An annual time-series regression model was fit to data collected for 30 years. After studying and analyzing the results, the error terms were found to be first-order autocorrelated, and the independent variable is lagged, i.e., the value of x in year 1-1 also affects the value of y in year t. So, the following pair of models was studied: y₁= Bo + B₁ x₁ +B₂x₁-1 + ß² t + & and & = £ 1-1 + a, where the a, are i.i.d. N(0,0¹) for each t, t= 1,...,30. By using the 30 data points and applying the approximate method, the following estimates of the coefficients are obtained:ßo= 10, ß₁= 3.2, ß₂= 1.1, ß3= 1.5, = 0.74. Use the fitted model to forecast the value of y in year t= 31, given that y30=85, X29= 8.5, X30 = 4.75, and 231 = 6.9.
An annual time-series regression model was fit to data collected for 30 years. After studying and analyzing the results, the error terms were found to be first-order autocorrelated, and the independent variable is lagged, i.e., the value of x in year 1-1 also affects the value of y in year t. So, the following pair of models was studied: y₁= Bo + B₁ x₁ +B₂x₁-1 + ß² t + & and & = £ 1-1 + a, where the a, are i.i.d. N(0,0¹) for each t, t= 1,...,30. By using the 30 data points and applying the approximate method, the following estimates of the coefficients are obtained:ßo= 10, ß₁= 3.2, ß₂= 1.1, ß3= 1.5, = 0.74. Use the fitted model to forecast the value of y in year t= 31, given that y30=85, X29= 8.5, X30 = 4.75, and 231 = 6.9.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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