Abstract
L 1-estimation of a location parameter is studied for the “product type” stochastic volatility models. The asymptotic distribution of the L 1-estimator is established under general conditions on the behavior of the distribution function of the errors near zero.
Similar content being viewed by others
References
J. Beran, “On Location Estimation for LARCH Processes”, J. Multivariate Anal. 97, 1766–1782 (2006).
J. Beran, “On M-Estimation under Long-Range Dependence in Volatility”, J. Time Ser. Anal. 28, 138–153 (2007).
J. Beran and M. Schützner, “The Effect of Long Memory in Volatility on Location Estimation”, Sankhya 70-B, 84–112 (2008).
H. A. David, Order Statistics (Wiley, New York, 1970).
R. A. Davis, “Gauss-Newton and M-Estimation for ARMA Processes with Infinite Variance”, Stochastic Process. Appl. 63, 750–95 (1996).
R. A. Davis and W. T. M. Dunsmuir, “Least Absolute Deviation Estimation for Regression with ARMA Errors”, J. Theoret. Probab. 10, 481–497 (1997).
R. A. Davis, K. Knight, and J. Liu, “M-Estimation for Autoregression with Infinite Variance”, Stochastic Process. Appl. 40, 145–180 (1992).
R. F. Engle, “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of the United Kingdom”, Econometrica 50, 987–1007 (1982).
P. Hall and C. Heyde, Martingale Limit Theory and its Applications (Academic Press, New York, 1980).
J. Jurečková, “Asymptotic Behavior of M-Estimators of Location in Nonregular Cases”, Statist. Decisions 1, 323–340 (1983).
K. Knight, “Rate of Convergence of Centered Estimates of Autoregression Parameters for Infinite Variance Autoregression”, J. Time Ser. Anal. 8, 51–60 (1987).
K. Knight, “Limiting Distributions for L 1 Regression Estimators under General Conditions”, Ann. Statist. 26, 755–770 (1998).
P. M. Robinson, “Testing for Strong Serial Correlation and Dynamic Conditional Heteroskedasticity in Multiple Regression”, J. Econometrics 47, 67–84 (1991).
P. M. Robinson, “The Memory of Stochastic Volatility Models”, J. Econometrics 101, 195–218 (2001).
P. M. Robinson and P. Zaffaroni, “Nonlinear Time Series with Long Memory: A Model for Stochastic Volatility”, J. Statist. Plan. Inference 68, 359–371 (1998).
R. T. Rockafellar, Convex Analysis (Princeton Univ. Press, New Jersey, 1970).
D. Surgailis and M. C. Viano, “Long Memory Properties and Covariance Structure of the EGARCH Model”, ESAIM: Probab. Statist. 6, 311–329 (2002).
J. Wang, Asymptotic Normality of L 1-Estimators in Nonlinear Regression, J. Multivariate Anal. 54, 227–238 (1995).
L. Wang, “Asymptotics of L 1-Estimators in Moving Average Time Series Models”, Commun. Statist. — Theory Methods 33, 107–118 (2004).
L. Wang, L 1 -Estimation for the Location Parameter in Stochastic Volatility Models, Working paper (Dept. of Math., Nanjing Univ., 2010).
P. Zaffaroni and B. d’Italia, “Gaussian Inference on Certain Long-Range Dependent Volatility Models”, J. Econometrics 115, 199–258 (2003).
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Wang, L. L 1-estimation for the location parameters in stochastic volatility models. Math. Meth. Stat. 20, 165–170 (2011). https://doi.org/10.3103/S1066530711020062
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066530711020062