Predykcja szeregów czasowych w warunkach autokorelacji składników losowych
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Date
1976
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Wydział Prawa i Administracji UAM
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Prediction Problems, in the Situation when Disturbances are Autocorrelated in the Linear Model
Abstract
In the article the autor discusses prediction problems in the general linear model where disturbances are autocorrelated. Suppose we have sample data for periods 1 to n from the model y=Xß+u with E(u)=0 and E(uu')=V. Suppose further that we are given the row vector xn + 1 of values of the explanatory variables
in period n+1. The problem now how to estimate yn+s when E(uu')=V=σ2 uΩ, where Ω is assumed to be known, symmetric, positivedefinite matrix. If the disturbances follows a first-order scheme ut=γ1ut-1+εt where |γ1|<1, then we can see that the best linear unbiased predictor is ŷn+1=xn+sb+(γ1)s·en where b is the generalized least-squares estimator and en is the last row of the vector e=y—Xb of generalized least-squares residuals. When the elements of Ω (that is, the value of γ1) were unknown formula pictured above should still be used for prediction purposes with b and γ1 replaced by estimates.
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Digitalizacja i deponowanie archiwalnych zeszytów RPEiS sfinansowane przez MNiSW w ramach realizacji umowy nr 541/P-DUN/2016
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Citation
Ruch Prawniczy, Ekonomiczny i Socjologiczny 38, 1976, z. 3, s. 199-208