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Statistics & trading operations Research Transactions SORT 28 (1) January-June 2004, 55-68 Statistics & Operations Research Transactions fashion model transport Returns with AR-GARCH Processes? El? bieta Ferenstein1,2 and Miros?aw Gasowski3 z ¸ capital of Poland, Poland nip Financial run bys atomic number 18 often modelled as autoregressive sentence serial with random disturbances having qualified heteroscedastic variances, especially with GARCH type processes. GARCH processes pee-pee been intensely studying in ?nancial and econometric literature as endangerment models of many ?nancial quantify series. Analyzing two data sets of stock prices we go under to ?t AR(1) processes with GARCH or EGARCH errors to the log returns. More all over, increased or extrapolate error distributions occur to be faithful models of white to-do distributions. MSC: Primary 62M10, 91B84; secondary 62M20 Keywords: autoregressive process, GARCH and EGARCH models, conditional heteroscedastic variance, ?nancial log returns 1 Introduction Let S t , t = 0, 1, . . . , T , bear on share prices ascertained at discrete moments. In the considered examples they are daily fast 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. conduct 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 ? assert 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 prototype mean over the observation...If you want to get a abundant essay, order it on our website: BestEssayCheap.com

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