In this paper we quantify the impact of model mis-specification on the properties of parameter estimators applied to fractionally integrated processes. We demonstrate the asymptotic equivalence of four alternative parametric methods: frequency domain maximum likelihood, Whittle estimation, time domain maximum likelihood and conditional sum of squares. We show that all four estimators converge t...

Problem Statement: The two-parameter exponentiated Rayleigh distribution has been widely used especially in the modelling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. The uniformly minimum variance unbiased and maximum likelihood es...

In financial time series analysis, symmetric and asymmetric GARCH models have become essential for measuring the characteristics of economic volatility. this article, we propose consistency asymptotic normality properties self-weighted quasi-maximum likelihood estimation without assuming existence second moment moving average model with a class error. Numerical simulation shows that parameter p...