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Mixture of distribution models offer such flexibility.
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Consistent with a stylized mixture-of-distributions hypothesis model in which the aggregate "news -arrival process possesses lonews -arrivalracteristics, the long-run hyprocessc decay rates apossessesbe common across each volong-memorylity pair.
The idea that volatility fluctuations cause non-Gaussian returns is not new – it was originally suggested several decades ago and is known as the mixture-of-distributions hypothesis [4], [12] [15].
These models can be estimated using a mixture of distributions, such as a categorical mediator or outcome in concert with a continuously distributed mediator or outcome.
Nevertheless, applications of mixture of distributions in the panel data setting appear to be limited.
This is a classical finite mixture of distributions with constant weights π and 1−π.
Mixture of distributions are in fact at the crossroad between parametric and non parametric families of distributions.
It is unclear exactly how one might define such a mixture of distributions automatically for any dataset.
The methods for cluster analysis present in literature can be roughly classified into two main families: probability-based methods (see e.g. [1]), which are based on the assumption that clusters come from a mixture of distributions, from a given family.
If π results to be close to 1 (or 0) we can reject the hypothesis of a mixture of distributions.
One can also hypothesize that the observed move distribution is indeed a mixture of distributions, as suggested in a different context by [18], finally yielding the appearance of a fat-tail [17].
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