Consistent estimation of the memory parameter for nonlinear time series
For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties are well established. However, except for some specific cases, little is known about the estimation of the memory parameter for nonlinear processes. The purpose of this paper is to provide general conditions under which the local Whittle estimator of the memory parameter of a stationary process is consistent and to examine its rate of convergence. We show that these conditions are satisfied for linear processes and a wide class of nonlinear models, among others, signal plus noise processes, nonlinear transforms of a Gaussian process ξt and EGARCH models. Special cases where the estimator satisfies the central limit theorem are discussed. The finite sample performance of the estimator is investigated in a small Monte-Carlo study
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- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994.
"Multivariate Stochastic Variance Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(2), pages 247-64, April.
- Tom Doan, . "RATS programs to estimate multivariate stochastic volatility models," Statistical Software Components RTZ00093, Boston College Department of Economics.
- Yixiao Sun & Peter C.B. Phillips, 2002.
"Nonlinear Log-Periodogram Regression for Perturbed Fractional Processes,"
Cowles Foundation Discussion Papers
1366, Cowles Foundation for Research in Economics, Yale University.
- Sun, Yixiao & Phillips, Peter C. B., 2003. "Nonlinear log-periodogram regression for perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 115(2), pages 355-389, August.
- Peter M. Robinson, 2001. "The memory of stochastic volatility models," LSE Research Online Documents on Economics 2298, London School of Economics and Political Science, LSE Library.
- Arteche, Josu, 2004.
"Gaussian semiparametric estimation in long memory in stochastic volatility and signal plus noise models,"
Journal of Econometrics,
Elsevier, vol. 119(1), pages 131-154, March.
- Arteche González, Jesús María, 2002. "Gaussian Semiparametric Estimation in Long Memory in Stochastic Volatility and Signal Plus Noise Models," BILTOKI 2002-02, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
- Peter M Robinson, 2001.
"The Memory of Stochastic Volatility Models,"
STICERD - Econometrics Paper Series
/2001/410, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Donald W.K. Andrews & Yixiao Sun, 2002.
"Adaptive Local Polynomial Whittle Estimation of Long-range Dependence,"
Cowles Foundation Discussion Papers
1384, Cowles Foundation for Research in Economics, Yale University.
- Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, 03.
- ANDREWS, DONALD W & Sun, Yixiao X, 2002. "Adaptive Local Polynomial Whittle Estimation of Long-Range Dependence," University of California at San Diego, Economics Working Paper Series qt9wt048tt, Department of Economics, UC San Diego.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204.
- Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005.
"Estimating Long Memory in Volatility,"
Econometric Society, vol. 73(4), pages 1283-1328, 07.
- Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(04), pages 686-710, August.
- Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
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