Estimation Of The Parameter Of Long Memory Model

The phenomenon of slowly declining autocorrelation was called long memory prop-erties which are often found in time series of hydrology,climatology ,econometrics and other natural sciences. Using long memory properties to model has drawn the attention of many researchers from very different areas of research.The estimation methods proposed to test for long-range dependence can be divided into two classes:parametric estimation and semi-parametric estimation. Semi-parametric methods do not require the modelling of a complete set of the autocovariances,we are only interested in the parametric d.If a complete set is built,such as an ARFIMA(p,d,q),we term the estimation "parametric". The main disadvantages of parametric methods are that they are computationally expensive (large number of parameters to estimate) and are subject to mispecification.On the other hand ,semi-parametric models consider d as the most important parameter of interest and it is robust to mispecification.However,the semi-parametric estimates are less efficient than well specified parameter counterparts.The main aim of this section is to introduce three parametric estimators and five semi-parametric estimators-EMLE estimator,AMLE estimator,,APE estimator,GPH es-timator,LPE estimator,QMLE estimator and wavelet OLS estimator,and discuss their advantages and disadvantages.Lastly,we take fractional white noise model for example to compare the two estimator-wavelet OLS estimator and GPH estimator.