2024-03-28T11:27:49Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/188962022-11-17T02:08:08Zhdl_2115_20039hdl_2115_116Explicit representation of finite predictor coefficients and its applicationsInoue, AkihikoKasahara, YukioPredictorAR coefficientsMA coefficientsfractional ARIMA processeslong memoryBaxter’s inequality413We consider the finite-past predictor coefficients of stationary time series, and establish an explicit representation for them, in terms of the MA and AR coefficients. The proof is based on the alternate applications of projection operators associated with the infinite past and the infinite future. Applying the result to long memory processes, we give the rate of convergence of the finite predictor coefficients and prove an inequality of Baxter-type.Institute of Mathematical StatisticsJournal Articleapplication/pdfhttp://hdl.handle.net/2115/18896https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/18896/1/AS32-2.pdf0090-5364The Annals of Statistics3429739932006-04enginfo:doi/10.1214/009053606000000209author