In a ARMA-APARCH time series model with innovations Z, the delta-stationarity condition of the APARCH process involves the delta-th moment of the difference between the absolute value of the innovations with the product of the asymmetry parameter and the innovations. This moment allows calculating more efficiently the estimates of the parameters of the model by maximum likelihood. In this article, we obtain explicit expressions of this delta - th moment where Z has stable and GEV distribution. These moments have been implemented in our GEVStableGarch package available in CRAN R-PROJECT developed to estimate the parameters of ARMA-GARCH / APARCH models with stable innovations and GEV.

In a ARMA-APARCH time series model with innovations Z, the delta-stationarity condition of the APARCH process involves the delta-th moment of the difference between the absolute value of the innovations with the product of the asymmetry parameter and the innovations. This moment allows calculating more efficiently the estimates of the parameters of the model by maximum likelihood. In this article, we obtain explicit expressions of this delta - th moment where Z has stable and GEV distribution. These moments have been implemented in our GEVStableGarch package available in CRAN R-PROJECT developed to estimate the parameters of ARMA-GARCH / APARCH models with stable innovations and GEV.

Stable distributions are extensively used to analyze earnings of financial assets, such as exchange rates and stock prices assets. In this paper we propose a simple and strongly consistent estimator for the scale parameter of a symmetric stable Levy distribution. The advantage of this estimator is that your computational time is minimum thus it can be used to initialize intensive computational procedure such as maximum likelihood. With random samples of sized n we testedthe efficacy of these estimators by Monte Carlo method. We also included applications for three data sets.

Stable distributions are extensively used to analyze earnings of financial assets, such as exchange rates and stock prices assets. In this paper we propose a simple and strongly consistent estimator for the scale parameter of a symmetric stable Levy distribution. The advantage of this estimator is that your computational time is minimum thus it can be used to initialize intensive computational procedure such as maximum likelihood. With random samples of sized n we testedthe efficacy of these estimators by Monte Carlo method. We also included applications for three data sets.