# Wavelet Estimation of Gegenbauer Processes: Simulation and Empirical Application

## Author

Listed:
• Heni Boubaker

()

## Abstract

The aim of this paper is to estimate the parameters of a stationary Gegenbauer process using a wavelet methodology where the selection of the orthonormal basis is given by generalized variance portmanteau test. Two other maximum likelihood estimators, including the Whittle and the wavelets—Whitcher (Technometrics 46:225–238, 2004 ) estimators, are also considered. We have shown by Monte-Carlo experiments that the new selection procedure improves considerably the Whittle and Whitcher estimators. Moreover, to assess the impact of volatility in the estimation methods, we assumed that the innovations $$\varepsilon _{t}$$ ε t are generated by univariate GARCH process. Simulation experiments show that the wavelets estimators perform better under most situations than the Whittle estimator. We then applied this new selection method to the consumer price index in monthly frequencies for the United States and find that this is more appropriate for forecasts. Copyright Springer Science+Business Media New York 2015

## Suggested Citation

• Heni Boubaker, 2015. "Wavelet Estimation of Gegenbauer Processes: Simulation and Empirical Application," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 551-574, December.
• Handle: RePEc:kap:compec:v:46:y:2015:i:4:p:551-574
DOI: 10.1007/s10614-014-9471-6
as

File URL: http://hdl.handle.net/10.1007/s10614-014-9471-6

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## References listed on IDEAS

as
1. Boubaker Heni & Boutahar Mohamed, 2011. "A wavelet-based approach for modelling exchange rates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 201-220, June.
2. Diongue Abdou Ka & Dominique Guegan, 2008. "Estimation of k-Factor Gigarch Process: A Monte Carlo Study," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00375758, HAL.
3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
4. Heni Boubaker & Anne Péguin-Feissolle, 2013. "Estimating the Long-Memory Parameter in Nonstationary Processes Using Wavelets," Computational Economics, Springer;Society for Computational Economics, vol. 42(3), pages 291-306, October.
5. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
6. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
7. Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
Full references (including those not matched with items on IDEAS)

### Keywords

Gegenbauer process; Wavelet analysis; Generalized variance portmanteau test; Heteroskedasticity; Monte-Carlo simulation; CPI; C13; C15; C22;

### JEL classification:

• C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
• C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
• C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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