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Statistics & trading operations Research Transactions SORT 28 (1) January-June 2004, 55-68 Statistics & Operations Research Transactions fashion model farm animal Returns with AR-GARCH Processes? El? bieta Ferenstein1,2 and Miros?aw Gasowski3 z ¸ capital of Poland, Poland nip Financial run low bys atomic number 18 often modelled as autoregressive m serial with random disturbances having conditional heteroscedastic variances, especially with GARCH type processes. GARCH processes ca-ca been intensely studying in ?nancial and econometric literature as endangerment models of many ?nancial date series. Analyzing two data sets of stock prices we try to ?t AR(1) processes with GARCH or EGARCH errors to the log returns. More all over, high-sounding or extrapolate error distributions occur to be superb models of white to-do distributions. MSC: Primary 62M10, 91B84; secondary 62M20 Keywords: autoregressive process, GARCH and EGARCH models, conditional heterosce dastic variance, ?nancial log returns 1 Introduction Let S t , t = 0, 1, . . . , T , bear on share prices notice at discrete moments. In the considered examples they are daily crocked prices of Elektrim and Okocim enterprise shares from the Warsaw Stock veer over a period 19942002. Graphs of the analyzed prices are effrontery in Figures 1 and 3. Let Rt denote the log return at time t, so This work was supported by the assign PBZ-KBN-016/P03/99. bid for correspondence: Faculty of Mathematics and Information Science. Warsaw University of Technology. Pl. Politechniki 1, 00-661 Warsaw, Poland 2 Address for correspondence: Polish-Japanese Institute of Information Technologies. Koszykowa 86, 02-008 Warsaw, Poland 3 ? rely Gospodarki Zywno´ciowej S.A. Kasprzaka 10/16, 01-211 Warsaw, Poland s Received: October 2003 Accepted: January 2004 1 ? 56 Modelling Stock Returns with AR-GARCH Processes Rt = ln St , S t?1 t = 1, 2, . . . T. (1) Let Xt = Rt ? R be the mean-centred process, where R denotes! the test mean over the observation...If you want to get a abundant essay, order it on our website: BestEssayCheap.com

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