Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139114796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139115588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139116919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139117282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139122596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139123945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139118953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139112650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139113725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.
{"title":"Quasi Maximum Likelihood Estimation of Vector Multiplicative Error Model using the ECCC-GARCH Representation","authors":"Yongdeng Xu","doi":"10.1515/jtse-2022-0018","DOIUrl":"https://doi.org/10.1515/jtse-2022-0018","url":null,"abstract":"Abstract We introduce an ECCC-GARCH representation for the vector Multiplicative Error Model (vMEM) that enables maximum likelihood estimation using the multivariate normal distribution. We show via Monte Carlo simulations that the QML estimator possesses desirable small sample properties (towards unbiasedness and efficiency). In the empirical application, we firstly use a two-dimensional vMEM for the squared return and realized volatility, which nests the High-frEquency-bAsed VolatilitY (HEAVY) and Realized GARCH model. We show that the Realized GARCH model is a more appropriate specification for the dynamics of the return-volatility relationship. The second empirical application is a four-dimensional vMEM for volatility spillover effects in the four European stock markets. The results confirm interdependence across European markets and the relative strength of volatility spillovers increases in the post-2010 turmoil periods.","PeriodicalId":42470,"journal":{"name":"Journal of Time Series Econometrics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139114015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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