2019/03/26 by Jiayuan Zhou, Feiyu Jiang, Zhou, Jiayuan +5
Mathematics · #Advanced Statistical Methods and Models #Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1903.12077
openalex publication_date 2019/03/26 · openalex created_date 2021/02/01 · openalex updated_date 2026/07/28
We propose a new Conditional BEKK matrix-F (CBF) model for the time-varying\nrealized covariance (RCOV) matrices. This CBF model is capable of capturing\nheavy-tailed RCOV, which is an important stylized fact but could not be handled\nadequately by the Wishart-based models. To further mimic the long memory\nfeature of the RCOV, a special CBF model with the conditional heterogeneous\nautoregressive (HAR) structure is introduced. Moreover, we give a systematical\nstudy on the probabilistic properties and statistical inferences of the CBF\nmodel, including exploring its stationarity, establishing the asymptotics of\nits maximum likelihood estimator, and giving some new inner-product-based tests\nfor its model checking. In order to handle a large dimensional RCOV matrix, we\nconstruct two reduced CBF models -- the variance-target CBF model (for moderate\nbut fixed dimensional RCOV matrix) and the factor CBF model (for high\ndimensional RCOV matrix). For both reduced models, the asymptotic theory of the\nestimated parameters is derived. The importance of our entire methodology is\nillustrated by simulation results and two real examples.\n