Lp-estimators in ARCH models |
| |
Institution: | 1. Department of Economics, Lund University, Box 7082, Lund 220 07, Sweden;2. Centre for Financial Econometrics, Faculty of Business and Law, Deakin University, Melbourne Burwood Campus, 221 Burwood Highway, Burwood Victoria 3125, Australia |
| |
Abstract: | For ergodic ARCH processes, we introduce a one-parameter family of Lp-estimators. The construction is based on the concept of weighted M-estimators. Under weak assumptions on the error distribution, the consistency is established. The asymptotic normality is proved for the special cases p=1 and 2. To prove the asymptotic normality of the L1-estimator, one needs the existence of a density of the squares of the errors, whereas for the L2-estimator the existence of fourth moments is assumed. The asymptotic covariance matrix of the estimator depends on the unknown parameter which can be substituted by consistent estimators. For the L1-estimator we construct a kernel estimator for the unknown density of the square of the errors. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|