Full versus quasi MLE for ARMA-GARCH models with infinitely divisible innovations

We compare the backtesting performance of ARMA-GARCH models with the most common types of infinitely divisible innovations, fit with both full maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE). The innovation types considered are the Gaussian, Student’s t, α-stable, classical tempered stable (CTS), normal tempered stable (NTS) and generalized hyperbolic (GH) distributions. In calm periods of decreasing volatility, MLE and QMLE produce near identical performance in forecasting value-at-risk (VaR) and conditional value-at-risk (CVaR). In more volatile periods, QMLE can actually produce superior performance for CTS, NTS and α-stable innovations. While the t-ARMA-GARCH model has the fewest number of VaR violations, rejections by the Kupeic and Berkowitz tests suggest excessively large forecasted losses. The α-stable, CTS and NTS innovations compare favourably, with the latter two also allowing for option pricing under a single market model.     

基于ARMA-GARCH模型的股指波动压力测试情景设计研究

针对股指收益率时间序列某期间的异方差、尖峰厚尾以及序列自相关等特性,将ARMA模型与GARCH模型相结合,回归建模测算相关股指年度收益率VaR值,可以有效预测类似市场条件下股指的波动以及相伴概率。因此,在证券公司压力测试实践中,基于相伴概率合理设计股指下跌的压力测试情景,可以进一步提高压力测试情景设计的科学性,增强压力测试结果的现实指导意义。同时,可以将本文研究思路推广应用于利率、汇率、市场交易量等历史数据较充分的金融时间序列的实证分析,借以指导债市波动、汇市波动以及市场交易量波动等压力测试情景的设计工作。     

Why Has Taiwan Been Immune to the Asian Financial Crisis?

This paper presents the reasons why Taiwan has been immune tothe Asian financial crisis. It shows that the purchasingpower parity theory applies to the N.T. dollar exchangerate and analyzes daily data on exchange rates andstock prices within the ARMA-GARCH regressionframework. Using the Granger causality test, it is shownthat the yen/U.S. dollar exchange rate caused the changein the N.T. dollar/U.S. dollar rate.     

沪市股票市场效率的分析——基于ARMA-GARCH模型

沪市是我国资本市场的重要组成部分,其运作的效率对我国资本配置有着重要的影响。本文利用ARMA-GARCH模型,以法马的市场有效性为评判依据,分阶段对沪市的市场有效性进行了检验,得出了沪市尚未达到弱式有效市场,但市场有效性已有了明显提升的结论。     

中国商品期货市场的周日历效应实证研究

利用中国商品期货市场的主要期货合约交易数据,本文采用ARMA-GARCH模型,对我国期货市场的周日历效应进行了研究。实证结果表明,橡胶、铜、大豆和豆粕四个国际化程度较高的期货合约具有正的周一效应,铜还具有正的周四效应,而相对独立的PTA和白糖合约没有发现周日历效应。     

The impact of terrorism on European tourism

This paper estimates the influence of terrorist attacks on European tourism through the short-term post hoc response of the airline industry and passengers. We use a seasonally-adjusted ARMA-GARCH methodology on unique datasets that examine changes in tourism as measured by ASKs, seats filled and changes in both fares and revenues. Traffic flows are found to fall despite significant fare reductions; however, this response varies substantially based on the flight origin and ticket-type purchased. We found that business travel slows substantially due to duty of care legislation for corporate transport. While we found evidence indicating substantial airline fare reductions, in the majority of investigated cases this response was unable to mitigate substantial reductions in passenger demand and flows across varying ticket types.     

Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models

The limit distribution of the quasi-maximum likelihood estimator (QMLE) for parameters in the ARMA-GARCH model remains an open problem when the process has infinite 4th moment. We propose a self-weighted QMLE and show that it is consistent and asymptotically normal under only a fractional moment condition. Based on this estimator, the asymptotic normality of the local QMLE is established for the ARMA model with GARCH (finite variance) and IGARCH errors. Using the self-weighted and the local QMLEs, we construct Wald statistics for testing linear restrictions on the parameters, and their limiting distributions are given. In addition, we show that the tail index of the IGARCH process is always 2, which is independently of interest.