorporates direct and indirect transmisión of shocks. Economics Letters 117(2012), no. 2, 452-454. doi: 10.1016/j.econlet.2012.06.031
C. Cruz, Modelos Dinâmicos Estocásticos de Equilibrio Geral com Choques Heterocedásticos. Tese de Doutorado, UFRJ, 2015.
R. Engle, Autoregressive Conditional Heteroscedasticity with Estimates of Variance of United Kingdom Inflation. Econometrica 50(1982), no. 4, 987-1008. doi: 10.2307/1912773
R. Engle, New frontiers for ARCH models. Journal of Applied Econometrics 17(2002), 425-446. doi: 10.1002/jae.683
R. Engle y K. Kroner, Multivariate simultaneous generalized ARCH. Econometric Theory 11(1995), no. 1, 122-150. doi: 10.1017/S0266466600009063
A. Ferreira Silva, A. Fagundes Carrara y N. Renn Castro, Inflation persistence for product groups in Brazil using the ARFIMA-GARCH model. Macroeconomics and Finance in Emerging Market Economies (2022), 1-20. doi: 10.1080/17520843.2022.2080345
T. Fonseca, V. Cerqueira, H. Migon y C. Cruz-Torres, Evaluating the performance of degrees of freedom estimation in Asymmetric GARCH models with Student-t innovations. Brazilian Review of Econometrics 40(2020), no. 2, 347-373. doi: 10.12660/bre.v40n22020.80292
T. Fonseca, M. Ferreira y H. Migon, Objective Bayesian analysis for the Student-t regression model. Biometrika 95(2008), no. 2, 325-333. doi: 10.1093/biomet/asn001
C. Francq y J. Zakoian, GARCH Models, Structure, Statistical Inference and Financial Applications. John Wiley & Sons Ltd, 2019. doi: 10.1002/9781119313472
D. Gamerman y H. Lopes, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference. Chapman & Hall/CRC, 2006. doi: 10.1201/9781482296426
K. Grier y M. Perry, Inflation, inflation uncertainty, and relative price dispersion: Evidence from bivariate GARCH-M models. Journal of Monetary Economics 38(1996), no. 2, 391-405. doi: 10.1016/S0304-3932(96)01280-9
S. Gulzar et al., Financial cointegration and spillover effect of global financial crisis: A study of emerging Asian financial markets. Economic Research-Ekonomska Istraživanja 32(2019), no. 1, 187-218. doi: 10.1080/1331677X.2018.1550001
J. Hamilton, Time Series Analysis. Princeton University Press, 1994. doi: 10.2307/j.ctv14jx6sm
M. Heracleous, Volatility Modeling Using the Student’s t Distribution. Doctoral Thesis, Virginia Polytechnic Institute and State University, 2003.
M. Hoffman y A. Gelman, The No-U-Turn Sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research 15(2014), 1593-1623.
E. Jackier, N. Polson y P. Rossi, Bayesian Analysis of Stochastics Volatility Models. Journal of Business & Economic Statistics 12(1994), no. 4, 371-389. doi: 10.2307/1392199
E. Jondeau y M. Rockinger, Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements. Journal of Economic Dynamics and Control 27(2003), no. 10, 1699-1737. doi: 10.1016/S0165-1889(02)00079-9
R. Kass y A. Raftery, Bayes factor. Journal of the American statistical association 90(1995), no. 430, 773-795. doi: 10.1080/01621459.1995.10476572
R. Lassance, V. Cerqueira y T. Fonseca, VARMA-GARCH-M with Multiple Degrees of Freedom. 2018.
D. Li, M. Li y W. Wu, On dynamics of volatilities in nonstationary GARCH models. Statistics & Probability Letters 94(2014), 86-90. doi: 10.1016/j.spl.2014.07.003
H. Lutkepohl, Introduction to Multiple Time Series Analysis. Springer-Verlag, 2005. doi: 10.1007/978-3-662-02691-5
R. Neal, MCMC Using Hamiltonian Dynamics. Handbook of Markov Chain Monte Carlo, 2011. doi: 10.1201/b10905
D. Nelson, Stationarity and Persistence in the GARCH(1,1) Model. Econometric Theory 6(1990), no. 3, 318-334. doi: 10.1017/S0266466600005296
D. Nelson, Conditional Heteroskedasticity in Asset Returns: A New Approach. Econometrica 59(1991), no. 2, 347-370. doi: 10.2307/2938260
E. Nortey, D. Ngoh, K. Doku-Amponsah y K. Ofori-Boateng, Modeling inflation rates and exchange rates in Ghana: application of multivariate GARCH models. SpringerPlus 4(2015), 1-10. doi: 10.1186/s40064-015-0837-6
W. Polasek y R. Lei, Generalized Impulse Response Functions for VARGARCH-M Models. Gaul W., Opitz O., Schader M. (eds) Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization (2000), 299-311. doi: 10.1007/978-3-642-58250-9 24
W. Polasek y L. Ren, A multivariate GARCH-M model for exchange rates in the US, Germany and Japan. Classification and Information Processing at the Turn of the Millennium (2000), 355-363. doi: 10.1007/978- 3- 642-57280-7 39
A. Raftery, M. Newton, J. Satagopan y P. Krivitsky, Estimating the Integrated Likelihood via Posterior Simulation Using the Harmonic Mean Identity. Bayesian Statistics 8(2007), no. 1, 1-45. doi: 10.1093/oso/9780199214655.003.0015
T. Takaishi, Rational GARCH model: An empirical test for stock returns. Physica A: Statistical Mechanics and Its Applications 473(2017), 451-460. doi: 10.1016/j.physa.2017.01.011
Z. F. Tan, J. Zhang, J. H. Wang y J. Xu, Day-ahead electricity price forecasting using wavelet transform combined with Arima and GARCH models. Applied Energy 87(2010), no. 11, 3606-3610. doi: 10.1016/j.apenergy.2010.05.012
R. Tsay, Analysis of Financial Time Series. Wiley Series in Probability and Stastistics, 2005. doi: 10.1002/0471746193
C. H. Tseng, S. T. Cheng, Y. H. Wang y J. T. Peng, Artificial neural network model of the hybrid EGARCH volatility of the Taiwan stock index option prices. Physica A: Statistical Mechanics and Its Applications 387(2008), no.13, 3192-3200. doi: 10.1016/j.physa.2008.01.074
Y. Wang, Y. Xiang, X. Lei e Y. Zhou, Volatility analysis based on GARCHtype models: Evidence from the Chinese stock market. Economic Research- Ekonomska Istraživanja 35(2022), no. 1, 2530-2554. doi: 10.1080/1331677X.2021.1967771
A. Wilhelmsson, GARCH forecasting performance under different distribution assumptions. Journal of Forecasting 25(2006), 561-578. doi: 10.1002/for.1009
Z. J. Xiao y R. Koenker, Conditional Quantile Estimation for Generalized Autoregressive Conditional Heteroscedasticity Models. Journal of the American Statistical Association 104(2009), no. 488, 1696-1712. doi: 10.1198/jasa.2009.tm09170
Y. Xu, X. Wang y H. Liu, Quantile-based GARCH-MIDAS: Estimating value-at-risk using mixed-frequency information. Finance Research Letters 43(2021). doi: 10.1016/j.frl.2021.101965
J.-M. Zakoian, Threshold heteroskedastic models. Journal of Economic Dynamics and Control 18(1994), no. 5, 931-955. doi: 10.1016/0165-1889(94)90039-6
Comentarios
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
Derechos de autor 2024 Cristian Cruz Torres