Library Header Image
LSE Research Online LSE Library Services

Approximating volatilities by asymmetric power GARCH functions

Penzer, Jeremy, Wang, Mingjin and Yao, Qiwei ORCID: 0000-0003-2065-8486 (2009) Approximating volatilities by asymmetric power GARCH functions. Australian and New Zealand Journal of Statistics, 51 (2). pp. 201-225. ISSN 1369-1473

PDF - Accepted Version
Download (1MB) | Preview

Identification Number: 10.1111/j.1467-842X.2009.00542.x


ARCH/GARCH representations of financial series usually attempt to model the serial correlation structure of squared returns. Although it is undoubtedly true that squared returns are correlated, there is increasing empirical evidence of stronger correlation in the absolute returns than in squared returns. Rather than assuming an explicit form for volatility, we adopt an approximation approach; we approximate the th power of volatility by an asymmetric GARCH function with the power index chosen so that the approximation is optimum. Asymptotic normality is established for both the quasi-maximum likelihood estimator (qMLE) and the least absolute deviations estimator (LADE) in our approximation setting. A consequence of our approach is a relaxation of the usual stationarity condition for GARCH models. In an application to real financial datasets, the estimated values for are found to be close to one, consistent with the stylized fact that the strongest autocorrelation is found in the absolute returns. A simulation study illustrates that the qMLE is inefficient for models with heavy-tailed errors, whereas the LADE is more robust.

Item Type: Article
Official URL:
Additional Information: © 2009 Australian Statistical Publishing Association Inc.
Divisions: Statistics
Subjects: Q Science > QA Mathematics
Date Deposited: 26 Jan 2011 10:04
Last Modified: 16 May 2024 00:56
Funders: Engineering and Physical Sciences Research Council, Natural Science Foundation of China

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics