چكيده انگليسي :
Linear prediction of ARMA processes with in nite variance Osman Norozi o norozi@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Sa eh Mahmoodi mahmoodi@cc iut ac ir Advisor Dr Soroush Alimoradi salimora@cc iut ac ir 2010 MSC 05C15 53C42 Keywords ARMA process regular variation stable process Abstract For ARMA processes in which the white noise sequence has nite variance predictors are usuallydetermined by minimizing the expected squared error see for example Fuller 1976 and Box andJenkins 1976 If the process is Gaussian this procedure also minimizes the probabilities of largedeviations For processes with in nite variance however an alternative criterion for selection of abest predictor is needed Alternative approaches which have been suggested include minimizationof the expected absolute error and the pseudo spectral technique of Cambanis and Soltani 1982 Most criteria are complicated to use and require precise knowledge of the distribution of the whitenoise Therefor it would be extremely useful in the in nite variance case to have a predictor whichis reasonably simple to compute which does not require full knowledge of the distribution of Zn andwhich in a sense to be speci ed minimizes the probabilities of large prediction errors In order topredict unobserved values of a linear process with in nite variance we introduce a linear predictorsbased on 3 13 When the linear process is driven by symmetric stable white noise one of the predictorsminimizes the scale parameter of the error distribution In the more general case when the drivingwhite noise process has regularly varying tails with index this predictor minimizes the size of theerror tail probabilities The procedure which minimizes the dispersion can be interpreted also asminimizing an appropriately de ned l distance between the predictor and the random variable tobe predicted Using this method we derive explicitly the best linear predictor of Xn 1 in terms ofX1 Xn for the process ARMA 1 1 and for the process AR p For higher order processes general
