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Statistics & trading operations Research Transactions SORT 28 (1) January-June 2004, 55-68

Statistics & Operations Research Transactions

fashion model Stock Returns with AR-GARCH Processes?
El? bieta Ferenstein1,2 and Miros?aw Gasowski3 z ¸
capital of Poland, Poland

nip Financial travel bys atomic number 18 often modelled as autoregressive time serial with random disturbances having conditional heteroscedastic variances, especially with GARCH type processes. GARCH processes have been intensely studying in ?nancial and econometric literature as endangerment models of many ?nancial time series. Analyzing two data sets of stock prices we resolve to ?t AR(1) processes with GARCH or EGARCH errors to the log returns. More all over, hyperbolic or extrapolate error distributions occur to be good 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 observed at discrete moments. In the considered examples they are daily close 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. Address 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 ? Bank Gospodarki Zywno´ciowej S.A. Kasprzaka 10/16, 01-211 Warsaw, Poland s Received: October 2003 Accepted: January 2004
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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 sample mean over the observation...If you want to get a full essay, order it on our website: Orderessay



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