Use of Stochastic Volatility Models in Epidemiological Data: Application to a Dengue Time Series in São Paulo City, Brazil
Abstract
Background: A study on the dengue daily counting in São Paulo city in a fixed period of time is assumed considering a new regression model approch.
Methods: Under a Bayesian approach, it is introduced a polynomial linear regression model in presence of some covariates which could affect the counts of dengue in São Paulo city considered in the logarithm scale, combined with existing stochastic volatility models usually assumed in financial data analysis. Markov Chain Monte Carlo methods are used to get the posterior summaries of interest.
Results: The new model approach showed some advantages when compared to other existing times series models usually used to model epidemics data.
Conclusion: The use of the polynomial regression model combined with existing volatility models under a Bayesian approach showed that it is possible to get very accurate fit for the counting dengue data in São Paulo city where it is possible to jointly model the means and volatilities (variances) of the epidemiological dengue time series.
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2. Cortes F, Martelli CM, de Alencar Ximenes RA, Montarroyos UR, Junior JBS, Cruz OG, Alexander N, de Souza WV. Time series analysis of dengue surveillance data in two Brazilian cities. Acta Tropica. 2018;182:190–197.
3. Box GE, Jenkins GM, Reinsel GC, Ljung GM. Time series analysis: forecasting and control. John Wiley & Sons, 2015.
4. Luz PM, Mende BV, Code¸co CT, Struchiner, CJ, Galvani AP. Time series analysis of dengue incidence in Rio de Janeiro, Brazil. The American Journal of Tropical Medicine and Hygiene. 2008;79(6):933–939.
5. Martinez EZ, Silva EASD. Predicting the number of cases of dengue infection in Ribeir˜ao Preto, S˜ao Paulo state, Brazil, using a SARIMA model. Cadernos de Saude Publica. 2011; 27:1809–1818.
6. Nobre FF, Monteiro ABS, Telles PR, Williamson GD. Dynamic linear model and SARIMA: A comparison of their forecasting performance in epidemiology. Statistics in Medicine. 2001; 20(20):3051-3069.
7. SilawanT,Singhasivanon P, Kaewkungwal J, Nimmanitya S, Suwonkerd W, et al. Temporal patterns and forecast of dengue infection in Northeastern Thailand. Southeast Asian Journal of Tropical Medicine and Public Health. 2008; 39(1):90.
8. Morato DG, Barreto FR, Braga JU, Natividade MS, Costa MDCN, Morato V, Teixeira MDGLC. The spatiotemporal trajectory of a dengue epidemic in a medium-sized city. Memorias do Instituto Oswaldo Cruz. 2015; 110(4):528–533.
9. Nelder JA, Wedderburn RW.Generalized linear models. Journal of the Royal Statistical Society:Series A (General). 1972; 135(3):370–384.
10. Dimitrakopoulos S, Kolossiatis M. Bayesian analysis of moving average stochastic volatility models: modeling in-mean effects and leverage for financial time series. Econometric Reviews.2020; 39(4):319–343.
11. Taspinar S, Dogan O, Chae J, Bera AK. Bayesian inference in spatial stochastic volatility models: An application to house price returns in Chicago. 2019. Available at SSRN 3104611.
12. Guo X, McAleer M, Wong WK, Zhu L. A Bayesian approach to excess volatility, short-term underreaction and long-term overreaction during financial crises. The North American Journal of Economics and Finance. 2017; 42:346–358.
13. Gelfand AE, Smith AF. Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association. 1990; 85(410):398–409.
14. Danielsson J. Stochastic volatility in asset prices estimation with simulated maximum likelihood. Journal of .1994; 64(1-2):375–400.
15. Yu J. Forecasting volatility in the New Zealand stock market. Applied Financial Economics. 2002; 12(3):193–202.
16. Engle RF. Autoregressive conditional heteroscedasticity with estimates of the variance of
United Kingdom inflation. Econometrica: Journal of the Econometric Society. 1982; 987–1007.
17. Ghysels E, Harvey A, Renault E. Stochastic Volatility.1996.
18. Kim S, Shephard N, Chib S. Stochastic volatility: Likelihood inference and compar- ison with ARCH models. The review of economic studies. 1998; 65(3):361–393.
19. Meyer R, Yu J. BUGS for a Bayesian analysis of stochastic volatility models. The Econometrics Journal. 2000; 3(2):198–215.
20. Spiegelhalter, D., Thomas, A., Best, N., and Lunn, D. WinBUGS user manual, version 1.4 MRC Biostatistics Unit. Cambridge, UK. 2003.
21. Draper NR, Smith H. Applied regression analysis, volume 326. John Wiley & Sons.1998.
22.Seber GAF, Wild CJ. Nonlinear regression. New Jersey, John Wiley & Sons.2003.
23. Spiegelhalter DJ, Best NG, Carlin BP, Van Der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc Ser B Stat Methodol. 2002; 64(4):583-639
| Files | ||
| Issue | Vol 6 No 1 (2020) | |
| Section | Original Article(s) | |
| DOI | https://doi.org/10.18502/jbe.v6i1.4755 | |
| Keywords | ||
| dengue count volatility models Bayesian approach MCMC methods. | ||
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How to Cite
1.
Achcar J, de Oliveira R, Barili E. Use of Stochastic Volatility Models in Epidemiological Data: Application to a Dengue Time Series in São Paulo City, Brazil. JBE. 2020;6(1):19-29.
