Author : Michel Riad Nehme
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (787 download)
Book Synopsis Maximum Likelihood Based Techniques in Identifying ARMA Models by : Michel Riad Nehme
Download or read book Maximum Likelihood Based Techniques in Identifying ARMA Models written by Michel Riad Nehme and published by . This book was released on 2005 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this thesis is to investigate some preliminary identification techniq ues in time series Autoregressive Moving Average, ARMA, models. In particular, w e take a look at the sample auto- correlation estimate as the primary identifica tion quantity for specifying a tentative model and propose a maximum likelihood estimator as an alternative estimator to the sample ones. It is shown empiricall y that the likelihood based technique performs more or less the same for large l ength series that follow the autoregressive model of order oe, AR(1). While, fo r short to moderate length AR(1) series, the maximum likelihood shows improved efficiency in comparison to the moment estimate. In chapter one, the popular Box and Jenkins ARMA models are introduced. For this class of models the general behavior and some properties are derived and discus sed for some specific ARMA processes. In chapter two, the identification techniques that are used to select a tentativ e model are presented and some diagnostic checks for the adequacy of the fitted model are listed. In particular, the portmanteau test for the presence of serial correlation is considered and some modifications that exist in the literature a re reviewed. In chapter three, we propose a modification for the Hasza maximum likelihood est imation of the first lag autocorrelation to the lag k- autocorrelation. This met hod requires the Newton Raphson to obtain recursively the estimate and its varia nce a by product of the algorithm. An empirical study is conducted to compare th e proposed estimate to the sample moment one. Finally, in chapter four, further directions for investigation of more efficient identification techniques are examined and left for future work.
