{"title":"具有重尾误差的GARCH(1,1)模型的最小二乘估计","authors":"Arie Preminger, Giuseppe Storti","doi":"10.1111/ectj.12089","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>GARCH(1,1) models are widely used for modelling processes with time-varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a novel log-transform-based least-squares approach to the estimation of GARCH(1,1) models. Within this approach, the scale of the estimated volatility is dependent on an unknown tuning constant. By means of a backtesting exercise on both real and simulated data, we show that knowledge of the tuning constant is not crucial for Value at Risk prediction. However, this does not apply to many other applications where correct identification of the volatility scale is required. In order to overcome this difficulty, we propose two alternative two-stage least-squares estimators and we derive their asymptotic properties under very mild moment conditions for the errors. In particular, we establish the consistency and asymptotic normality at the standard convergence rate of for our estimators. Their finite sample properties are assessed by means of an extensive simulation study.</p></div>","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":null,"pages":null},"PeriodicalIF":2.9000,"publicationDate":"2017-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1111/ectj.12089","citationCount":"5","resultStr":"{\"title\":\"Least-squares estimation of GARCH(1,1) models with heavy-tailed errors\",\"authors\":\"Arie Preminger, Giuseppe Storti\",\"doi\":\"10.1111/ectj.12089\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>GARCH(1,1) models are widely used for modelling processes with time-varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a novel log-transform-based least-squares approach to the estimation of GARCH(1,1) models. Within this approach, the scale of the estimated volatility is dependent on an unknown tuning constant. By means of a backtesting exercise on both real and simulated data, we show that knowledge of the tuning constant is not crucial for Value at Risk prediction. However, this does not apply to many other applications where correct identification of the volatility scale is required. In order to overcome this difficulty, we propose two alternative two-stage least-squares estimators and we derive their asymptotic properties under very mild moment conditions for the errors. In particular, we establish the consistency and asymptotic normality at the standard convergence rate of for our estimators. Their finite sample properties are assessed by means of an extensive simulation study.</p></div>\",\"PeriodicalId\":50555,\"journal\":{\"name\":\"Econometrics Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2017-03-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1111/ectj.12089\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Econometrics Journal\",\"FirstCategoryId\":\"96\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/ectj.12089\",\"RegionNum\":4,\"RegionCategory\":\"经济学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ECONOMICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrics Journal","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/ectj.12089","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
Least-squares estimation of GARCH(1,1) models with heavy-tailed errors
GARCH(1,1) models are widely used for modelling processes with time-varying volatility. These include financial time series, which can be particularly heavy tailed. In this paper, we propose a novel log-transform-based least-squares approach to the estimation of GARCH(1,1) models. Within this approach, the scale of the estimated volatility is dependent on an unknown tuning constant. By means of a backtesting exercise on both real and simulated data, we show that knowledge of the tuning constant is not crucial for Value at Risk prediction. However, this does not apply to many other applications where correct identification of the volatility scale is required. In order to overcome this difficulty, we propose two alternative two-stage least-squares estimators and we derive their asymptotic properties under very mild moment conditions for the errors. In particular, we establish the consistency and asymptotic normality at the standard convergence rate of for our estimators. Their finite sample properties are assessed by means of an extensive simulation study.
期刊介绍:
The Econometrics Journal was established in 1998 by the Royal Economic Society with the aim of creating a top international field journal for the publication of econometric research with a standard of intellectual rigour and academic standing similar to those of the pre-existing top field journals in econometrics. The Econometrics Journal is committed to publishing first-class papers in macro-, micro- and financial econometrics. It is a general journal for econometric research open to all areas of econometrics, whether applied, computational, methodological or theoretical contributions.