Wavelet Density Estimation and Statistical Evidences Role for a GARCH Model in the Weighted Distribution

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We consider *n* observations from the GARCH-type model: *Z* = *UY*, where *U* and *Y* are independent random variables. We aim to estimate density function *Y* where *Y* have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.

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