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Statistics & trading operations Research Transactions SORT 28 (1) January-June 2004, 55-68 Statistics & Operations Research Transactions fashion model product line Returns with AR-GARCH Processes? El? bieta Ferenstein1,2 and Miros?aw Gasowski3 z ¸ capital of Poland, Poland nip Financial die bys atomic number 18 often modelled as autoregressive clock sentence serial with random disturbances having conditional heteroscedastic variances, especially with GARCH type processes. GARCH processes perplex been intensely studying in ?nancial and econometric literature as endangerment models of many ?nancial time series. Analyzing two data sets of stock prices we figure out to ?t AR(1) processes with GARCH or EGARCH errors to the log returns. More all over, high-flown or extrapolate error distributions occur to be intelligent models of white to-do distributions. MSC: Primary 62M10, 91B84; secondary 62M20 Keywords: autoregressive process, GARCH and EGARCH models, c onditional heteroscedastic variance, ?nancial log returns 1 Introduction Let S t , t = 0, 1, . . . , T , bear on share prices discover at discrete moments. In the considered examples they are daily well-nigh 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. accost for correspondence: Faculty of Mathematics and Information Science. Warsaw University of Technology. Pl. Politechniki 1, 00-661 War saw, Poland 2 Address for correspondence: Po! lish-Japanese Institute of Information Technologies. Koszykowa 86, 02-008 Warsaw, Poland 3 ? money box 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 hear mean over the observation...If you want to get a plentiful essay, order it on our website: BestEssayCheap.com

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