Contents
What are multivariate GARCH models?
MGARCH stands for multivariate GARCH, or multivariate generalized autoregressive conditional heteroskedasticity. MGARCH allows the conditional-on-past-history covariance matrix of the dependent variables to follow a flexible dynamic structure. Stata fits MGARCH models.
What is BEKK GARCH?
The BEKK GARCH model introduced by Baba, et. BEKK GARCH is known for its ease of obtaining a positive definite variance-covariance matrix and its efficiency in reducing the number of parameters estimated.
What is bivariate GARCH?
We use a bivariate GJR-GARCH model to investigate simultaneously the contemporaneous and causal relations between trading volume and stock returns and the causal relation between trading volume and return volatility in a one-step estimation procedure, which leads to the more efficient estimates and is more consistent …
What is a BEKK model?
The so-called BEKK-model (named after Baba, Engle, Kraft and Kroner, 1990) provides a richer dynamic structure compared to both restricted processes mentioned before. Defining matrices and and an upper triangular matrix the BEKK-model reads in a general version as follows: (10.6)
How do you calculate conditional correlation?
Definition: A conditional correlation analysis (CCR) for two variables x and y over a dataset D (representing an application) is given by a pattern P (over the attributes of D), together with a linear regression model of the form y = αP + βP ∗ x that describes the correlation strength between x and y on the local …
What are the different types of GARCH models?
In the first category we have VEC, BEKK and factor models. Related models like the flexible MGARCH, Riskmetrics, Cholesky and full factor GARCH models are also in this category. In the second category we have (generalized) orthogonal models and latent factor models.
When was the multivariate GARCH model first developed?
MGARCH models were initially developed in the late 1980s and the first half of the 1990s, and after a period of tranquillity in the second half of the 1990s, this area seems to be experiencing again a quick expansion phase.
How are multivariate GARCH models used in hedging?
Like in the hedging case, since the β is the ratio of a covariance to a variance, an MGARCH model can be used to estimate time-varying β coefficients. See Bollerslev et al. ( 1988 ), De Santis and Gérard ( 1998 ), Hafner and Herwartz ( 1998) for examples.
How are HT and µ t dependent in GARCH models?
Both Ht and µ t depend on the unknown parameter vector θ, which can in most cases be split into two disjoint parts, one for µ t and one for Ht. 4 A case where this is not true is that of GARCH-in-mean models, where µ t is functionally dependent on Ht. In this section, we take no account of the conditional mean vector for notational ease.